Update 2022-02-08 07:07

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Jean-Sébastien 2022-02-08 07:07:41 +01:00
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<!DOCTYPE html> <!DOCTYPE html>
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<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
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<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1885,7 +1629,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

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@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1968,7 +1712,7 @@ Wiley, 1986 [2nd edition]
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1885,7 +1629,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1891,7 +1635,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1887,7 +1631,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li class="toc-currentpage">
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details open="">
<summary class="toc-currentpage">
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1868,7 +1612,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </nav>
<ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_cs_sph_lap.html">Laplacian&emsp;<small>[c.m.cs.sph.lap]</small></a></li><li>Next:&nbsp;<a href="c_m_cs_cyl_grad.html">Gradient&emsp;<small>[c.m.cs.cyl.grad]</small></a></li><li>Up:&nbsp;<a href="c_m_cs.html">Coordinate Systems&emsp;<small>[c.m.cs]</small></a></li></ul><div id="outline-container-c_m_cs_cyl" class="outline-5"> <ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_cs_sph.html">Spherical Coordinates&emsp;<small>[c.m.cs.sph]</small></a></li><li>Next:&nbsp;<a href="c_m_cs_hyp.html">Hyperbolic Coordinates&emsp;<small>[c.m.cs.hyp]</small></a></li><li>Up:&nbsp;<a href="c_m_cs.html">Coordinate Systems&emsp;<small>[c.m.cs]</small></a></li></ul><div id="outline-container-c_m_cs_cyl" class="outline-5">
<h5 id="c_m_cs_cyl">Cylindrical Coordinates<a class="headline-permalink" href="./c_m_cs_cyl.html#c_m_cs_cyl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16"> <h5 id="c_m_cs_cyl">Cylindrical Coordinates<a class="headline-permalink" href="./c_m_cs_cyl.html#c_m_cs_cyl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/> <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/> <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
@ -1928,14 +1672,14 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
<div id="outline-container-c_m_cs_cyl_grad" class="outline-6"> <div id="outline-container-c_m_cs_cyl_grad" class="outline-6">
<h6 id="c_m_cs_cyl_grad"><a href="#c_m_cs_cyl_grad">Gradient</a></h6> <h6 id="c_m_cs_cyl_grad"><a href="#c_m_cs_cyl_grad">Gradient</a></h6>
<div class="outline-text-6" id="text-c_m_cs_cyl_grad"> <div class="outline-text-6" id="text-c_m_cs_cyl_grad">
<div class="eqlabel" id="org958f79a"> <div class="eqlabel" id="org1f82008">
<p> <p>
<a id="cylgrad"></a><a href="./c_m_cs_cyl.html#cylgrad"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16"> <a id="cylgrad"></a><a href="./c_m_cs_cyl.html#cylgrad"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/> <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/> <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a> </svg></a>
</p> </p>
<div class="alteqlabels" id="org6b4b020"> <div class="alteqlabels" id="org0d07fad">
<ul class="org-ul"> <ul class="org-ul">
<li>Gr4(1.79)</li> <li>Gr4(1.79)</li>
</ul> </ul>
@ -1962,14 +1706,14 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
<div id="outline-container-c_m_cs_cyl_div" class="outline-6"> <div id="outline-container-c_m_cs_cyl_div" class="outline-6">
<h6 id="c_m_cs_cyl_div"><a href="#c_m_cs_cyl_div">Divergence</a></h6> <h6 id="c_m_cs_cyl_div"><a href="#c_m_cs_cyl_div">Divergence</a></h6>
<div class="outline-text-6" id="text-c_m_cs_cyl_div"> <div class="outline-text-6" id="text-c_m_cs_cyl_div">
<div class="eqlabel" id="orgb4915c4"> <div class="eqlabel" id="org9646f8e">
<p> <p>
<a id="cyl_div"></a><a href="./c_m_cs_cyl.html#cyl_div"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16"> <a id="cyl_div"></a><a href="./c_m_cs_cyl.html#cyl_div"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/> <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/> <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a> </svg></a>
</p> </p>
<div class="alteqlabels" id="org482df89"> <div class="alteqlabels" id="orgef4d1a0">
<ul class="org-ul"> <ul class="org-ul">
<li>Gr4(2.21)</li> <li>Gr4(2.21)</li>
</ul> </ul>
@ -1980,10 +1724,10 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
<p> <p>
\[ \[
{\boldsymbol ∇} ⋅ {\bf v} = \frac{1}{r} \frac{\partial}{\partial r} (r v<sub>r</sub>) {\boldsymbol ∇} ⋅ {\bf v} = \frac{1}{r} \frac{\partial}{\partial r} (r v_r)
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>\frac{1}{r} \frac{∂ v<sub>φ</sub>}{∂ φ} + \frac{\partial v_z}{\partial z}.</li> <li>\frac{1}{r} \frac{∂ v_{φ}}{∂ φ} + \frac{\partial v_z}{\partial z}.</li>
</ul> </ul>
<p> <p>
\tag{cyl_div} \tag{cyl_div}
@ -1996,14 +1740,14 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
<div id="outline-container-c_m_cs_cyl_curl" class="outline-6"> <div id="outline-container-c_m_cs_cyl_curl" class="outline-6">
<h6 id="c_m_cs_cyl_curl"><a href="#c_m_cs_cyl_curl">Curl</a></h6> <h6 id="c_m_cs_cyl_curl"><a href="#c_m_cs_cyl_curl">Curl</a></h6>
<div class="outline-text-6" id="text-c_m_cs_cyl_curl"> <div class="outline-text-6" id="text-c_m_cs_cyl_curl">
<div class="eqlabel" id="org79951eb"> <div class="eqlabel" id="org174b722">
<p> <p>
<a id="cyl_curl"></a><a href="./c_m_cs_cyl.html#cyl_curl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16"> <a id="cyl_curl"></a><a href="./c_m_cs_cyl.html#cyl_curl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/> <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/> <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a> </svg></a>
</p> </p>
<div class="alteqlabels" id="org53de84b"> <div class="alteqlabels" id="org9f83d45">
<ul class="org-ul"> <ul class="org-ul">
<li>Gr4(2.21)</li> <li>Gr4(2.21)</li>
</ul> </ul>
@ -2014,11 +1758,11 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
<p> <p>
\[ \[
{\boldsymbol ∇} × {\bf v} = \left( \frac{1}{r} \frac{\partial v_z}{\partial \phi} - \frac{∂ v<sub>φ</sub>}{∂ z}\right) ~\hat{\bf r} {\boldsymbol ∇} × {\bf v} = \left( \frac{1}{r} \frac{\partial v_z}{\partial \phi} - \frac{∂ v_{φ}}{∂ z}\right) ~\hat{\bf r}
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>\left( \frac{\partial v_r}{\partial z} - \frac{\partial v_z}{\partial r} \right) ~\hat{\boldsymbol \phi}</li> <li>\left( \frac{\partial v_r}{\partial z} - \frac{\partial v_z}{\partial r} \right) ~\hat{\boldsymbol \phi}</li>
<li>\frac{1}{r} \left( \frac{\partial}{\partial r} (r v<sub>φ</sub>) - \frac{\partial v_r}{\partial \phi} \right) ~\hat{\bf z}</li> <li>\frac{1}{r} \left( \frac{\partial}{\partial r} (r v_{φ}) - \frac{\partial v_r}{\partial \phi} \right) ~\hat{\bf z}</li>
</ul> </ul>
<p> <p>
\tag{cyl_curl} \tag{cyl_curl}
@ -2033,7 +1777,7 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
<div class="outline-text-6" id="text-c_m_cs_cyl_lap"> <div class="outline-text-6" id="text-c_m_cs_cyl_lap">
<p> <p>
\[ \[
{\boldsymbol ∇}<sup>2</sup> T = \frac{1}{r} \frac{\partial}{\partial r} \left( r \frac{\partial T}{\partial r} \right) {\boldsymbol ∇}^2 T = \frac{1}{r} \frac{\partial}{\partial r} \left( r \frac{\partial T}{\partial r} \right)
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>\frac{1}{r^2} \frac{\partial^2 T}{\partial \phi^2} + \frac{\partial^2 T}{\partial z^2}</li> <li>\frac{1}{r^2} \frac{\partial^2 T}{\partial \phi^2} + \frac{\partial^2 T}{\partial z^2}</li>
@ -2051,7 +1795,7 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li class="toc-currentpage"> <li class="toc-currentpage">
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1868,7 +1612,7 @@ Table of contents
</ul> </ul>
</details> </details>
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<h5 id="c_m_cs_hyp">Hyperbolic Coordinates<a class="headline-permalink" href="./c_m_cs_hyp.html#c_m_cs_hyp"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16"> <h5 id="c_m_cs_hyp">Hyperbolic Coordinates<a class="headline-permalink" href="./c_m_cs_hyp.html#c_m_cs_hyp"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/> <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
@ -1880,7 +1624,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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@ -1,7 +1,7 @@
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<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
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<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1702,63 +1513,13 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li class="toc-currentpage">
<details open="">
<summary class="toc-currentpage">
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1868,19 +1612,12 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </nav>
<ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_cs.html">Coordinate Systems&emsp;<small>[c.m.cs]</small></a></li><li>Next:&nbsp;<a href="c_m_cs_sph_grad.html">Gradient&emsp;<small>[c.m.cs.sph.grad]</small></a></li><li>Up:&nbsp;<a href="c_m_cs.html">Coordinate Systems&emsp;<small>[c.m.cs]</small></a></li></ul><div id="outline-container-c_m_cs_sph" class="outline-5"> <ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_cs.html">Coordinate Systems&emsp;<small>[c.m.cs]</small></a></li><li>Next:&nbsp;<a href="c_m_cs_cyl.html">Cylindrical Coordinates&emsp;<small>[c.m.cs.cyl]</small></a></li><li>Up:&nbsp;<a href="c_m_cs.html">Coordinate Systems&emsp;<small>[c.m.cs]</small></a></li></ul><div id="outline-container-c_m_cs_sph" class="outline-5">
<h5 id="c_m_cs_sph">Spherical Coordinates<a class="headline-permalink" href="./c_m_cs_sph.html#c_m_cs_sph"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16"> <h5 id="c_m_cs_sph">Spherical Coordinates<a class="headline-permalink" href="./c_m_cs_sph.html#c_m_cs_sph"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/> <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/> <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a><span class="headline-id">c.m.cs.sph</span></h5> </svg></a><span class="headline-id">c.m.cs.sph</span></h5>
<div class="outline-text-5" id="text-c_m_cs_sph"> <div class="outline-text-5" id="text-c_m_cs_sph">
<figure id="org7966655">
<img src="fig/sphere.png" alt="sphere" title="sphere" width="200px">
<figcaption><span class="figure-number">Figure 1: </span>Sphere drawn with Asymptote</figcaption>
</figure>
<p> <p>
\((r, \theta, \phi)\). \(\theta\) is the <b>polar angle</b>, \(\phi\) the <b>azimuthal angle</b>. \((r, \theta, \phi)\). \(\theta\) is the <b>polar angle</b>, \(\phi\) the <b>azimuthal angle</b>.
</p> </p>
@ -1970,10 +1707,10 @@ Infinitesimal surface element: depends on situation.
<div class="outline-text-6" id="text-c_m_cs_sph_div"> <div class="outline-text-6" id="text-c_m_cs_sph_div">
<p> <p>
\[ \[
{\boldsymbol ∇} ⋅ {\bf v} = \frac{1}{r^2} \frac{\partial}{\partial r} (r<sup>2</sup> v<sub>r</sub>) + \frac{1}{r\sin \theta} \frac{\partial}{\partial \theta} (sinθ v<sub>θ</sub>) {\boldsymbol ∇} ⋅ {\bf v} = \frac{1}{r^2} \frac{\partial}{\partial r} (r^2 v_r) + \frac{1}{r\sin \theta} \frac{\partial}{\partial \theta} (sinθ v_{θ})
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>\frac{1}{r \sin \theta} \frac{∂ v<sub>φ</sub>}{∂ φ}</li> <li>\frac{1}{r \sin \theta} \frac{∂ v_{φ}}{∂ φ}</li>
</ul> </ul>
<p> <p>
\label{Gr(1.71)} \label{Gr(1.71)}
@ -1987,11 +1724,11 @@ Infinitesimal surface element: depends on situation.
<div class="outline-text-6" id="text-c_m_cs_sph_curl"> <div class="outline-text-6" id="text-c_m_cs_sph_curl">
<p> <p>
\[ \[
{\boldsymbol ∇} × {\bf v} = \frac{1}{r\sin \theta} \left[ \frac{\partial}{\partial \theta} (sin θ v<sub>φ</sub>) - \frac{∂ v<sub>θ</sub>}{∂ φ} \right] \hat{\bf r} {\boldsymbol ∇} × {\bf v} = \frac{1}{r\sin \theta} \left[ \frac{\partial}{\partial \theta} (sin θ v_{φ}) - \frac{∂ v_{θ}}{∂ φ} \right] \hat{\bf r}
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>\frac{1}{r} \left[ \frac{1}{\sin \theta} \frac{\partial v_r}{\partial \phi} - \frac{\partial}{\partial r} (r v<sub>φ</sub>) \right] \hat{\boldsymbol \theta}</li> <li>\frac{1}{r} \left[ \frac{1}{\sin \theta} \frac{\partial v_r}{\partial \phi} - \frac{\partial}{\partial r} (r v_{φ}) \right] \hat{\boldsymbol \theta}</li>
<li>\frac{1}{r} \left[ \frac{\partial}{\partial r} (r v<sub>θ</sub>) - \frac{\partial v_r}{\partial \theta} \right] \hat{\boldsymbol \phi}</li> <li>\frac{1}{r} \left[ \frac{\partial}{\partial r} (r v_{θ}) - \frac{\partial v_r}{\partial \theta} \right] \hat{\boldsymbol \phi}</li>
</ul> </ul>
<p> <p>
\label{Gr(1.72)} \label{Gr(1.72)}
@ -2005,7 +1742,7 @@ Infinitesimal surface element: depends on situation.
<div class="outline-text-6" id="text-c_m_cs_sph_lap"> <div class="outline-text-6" id="text-c_m_cs_sph_lap">
<p> <p>
\[ \[
{\boldsymbol ∇}<sup>2</sup> T = \frac{1}{r^2} \frac{\partial}{\partial r} \left(r<sup>2</sup> \frac{\partial T}{\partial r}\right) {\boldsymbol ∇}^2 T = \frac{1}{r^2} \frac{\partial}{\partial r} \left(r^2 \frac{\partial T}{\partial r}\right)
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>\frac{1}{r^2 \sin \theta} \frac{\partial}{\partial \theta} \left( sin θ \frac{\partial T}{\partial \theta}\right)</li> <li>\frac{1}{r^2 \sin \theta} \frac{\partial}{\partial \theta} \left( sin θ \frac{\partial T}{\partial \theta}\right)</li>
@ -2024,7 +1761,7 @@ Infinitesimal surface element: depends on situation.
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1890,7 +1634,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1892,7 +1636,7 @@ v_x &amp; v_y &amp; v_z \end{array} \right| \nonumber \\
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1598,38 +1459,9 @@ Table of contents
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span> <a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
</li> </li>
<li> <li class="toc-currentpage">
<details open="">
<summary class="toc-currentpage">
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1868,7 +1612,7 @@ Table of contents
</ul> </ul>
</details> </details>
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<h5 id="c_m_dc_d2">Second Derivatives<a class="headline-permalink" href="./c_m_dc_d2.html#c_m_dc_d2"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16"> <h5 id="c_m_dc_d2">Second Derivatives<a class="headline-permalink" href="./c_m_dc_d2.html#c_m_dc_d2"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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@ -1876,9 +1620,9 @@ Table of contents
<div class="outline-text-5" id="text-c_m_dc_d2"> <div class="outline-text-5" id="text-c_m_dc_d2">
</div> </div>
<div id="outline-container-orge025182" class="outline-6"> <div id="outline-container-orgc3b89bb" class="outline-6">
<h6 id="orge025182"><a href="#orge025182">Divergence of gradient</a></h6> <h6 id="orgc3b89bb"><a href="#orgc3b89bb">Divergence of gradient</a></h6>
<div class="outline-text-6" id="text-orge025182"> <div class="outline-text-6" id="text-orgc3b89bb">
<p> <p>
\({\boldsymbol \nabla} \cdot ({\boldsymbol \nabla} T) \equiv {\boldsymbol \nabla}^2 T\) is called the <b>Laplacian</b> of the scalar field \(T\). \({\boldsymbol \nabla} \cdot ({\boldsymbol \nabla} T) \equiv {\boldsymbol \nabla}^2 T\) is called the <b>Laplacian</b> of the scalar field \(T\).
The Laplacian of a vector field \({\boldsymbol \nabla}^2 {\bf v}\) is also defined as the vector with components The Laplacian of a vector field \({\boldsymbol \nabla}^2 {\bf v}\) is also defined as the vector with components
@ -1887,36 +1631,36 @@ given by the Laplacian of the corresponding vector elements.
</div> </div>
</div> </div>
<div id="outline-container-orgacb930d" class="outline-6"> <div id="outline-container-org5caf3f5" class="outline-6">
<h6 id="orgacb930d"><a href="#orgacb930d">Curl of a gradient</a></h6> <h6 id="org5caf3f5"><a href="#org5caf3f5">Curl of a gradient</a></h6>
<div class="outline-text-6" id="text-orgacb930d"> <div class="outline-text-6" id="text-org5caf3f5">
<p> <p>
This always vanishes. This always vanishes.
</p> </p>
</div> </div>
</div> </div>
<div id="outline-container-org6caee98" class="outline-6"> <div id="outline-container-org4f9116a" class="outline-6">
<h6 id="org6caee98"><a href="#org6caee98">Gradient of the divergence</a></h6> <h6 id="org4f9116a"><a href="#org4f9116a">Gradient of the divergence</a></h6>
<div class="outline-text-6" id="text-org6caee98"> <div class="outline-text-6" id="text-org4f9116a">
<p> <p>
\({\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v})\) does not appear often in physics. No special name. \({\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v})\) does not appear often in physics. No special name.
</p> </p>
</div> </div>
</div> </div>
<div id="outline-container-orgb5da747" class="outline-6"> <div id="outline-container-org2c1c081" class="outline-6">
<h6 id="orgb5da747"><a href="#orgb5da747">Divergence of a curl</a></h6> <h6 id="org2c1c081"><a href="#org2c1c081">Divergence of a curl</a></h6>
<div class="outline-text-6" id="text-orgb5da747"> <div class="outline-text-6" id="text-org2c1c081">
<p> <p>
This always vanishes. This always vanishes.
</p> </p>
</div> </div>
</div> </div>
<div id="outline-container-orgebcbadc" class="outline-6"> <div id="outline-container-orgc977e97" class="outline-6">
<h6 id="orgebcbadc"><a href="#orgebcbadc">Curl of curl</a></h6> <h6 id="orgc977e97"><a href="#orgc977e97">Curl of curl</a></h6>
<div class="outline-text-6" id="text-orgebcbadc"> <div class="outline-text-6" id="text-orgc977e97">
<p> <p>
\[ \[
{\boldsymbol \nabla} \times ({\boldsymbol \nabla} \times {\bf v}) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v}) - {\boldsymbol \nabla}^2 {\bf v} {\boldsymbol \nabla} \times ({\boldsymbol \nabla} \times {\bf v}) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v}) - {\boldsymbol \nabla}^2 {\bf v}
@ -1930,7 +1674,7 @@ This always vanishes.
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
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<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1891,7 +1635,7 @@ The <b>del/grad/nabla operator</b> is defined as
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1888,7 +1632,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1912,7 +1656,7 @@ is a vector called the <b>gradient</b> of \(T\).
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1885,7 +1629,7 @@ Six product rules (on inside front cover of Gr).
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1887,7 +1631,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1899,7 +1643,7 @@ Consequences: for any smooth differentiable function \(f(x)\),
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1903,11 +1647,27 @@ Resolution of divergence of \(\hat{\bf r}/r^2\) paradox:
More generally, More generally,
</p> </p>
<div class="eqlabel" id="org99c1900">
<p>
<a id="divdel"></a><a href="./c_m_dd_3d.html#divdel"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a>
</p>
<div class="alteqlabels" id="orge7a14d6">
<ul class="org-ul">
<li>Gr (1.100)</li>
</ul>
</div>
</div>
<p> <p>
\[ \[
\boxed{ \boxed{
{\boldsymbol \nabla} \cdot \left(\frac{{\bf r} - {\bf r}'}{|{\bf r} - {\bf r}'|^3} \right)= 4\pi \delta^{(3)} ({\bf r}). {\boldsymbol \nabla} \cdot \left(\frac{{\bf r} - {\bf r}'}{|{\bf r} - {\bf r}'|^3} \right)= 4\pi \delta^{(3)} ({\bf r}).
}\label{Gr(1.100)} }
\tag{divdel}\label{divdel}
\] \]
</p> </p>
@ -1938,7 +1698,7 @@ we have that
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1909,7 +1653,7 @@ Problem: in (1.84), we've divided by zero when \(r = 0\).
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1868,7 +1612,7 @@ Table of contents
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<h4 id="c_m_ic">Integral Calculus<a class="headline-permalink" href="./c_m_ic.html#c_m_ic"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16"> <h4 id="c_m_ic">Integral Calculus<a class="headline-permalink" href="./c_m_ic.html#c_m_ic"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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@ -1890,7 +1634,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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@ -1,7 +1,7 @@
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<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li class="toc-currentpage"> <li class="toc-currentpage">
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1868,7 +1612,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </nav>
<ul class="navigation-links"><li>Prev:&nbsp;<a href="org5c24b4a.html">Volume Integrals&emsp;<small>[org5c24b4a]</small></a></li><li>Next:&nbsp;<a href="c_m_ic_ftg.html">The Fundamental Theorem for Gradients&emsp;<small>[c.m.ic.ftg]</small></a></li><li>Up:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li></ul><div id="outline-container-c_m_ic_ftc" class="outline-5"> <ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_ic_lsv.html">Line, Surface and Volume Integrals&emsp;<small>[c.m.ic.lsv]</small></a></li><li>Next:&nbsp;<a href="c_m_ic_ftg.html">The Fundamental Theorem for Gradients&emsp;<small>[c.m.ic.ftg]</small></a></li><li>Up:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li></ul><div id="outline-container-c_m_ic_ftc" class="outline-5">
<h5 id="c_m_ic_ftc">The Fundamental Theorem of Calculus<a class="headline-permalink" href="./c_m_ic_ftc.html#c_m_ic_ftc"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16"> <h5 id="c_m_ic_ftc">The Fundamental Theorem of Calculus<a class="headline-permalink" href="./c_m_ic_ftc.html#c_m_ic_ftc"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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@ -1888,7 +1632,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1897,7 +1641,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1891,7 +1635,7 @@ This is know either as <b>Gauss' theorem</b>, <b>Green's theorem</b> or the <b>d
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1878,39 +1622,27 @@ Table of contents
Example: \({\boldsymbol \nabla} \cdot (f{\bf A}) = f({\boldsymbol \nabla} \cdot {\bf A}) + {\bf A} \cdot ({\boldsymbol \nabla} f)\) implies (via Gauss' theorem) Example: \({\boldsymbol \nabla} \cdot (f{\bf A}) = f({\boldsymbol \nabla} \cdot {\bf A}) + {\bf A} \cdot ({\boldsymbol \nabla} f)\) implies (via Gauss' theorem)
</p> </p>
<p> \begin{equation*}
\[ \int_{\cal V} {\boldsymbol \nabla} \cdot (f{\bf A}) d\tau = \int_{\cal V} f({\boldsymbol \nabla} \cdot {\bf A}) d\tau
<sub>\cal V</sub> {\boldsymbol ∇} ⋅ (f{\bf A}) dτ = ∫<sub>\cal V</sub> f({\boldsymbol ∇} ⋅ {\bf A}) dτ + \int_{\cal V} {\bf A} \cdot ({\boldsymbol \nabla} f) d\tau = \oint f{\bf A} \cdot d{\bf a},
</p> \end{equation*}
<ul class="org-ul">
<li><sub>\cal V</sub> {\bf A} ⋅ ({\boldsymbol ∇} f) dτ = \oint f{\bf A} ⋅ d{\bf a},</li>
</ul>
<p>
\]
</p>
<p> <p>
or in other words or in other words
</p> </p>
<p> \begin{equation}
\[ \int_{\cal V} f({\boldsymbol \nabla} \cdot {\bf A}) d\tau = -\int_{\cal V} {\bf A} \cdot ({\boldsymbol \nabla} f) d\tau
<sub>\cal V</sub> f({\boldsymbol ∇} ⋅ {\bf A}) dτ = -∫<sub>\cal V</sub> {\bf A} ⋅ ({\boldsymbol ∇} f) dτ + \oint_{\cal S} f{\bf A} \cdot d{\bf a}.
</p>
<ul class="org-ul">
<li>\oint<sub>\cal S</sub> f{\bf A} ⋅ d{\bf a}.</li>
</ul>
<p>
\label{Gr(1.59)} \label{Gr(1.59)}
\] \end{equation}
</p>
</div> </div>
</div> </div>
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1644,30 +1476,9 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li class="toc-currentpage">
<details open="">
<summary class="toc-currentpage">
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1868,7 +1612,7 @@ Table of contents
</ul> </ul>
</details> </details>
</nav> </nav>
<ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li><li>Next:&nbsp;<a href="org638a76f.html">Line Integrals&emsp;<small>[org638a76f]</small></a></li><li>Up:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li></ul><div id="outline-container-c_m_ic_lsv" class="outline-5"> <ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li><li>Next:&nbsp;<a href="c_m_ic_ftc.html">The Fundamental Theorem of Calculus&emsp;<small>[c.m.ic.ftc]</small></a></li><li>Up:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li></ul><div id="outline-container-c_m_ic_lsv" class="outline-5">
<h5 id="c_m_ic_lsv">Line, Surface and Volume Integrals<a class="headline-permalink" href="./c_m_ic_lsv.html#c_m_ic_lsv"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16"> <h5 id="c_m_ic_lsv">Line, Surface and Volume Integrals<a class="headline-permalink" href="./c_m_ic_lsv.html#c_m_ic_lsv"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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@ -1876,9 +1620,9 @@ Table of contents
<div class="outline-text-5" id="text-c_m_ic_lsv"> <div class="outline-text-5" id="text-c_m_ic_lsv">
</div> </div>
<div id="outline-container-org638a76f" class="outline-6"> <div id="outline-container-org860e5de" class="outline-6">
<h6 id="org638a76f"><a href="#org638a76f">Line Integrals</a></h6> <h6 id="org860e5de"><a href="#org860e5de">Line Integrals</a></h6>
<div class="outline-text-6" id="text-org638a76f"> <div class="outline-text-6" id="text-org860e5de">
<p> <p>
\[ \[
{\int_{\bf a}^{\bf b}}_{\cal P} {\bf v} \cdot d{\bf l} {\int_{\bf a}^{\bf b}}_{\cal P} {\bf v} \cdot d{\bf l}
@ -1907,9 +1651,9 @@ Integral over a closed loop:
</div> </div>
</div> </div>
<div id="outline-container-orgd8e925a" class="outline-6"> <div id="outline-container-orged48130" class="outline-6">
<h6 id="orgd8e925a"><a href="#orgd8e925a">Surface Integrals</a></h6> <h6 id="orged48130"><a href="#orged48130">Surface Integrals</a></h6>
<div class="outline-text-6" id="text-orgd8e925a"> <div class="outline-text-6" id="text-orged48130">
<p> <p>
\[ \[
\int_{\cal S} {\bf v} \cdot d{\bf a} \int_{\cal S} {\bf v} \cdot d{\bf a}
@ -1929,9 +1673,9 @@ Over a closed surface:
</div> </div>
</div> </div>
<div id="outline-container-org5c24b4a" class="outline-6"> <div id="outline-container-org4728536" class="outline-6">
<h6 id="org5c24b4a"><a href="#org5c24b4a">Volume Integrals</a></h6> <h6 id="org4728536"><a href="#org4728536">Volume Integrals</a></h6>
<div class="outline-text-6" id="text-org5c24b4a"> <div class="outline-text-6" id="text-org4728536">
<p> <p>
\[ \[
\int_{\cal V} T d\tau \int_{\cal V} T d\tau
@ -1959,7 +1703,7 @@ d\tau = dx dy dz
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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@ -1,7 +1,7 @@
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<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1874,10 +1618,25 @@ Table of contents
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/> <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a><span class="headline-id">c.m.ic.stokes</span></h5> </svg></a><span class="headline-id">c.m.ic.stokes</span></h5>
<div class="outline-text-5" id="text-c_m_ic_stokes"> <div class="outline-text-5" id="text-c_m_ic_stokes">
<div class="eqlabel" id="orgda53253">
<p>
<a id="Stokes"></a><a href="./c_m_ic_stokes.html#Stokes"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a>
</p>
<div class="alteqlabels" id="org14a6dc8">
<ul class="org-ul">
<li>Gr (1.57)</li>
</ul>
</div>
</div>
<p> <p>
\[ \[
\int_{\cal S} ({\boldsymbol \nabla} \times {\bf v}) \cdot d{\bf a} = \oint_{\cal P} {\bf v} \cdot d{\bf l}. \int_{\cal S} ({\boldsymbol \nabla} \times {\bf v}) \cdot d{\bf a} = \oint_{\cal P} {\bf v} \cdot d{\bf l}.
\label{Gr(1.57)} \tag{Stokes}\label{Stokes}
\] \]
</p> </p>
@ -1898,7 +1657,7 @@ the boundary shrinks to a point.
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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@ -1,7 +1,7 @@
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<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1868,7 +1612,7 @@ Table of contents
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<ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_vf_pot_solen.html">Theorem 2: Divergence-less (solenoidal) fields&emsp;<small>[c.m.vf.pot.solen]</small></a></li><li>Next:&nbsp;<a href="c_m_uf_cyl.html">Cylindrical coordinates&emsp;<small>[c.m.uf.cyl]</small></a></li><li>Up:&nbsp;<a href="c_m.html">Mathematics&emsp;<small>[c.m]</small></a></li></ul> <ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_vf_pot.html">Potentials&emsp;<small>[c.m.vf.pot]</small></a></li><li>Next:&nbsp;<a href="c_m_uf_cyl.html">Cylindrical coordinates&emsp;<small>[c.m.uf.cyl]</small></a></li><li>Up:&nbsp;<a href="c_m.html">Mathematics&emsp;<small>[c.m]</small></a></li></ul>
<h4 id="c_m_uf">Useful Formulas<a class="headline-permalink" href="./c_m_uf.html#c_m_uf"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16"> <h4 id="c_m_uf">Useful Formulas<a class="headline-permalink" href="./c_m_uf.html#c_m_uf"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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@ -1887,7 +1631,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1900,7 +1644,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1900,7 +1644,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1903,7 +1647,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1889,7 +1633,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1874,18 +1618,12 @@ Table of contents
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/> <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a><span class="headline-id">c.m.va.cp</span></h5> </svg></a><span class="headline-id">c.m.va.cp</span></h5>
<div class="outline-text-5" id="text-c_m_va_cp"> <div class="outline-text-5" id="text-c_m_va_cp">
<p> \begin{equation*}
\[ {\bf A} \times {\bf B} = \left| \begin{array}{ccc} \hat{x} &amp; \hat{y} &amp; \hat{z} \\
{\bf A} × {\bf B} = \left| \begin{array}{ccc} \hat{x} &amp; \hat{y} &amp; \hat{z} <br> A_x &amp; A_y &amp; A_z \\ B_x &amp; B_y &amp; B_z \end{array} \right|
A<sub>x</sub> &amp; A<sub>y</sub> &amp; A<sub>z</sub> \\ B<sub>x</sub> &amp; B<sub>y</sub> &amp; B<sub>z</sub> \end{array} \right| = \left( A_y B_z - A_z B_y \right) \hat{x} + \left( B_z A_x - B_x A_z \right) \hat{y}
= \left( A<sub>y</sub> B<sub>z</sub> - A<sub>z</sub> B<sub>y</sub> \right) \hat{x} + \left( B<sub>z</sub> A<sub>x</sub> - B<sub>x</sub> A<sub>z</sub> \right) \hat{y} + \left( A_x B_y - A_y B_x \right) \hat{z}
</p> \end{equation*}
<ul class="org-ul">
<li>\left( A<sub>x</sub> B<sub>y</sub> - A<sub>y</sub> B<sub>x</sub> \right) \hat{z}</li>
</ul>
<p>
\]
</p>
<p> <p>
The cross product is distributive: The cross product is distributive:
@ -1924,7 +1662,7 @@ this relation making plain that
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1913,7 +1657,7 @@ Component notation (in \({\mathbb R}^3\) with cartesian coordinates):
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1947,7 +1691,7 @@ Separation vector: for two position vectors \({\bf r}_a, {\bf r}_b\),
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1913,7 +1657,7 @@ In a general coordinate system with metric \(g\),
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

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@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1960,7 +1704,7 @@ All higher vector products can be reduced to combinations of single vector produ
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1886,7 +1630,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1905,7 +1649,7 @@ where
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1806,26 +1567,9 @@ Table of contents
<a href="./c_m_vf_helm.html#c_m_vf_helm">The Helmholtz Theorem</a><span class="headline-id">c.m.vf.helm</span> <a href="./c_m_vf_helm.html#c_m_vf_helm">The Helmholtz Theorem</a><span class="headline-id">c.m.vf.helm</span>
</li> </li>
<li> <li class="toc-currentpage">
<details open="">
<summary class="toc-currentpage">
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1868,7 +1612,7 @@ Table of contents
</ul> </ul>
</details> </details>
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<ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_vf_helm.html">The Helmholtz Theorem&emsp;<small>[c.m.vf.helm]</small></a></li><li>Next:&nbsp;<a href="c_m_vf_pot_irrot.html">Theorem 1: Curl-less (irrotational) fields&emsp;<small>[c.m.vf.pot.irrot]</small></a></li><li>Up:&nbsp;<a href="c_m_vf.html">Vector Fields&emsp;<small>[c.m.vf]</small></a></li></ul><div id="outline-container-c_m_vf_pot" class="outline-5"> <ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_vf_helm.html">The Helmholtz Theorem&emsp;<small>[c.m.vf.helm]</small></a></li><li>Next:&nbsp;<a href="c_m_uf.html">Useful Formulas&emsp;<small>[c.m.uf]</small></a></li><li>Up:&nbsp;<a href="c_m_vf.html">Vector Fields&emsp;<small>[c.m.vf]</small></a></li></ul><div id="outline-container-c_m_vf_pot" class="outline-5">
<h5 id="c_m_vf_pot">Potentials<a class="headline-permalink" href="./c_m_vf_pot.html#c_m_vf_pot"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16"> <h5 id="c_m_vf_pot">Potentials<a class="headline-permalink" href="./c_m_vf_pot.html#c_m_vf_pot"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/> <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
@ -1934,7 +1678,7 @@ The following conditions are equivalent:
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1875,8 +1619,8 @@ Table of contents
</svg></a><span class="headline-id">d</span></h2> </svg></a><span class="headline-id">d</span></h2>
<div class="outline-text-2" id="text-d"> <div class="outline-text-2" id="text-d">
<details class="objectives" id="org9eceddd"> <details class="objectives" id="org8e87179">
<summary id="org7f1879e"> <summary id="org5aefd0c">
Objectives Objectives
</summary> </summary>
@ -1927,7 +1671,7 @@ I have little doubt you'll pass the course.
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1907,7 +1651,7 @@ As a strict minimum, you should be able to:
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1902,7 +1646,7 @@ As a strict minimum, you should be able to:
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1905,7 +1649,7 @@ As a strict minimum, you should be able to:
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1902,7 +1646,7 @@ As a strict minimum, you should be able to:
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1924,7 +1668,7 @@ As a strict minimum, you should be able to:
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1907,7 +1651,7 @@ a point source charge \(q\) at \({\bf r}_s\) with an infinite grounded conductin
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1904,7 +1648,7 @@ As a strict minimum, you should be able to:
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1907,7 +1651,7 @@ As a strict minimum, you should be able to:
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1905,7 +1649,7 @@ As a strict minimum, you should be able to:
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1915,7 +1659,7 @@ Things you should be able to do (ideally: from scratch, on a blank sheet of pape
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1909,7 +1653,7 @@ As a strict minimum, you should be able to:
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1875,8 +1619,8 @@ Table of contents
</svg></a><span class="headline-id">emd</span></h2> </svg></a><span class="headline-id">emd</span></h2>
<div class="outline-text-2" id="text-emd"> <div class="outline-text-2" id="text-emd">
<details class="prereq" id="orgbacc774"> <details class="prereq" id="orgfca423d">
<summary id="org2beb4f2"> <summary id="org226d692">
Prerequisites Prerequisites
</summary> </summary>
<ul class="org-ul"> <ul class="org-ul">
@ -1885,8 +1629,8 @@ Prerequisites
</ul> </ul>
</details> </details>
<details class="objectives" id="org53819c5"> <details class="objectives" id="org9195c9d">
<summary id="org725bc8f"> <summary id="org58d183b">
Objectives Objectives
</summary> </summary>
<ul class="org-ul"> <ul class="org-ul">
@ -1914,7 +1658,7 @@ Objectives
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1888,7 +1632,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1915,7 +1659,7 @@ Empirically: the changing magnetic field induces an electric current around
the circuit. This current is really driven by an electric field having a component the circuit. This current is really driven by an electric field having a component
along the wire. The line integral of this field is called the along the wire. The line integral of this field is called the
</p> </p>
<div class="core div" id="orgd356b92"> <div class="core div" id="org9907fe5">
<p> <p>
<b>Electromotive force (or electromotance)</b>, <b>Electromotive force (or electromotance)</b>,
\[ \[
@ -1937,7 +1681,7 @@ to the rate of change of the magnetic flux,
\] \]
so we obtain so we obtain
</p> </p>
<div class="core div" id="org32cfcb5"> <div class="core div" id="org511a243">
<p> <p>
<b>Faraday's law</b> (integral form <i>N.B.: for a stationary loop</i>) <b>Faraday's law</b> (integral form <i>N.B.: for a stationary loop</i>)
\[ \[
@ -1955,7 +1699,7 @@ for any loop (on a wire or not). Using Stokes' theorem,
\] \]
we obtain we obtain
</p> </p>
<div class="core div" id="org1c1c2f9"> <div class="core div" id="orgb9e0e05">
<p> <p>
<b>Faraday's law</b> (differential form) <b>Faraday's law</b> (differential form)
\[ \[
@ -1968,7 +1712,7 @@ we obtain
<p> <p>
Right-hand rule always sorts signs out. Easier rule: {\bf Lenz's law}, which Right-hand rule always sorts signs out. Easier rule: {\bf Lenz's law}, which
states that {\bf nature resists a change in flux}. This is in fact just states that {\bf nature resists a change in flux}. This is in fact just
{\bf Le Ch\<sup>atelier</sup>'s principle} of any action at an equilibrium point leading {\bf Le Ch\^atelier's principle} of any action at an equilibrium point leading
to an opposing counter-reaction. to an opposing counter-reaction.
</p> </p>
</div> </div>
@ -1979,7 +1723,7 @@ to an opposing counter-reaction.
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1934,7 +1678,7 @@ W = \frac{1}{2\mu_0} \left[ \int_{\cal V} d\tau B^2 - \int_{\cal V} d\tau {\bold
\] \]
We can integrate over all space: after neglecting boundary terms (assuming fields fall to zero at infinity), we are left with We can integrate over all space: after neglecting boundary terms (assuming fields fall to zero at infinity), we are left with
</p> </p>
<div class="core div" id="orga28c6ab"> <div class="core div" id="org0a53c4e">
<p> <p>
\[ \[
W_{mag} = \frac{1}{2\mu_0} \int d\tau B^2 W_{mag} = \frac{1}{2\mu_0} \int d\tau B^2
@ -1955,7 +1699,7 @@ W_{mag} = \frac{1}{2} \int d\tau ({\bf A} \cdot {\bf J}) = \frac{1}{2\mu_0} \int
\hspace{2cm} \mbox{(7.31 and 7.34)} \hspace{2cm} \mbox{(7.31 and 7.34)}
\end{align} \end{align}
<div class="example div" id="orgda554ea"> <div class="example div" id="orge7b1ecf">
<p> <p>
\paragraph{Example 7.13:} coaxial cable (inner cylinder radius \(a\), outer \(b\)) carries current \(I\). \paragraph{Example 7.13:} coaxial cable (inner cylinder radius \(a\), outer \(b\)) carries current \(I\).
Find energy stored in section of length \(l\). Find energy stored in section of length \(l\).
@ -1981,7 +1725,7 @@ Note: gives easy way to find inductance, since \(W = \frac{1}{2} L I^2\).
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1914,7 +1658,7 @@ M_{12} = M_{21}
\] \]
</p> </p>
<div class="example div" id="orgd531765"> <div class="example div" id="orgc2d0a32">
<p> <p>
\paragraph{Example 7.10:} \paragraph{Example 7.10:}
short solenoid (length \(l\), radius \(a\), \(n_1\) turns per unit length) lies concentrically inside short solenoid (length \(l\), radius \(a\), \(n_1\) turns per unit length) lies concentrically inside
@ -1964,7 +1708,7 @@ Inductance: measured in {\bf henries} (\(H\)). \(H = V s/A\).
</p> </p>
<div class="example div" id="org702ff70"> <div class="example div" id="org7f4b3fa">
<p> <p>
\paragraph{Example 7.11:} find self-inductance of toroidal coil with \paragraph{Example 7.11:} find self-inductance of toroidal coil with
rectangular cross-section (inner radius \(a\), outer radius \(b\), height \(h\)) rectangular cross-section (inner radius \(a\), outer radius \(b\), height \(h\))
@ -1991,7 +1735,7 @@ Total flux: \(N\) times this, so self-inductance is
Inductance (like capacitance) is intrinsically positive. Use Lenz law. Think of {\bf back EMF}. Inductance (like capacitance) is intrinsically positive. Use Lenz law. Think of {\bf back EMF}.
</p> </p>
<div class="example div" id="org6b58768"> <div class="example div" id="org37841ae">
<p> <p>
\paragraph{Example 7.12:} circuit with inductance \(L\), resistor \(R\) and battery \({\cal E}_0\). \paragraph{Example 7.12:} circuit with inductance \(L\), resistor \(R\) and battery \({\cal E}_0\).
What is the current ? What is the current ?
@ -2017,7 +1761,7 @@ where \(\tau \equiv L/R\) is the {\bf time constant} of the circuit.
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1898,7 +1642,7 @@ law in integral form:
<div class="example div" id="org1bfc56c"> <div class="example div" id="orgfe52c32">
<p> <p>
{\bf Example 7.7:} {\bf Example 7.7:}
\({\bf B}(t)\) points up in circular region of radius \(R\). What is the induced \({\bf E}(t)\) ? \({\bf B}(t)\) points up in circular region of radius \(R\). What is the induced \({\bf E}(t)\) ?
@ -1914,7 +1658,7 @@ Increasing \({\bf B}\): clockwise (viewed from above) \({\bf E}\) from Lenz.
</div> </div>
<div class="example div" id="orgd8b7646"> <div class="example div" id="orgb289794">
<p> <p>
{\bf Example 7.8:} wheel or radius \(b\) with line charge \(\lambda\) on the rim. {\bf Example 7.8:} wheel or radius \(b\) with line charge \(\lambda\) on the rim.
Uniform magnetic field \({\bf B}_0\) in central region up to \(a &lt; b\), Uniform magnetic field \({\bf B}_0\) in central region up to \(a &lt; b\),
@ -1948,7 +1692,7 @@ called the {\bf quasistatic} approximation, and works provided we deal with
'slow enough' phenomena. 'slow enough' phenomena.
</p> </p>
<div class="example div" id="orge89f57b"> <div class="example div" id="orgd4a9b9d">
<p> <p>
{\bf Example 7.9:} infinitely long straight wire carries \(I(t)\). Find {\bf Example 7.9:} infinitely long straight wire carries \(I(t)\). Find
induced \({\bf E}\) field as a function of distance \(s\) from wire. induced \({\bf E}\) field as a function of distance \(s\) from wire.
@ -1983,7 +1727,7 @@ Reason: in this case, we've overstepped the quasistatic limit. We need
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1888,7 +1632,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1877,7 +1621,7 @@ Table of contents
<p> <p>
Full set of equations for the electromagnetic field: Full set of equations for the electromagnetic field:
</p> </p>
<div class="core div" id="orgc046634"> <div class="core div" id="org152d250">
<p> <p>
{\bf Maxwell's equations} {\it (in vacuum)} {\bf Maxwell's equations} {\it (in vacuum)}
</p> </p>
@ -1893,7 +1637,7 @@ Full set of equations for the electromagnetic field:
<p> <p>
Complement: Complement:
</p> </p>
<div class="core div" id="org29d2a12"> <div class="core div" id="org1c66368">
<p> <p>
{\bf Force law} {\bf Force law}
\[ \[
@ -1917,7 +1661,7 @@ take divergence of \((iv)\).
<p> <p>
Better way of writing: all fields on left, all sources on right, Better way of writing: all fields on left, all sources on right,
</p> </p>
<div class="core div" id="orgd4cf9e7"> <div class="core div" id="org1958d41">
\begin{align} \begin{align}
(i) &amp;{\boldsymbol \nabla} \cdot {\bf E} = \frac{\rho}{\varepsilon_0}, (i) &amp;{\boldsymbol \nabla} \cdot {\bf E} = \frac{\rho}{\varepsilon_0},
&amp;(iii) {\boldsymbol \nabla} \times {\bf E} + \frac{\partial {\bf B}}{\partial t} = 0, \\ &amp;(iii) {\boldsymbol \nabla} \times {\bf E} + \frac{\partial {\bf B}}{\partial t} = 0, \\
@ -1934,7 +1678,7 @@ Better way of writing: all fields on left, all sources on right,
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1884,7 +1628,7 @@ the continuity equation as
\] \]
The extra term would thus be eliminated if we were to put The extra term would thus be eliminated if we were to put
</p> </p>
<div class="core div" id="orgf659cb5"> <div class="core div" id="orgff64dd3">
<p> <p>
\[ \[
{\boldsymbol \nabla} \times {\bf B} = \mu_0 {\bf J} + \mu_0 \varepsilon_0 \frac{\partial {\bf E}}{\partial t} {\boldsymbol \nabla} \times {\bf B} = \mu_0 {\bf J} + \mu_0 \varepsilon_0 \frac{\partial {\bf E}}{\partial t}
@ -1908,7 +1652,7 @@ Real confirmation of Maxwell's theory: 1888, Hertz's experiments on propagation
<p> <p>
Maxwell baptized this term the Maxwell baptized this term the
</p> </p>
<div class="core div" id="orgfe5954d"> <div class="core div" id="org4206404">
<p> <p>
{\bf Displacement current} {\bf Displacement current}
\[ \[
@ -1943,7 +1687,7 @@ Flat surface: OK, \(E = 0\) and \(I_{\mbox{enc}} = I\). Balloon surface: \(I
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1913,7 +1657,7 @@ So for non-steady currents, the 'current enclosed by a loop' is ill-defined.
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1911,7 +1655,7 @@ Maxwell's equations {\bf beg} for magnetic charges. But we've never found any!
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1875,8 +1619,8 @@ Table of contents
</svg></a><span class="headline-id">emd.ce</span></h3> </svg></a><span class="headline-id">emd.ce</span></h3>
<div class="outline-text-3" id="text-emd_ce"> <div class="outline-text-3" id="text-emd_ce">
<details class="prereq" id="org51d68a7"> <details class="prereq" id="orge209dc2">
<summary id="orge489a25"> <summary id="org650a07d">
Prerequisites Prerequisites
</summary> </summary>
<ul class="org-ul"> <ul class="org-ul">
@ -1884,8 +1628,8 @@ Prerequisites
</ul> </ul>
</details> </details>
<details class="objectives" id="orgcbf139d"> <details class="objectives" id="org4962fbd">
<summary id="orga5dd4b1"> <summary id="org509fe5e">
Objectives Objectives
</summary> </summary>
<ul class="org-ul"> <ul class="org-ul">
@ -1910,7 +1654,7 @@ Objectives
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1877,7 +1621,7 @@ Table of contents
<p> <p>
The angular momentum of EM fields is directly given by The angular momentum of EM fields is directly given by
</p> </p>
<div class="main div" id="orgec38a1b"> <div class="main div" id="org3de73d0">
<p> <p>
{\bf Angular momentum of EM fields} {\bf Angular momentum of EM fields}
\[ \[
@ -1894,7 +1638,7 @@ The angular momentum of EM fields is directly given by
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1896,7 +1640,7 @@ This means that
\] \]
Since this is true for any volume, we have (re)derived the Since this is true for any volume, we have (re)derived the
</p> </p>
<div class="core div" id="orgcc05f97"> <div class="core div" id="org20202cd">
<p> <p>
{\bf Continuity equation} {\bf Continuity equation}
\[ \[
@ -1924,7 +1668,7 @@ imposes a functional constraint on these sources: not {\it any} \(\rho\) and
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1889,7 +1633,7 @@ in which the first integral can be interpreted as the momentum stored in the EM
<p> <p>
This is thus simply a conservation law for momentum, with This is thus simply a conservation law for momentum, with
</p> </p>
<div class="main div" id="orga07b125"> <div class="main div" id="org2bb42ec">
<p> <p>
{\bf Momentum density in the EM fields} {\bf Momentum density in the EM fields}
\[ \[
@ -1901,7 +1645,7 @@ This is thus simply a conservation law for momentum, with
<p> <p>
In a region in which the mechanical momentum is not changing due to external influences, we then have the In a region in which the mechanical momentum is not changing due to external influences, we then have the
</p> </p>
<div class="main div" id="org2f1f4d2"> <div class="main div" id="orgaafc4b4">
<p> <p>
{\bf Continuity equation for EM momentum} {\bf Continuity equation for EM momentum}
\[ \[
@ -1917,7 +1661,7 @@ In a region in which the mechanical momentum is not changing due to external inf
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
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<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1931,14 +1675,14 @@ and similarly for \({\boldsymbol B}\). We thus get
<p> <p>
This expression can be greatly simplified by introducing the This expression can be greatly simplified by introducing the
</p> </p>
<div class="main div" id="org36b6781"> <div class="main div" id="org9016172">
<p> <p>
{\bf Maxwell stress tensor} {\bf Maxwell stress tensor}
\[ \[
T<sub>ij</sub> ≡ ε<sub>0</sub> \left( E<sub>i</sub> E<sub>j</sub> - \frac{1}{2} δ<sub>ij</sub> E<sup>2\right</sup>) T_{ij} ≡ ε_0 \left( E_i E_j - \frac{1}{2} δ_{ij} E^2\right)
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>\frac{1}{\mu_0} \left( B<sub>i</sub> B<sub>j</sub> - \frac{1}{2} δ<sub>ij</sub> B<sup>2</sup> \right)</li> <li>\frac{1}{\mu_0} \left( B_i B_j - \frac{1}{2} δ_{ij} B^2 \right)</li>
</ul> </ul>
<p> <p>
\] \]
@ -1954,7 +1698,7 @@ The element \(T_{ij}\) represents the force per unit area in the $i$th direction
<p> <p>
We then obtain We then obtain
</p> </p>
<div class="main div" id="org568f504"> <div class="main div" id="org39d7962">
<p> <p>
{\bf EM force per unit volume} {\bf EM force per unit volume}
\[ \[
@ -1966,7 +1710,7 @@ We then obtain
<p> <p>
where \({\boldsymbol S}\) is the Poynting vector. Integrating, we obtain the where \({\boldsymbol S}\) is the Poynting vector. Integrating, we obtain the
</p> </p>
<div class="main div" id="org29c117c"> <div class="main div" id="org384fd10">
<p> <p>
{\bf Total force on charges in volume} {\bf Total force on charges in volume}
\[ \[
@ -1982,7 +1726,7 @@ where \({\boldsymbol S}\) is the Poynting vector. Integrating, we obtain the
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1932,7 +1676,7 @@ But obviously,
\] \]
so we get so we get
\[ \[
{\bf E} ⋅ {\bf J} = -\frac{1}{2} \frac{\partial}{\partial t} \left( ε<sub>0</sub> E<sup>2</sup> + \frac{1}{\mu_0} B<sup>2</sup> \right) {\bf E} ⋅ {\bf J} = -\frac{1}{2} \frac{\partial}{\partial t} \left( ε_0 E^2 + \frac{1}{\mu_0} B^2 \right)
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>\frac{1}{\mu_0} {\boldsymbol ∇} ⋅ ({\bf E} × {\bf B}).</li> <li>\frac{1}{\mu_0} {\boldsymbol ∇} ⋅ ({\bf E} × {\bf B}).</li>
@ -1943,14 +1687,14 @@ so we get
Substituting this in \ref{Gr(8.6)} and using the divergence theorem, Substituting this in \ref{Gr(8.6)} and using the divergence theorem,
we obtain we obtain
</p> </p>
<div class="main div" id="org27d4e56"> <div class="main div" id="org4fee5c1">
<p> <p>
{\bf Poynting's theorem} {\bf Poynting's theorem}
\[ \[
\frac{dW}{dt} = -\frac{d}{d t} ∫<sub>\cal V</sub> dτ \frac{1}{2} \left( ε<sub>0</sub> E<sup>2</sup> + \frac{1}{\mu_0} B<sup>2</sup> \right) \frac{dW}{dt} = -\frac{d}{d t} ∫_{\cal V} dτ \frac{1}{2} \left( ε_0 E^2 + \frac{1}{\mu_0} B^2 \right)
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>\frac{1}{\mu_0} \oint<sub>\cal S</sub> d{\bf a} ⋅ ({\bf E} × {\bf B})</li> <li>\frac{1}{\mu_0} \oint_{\cal S} d{\bf a} ⋅ ({\bf E} × {\bf B})</li>
</ul> </ul>
<p> <p>
\label{Gr(8.9)} \label{Gr(8.9)}
@ -1968,7 +1712,7 @@ energy is carried by EM fields out of \({\cal V}\) across its boundary surface.
<p> <p>
Energy per unit time, per unit area carried by EM fields: Energy per unit time, per unit area carried by EM fields:
</p> </p>
<div class="core div" id="org5a8440f"> <div class="core div" id="org31c447f">
<p> <p>
{\bf Poynting vector} {\bf Poynting vector}
\[ \[
@ -1981,7 +1725,7 @@ Energy per unit time, per unit area carried by EM fields:
<p> <p>
We can thus express Poynting's theorem more compactly: We can thus express Poynting's theorem more compactly:
</p> </p>
<div class="core div" id="org70a18d5"> <div class="core div" id="org0a1de2b">
<p> <p>
{\bf Poynting's theorem} {\bf Poynting's theorem}
\[ \[
@ -1994,7 +1738,7 @@ We can thus express Poynting's theorem more compactly:
<p> <p>
where we have defined the total where we have defined the total
</p> </p>
<div class="core div" id="orgbd2e763"> <div class="core div" id="org18b8949">
<p> <p>
{\bf Energy in electromagnetic fields} {\bf Energy in electromagnetic fields}
\[ \[
@ -2017,7 +1761,7 @@ Then,
\] \]
so we get the so we get the
</p> </p>
<div class="core div" id="org785fb4f"> <div class="core div" id="org3f5d20d">
<p> <p>
{\bf Poynting theorem (differential form)} {\bf Poynting theorem (differential form)}
\[ \[
@ -2034,7 +1778,7 @@ and has a similar for to the continuity equation
<div class="example div" id="org542e42c"> <div class="example div" id="org9d76705">
<p> <p>
\paragraph{Example 8.1} Current in a wire: Joule heating. Energy per unit time delivered to wire: from Poynting. \paragraph{Example 8.1} Current in a wire: Joule heating. Energy per unit time delivered to wire: from Poynting.
Assuming that the field is uniform, the electric field parallel to the wire is Assuming that the field is uniform, the electric field parallel to the wire is
@ -2066,7 +1810,7 @@ and the value is as expected.
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1875,8 +1619,8 @@ Table of contents
</svg></a><span class="headline-id">emd.emw</span></h3> </svg></a><span class="headline-id">emd.emw</span></h3>
<div class="outline-text-3" id="text-emd_emw"> <div class="outline-text-3" id="text-emd_emw">
<details class="prereq" id="org90cfed8"> <details class="prereq" id="orgdd3d3f8">
<summary id="orge5b2ad7"> <summary id="orgd8f94af">
Prerequisites Prerequisites
</summary> </summary>
<ul class="org-ul"> <ul class="org-ul">
@ -1885,8 +1629,8 @@ Prerequisites
</ul> </ul>
</details> </details>
<details class="objectives" id="org2dafde2"> <details class="objectives" id="org8ebd2c8">
<summary id="org9224cce"> <summary id="org56a0c80">
Objectives Objectives
</summary> </summary>
<ul class="org-ul"> <ul class="org-ul">
@ -1914,7 +1658,7 @@ Objectives
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1905,7 +1649,7 @@ so for a monochromatic EM plan wave,
\] \]
or more succinctly: or more succinctly:
</p> </p>
<div class="main div" id="org96a5e5a"> <div class="main div" id="org5ab2d39">
<p> <p>
{\bf Poynting vector of a monochromatic EM wave} {\bf Poynting vector of a monochromatic EM wave}
\[ \[
@ -1921,7 +1665,7 @@ This has a transparent physical interpretation: the energy density \(u\) flows w
<p> <p>
Similary, we get the Similary, we get the
</p> </p>
<div class="main div" id="orgcfdec88"> <div class="main div" id="org703b070">
<p> <p>
{\bf Momentum density of a monochromatic EM wave} {\bf Momentum density of a monochromatic EM wave}
\[ \[
@ -1959,7 +1703,7 @@ The {\it radiation pressure} is the momentum transfer per unit area per unit of
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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@ -1,7 +1,7 @@
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<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
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<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1906,7 +1650,7 @@ B_0 = \frac{k}{\omega} E_0 = \frac{1}{c} E_0.
Generalizing to propagation in the direction of an arbitrary wavevector Generalizing to propagation in the direction of an arbitrary wavevector
\({\boldsymbol k}\) and (transverse) polarization vector \(\hat{\boldsymbol n}\), we have the \({\boldsymbol k}\) and (transverse) polarization vector \(\hat{\boldsymbol n}\), we have the
</p> </p>
<div class="core div" id="orga2608fb"> <div class="core div" id="orgf8f14a8">
<p> <p>
{\bf E and B fields for a monochromatic EM plane wave} {\bf E and B fields for a monochromatic EM plane wave}
\[ \[
@ -1937,7 +1681,7 @@ or if you prefer explicit real parts (adding a possible phase shift \(\delta\)):
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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@ -1,7 +1,7 @@
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<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1903,7 +1647,7 @@ These take the form of coupled first-order partial differential equations for \(
Since \({\boldsymbol \nabla} \cdot {\bf E} = 0\) and \({\boldsymbol \nabla} \cdot {\bf B} = 0\), Since \({\boldsymbol \nabla} \cdot {\bf E} = 0\) and \({\boldsymbol \nabla} \cdot {\bf B} = 0\),
we get the we get the
</p> </p>
<div class="core div" id="orgde95589"> <div class="core div" id="org6e2c86d">
<p> <p>
{\bf Wave equations for electric and magnetic fields in vacuum} {\bf Wave equations for electric and magnetic fields in vacuum}
\[ \[
@ -1946,7 +1690,7 @@ the actual electric and magnetic fields are given by the real part.
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1886,7 +1630,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1886,7 +1630,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1910,7 +1654,7 @@ dI = \frac{\partial \sigma_b}{\partial t} da_{\perp} = \frac{\partial P}{\partia
\] \]
We therefore have the We therefore have the
</p> </p>
<div class="core div" id="orgb5c72da"> <div class="core div" id="orgb555ebf">
<p> <p>
{\bf Polarization current density} {\bf Polarization current density}
\[ \[
@ -1928,7 +1672,7 @@ the polarization current is the result of linear motion of charge when
polarization changes). We can check consistency with the continuity equation polarization changes). We can check consistency with the continuity equation
associated to the conservation of bound charges: associated to the conservation of bound charges:
</p> </p>
<aside id="org7ce3b70"> <aside id="org86c5ff2">
<p> <p>
Note the unfortunate labelling: it would have been nicer to have \(\rho_b\) be the charge associated to current Note the unfortunate labelling: it would have been nicer to have \(\rho_b\) be the charge associated to current
\({\boldsymbol J}_b\) but this is not the convention used here. \({\boldsymbol J}_b\) but this is not the convention used here.
@ -1951,7 +1695,7 @@ Changing magnetization does not lead to analogous accumulation of charge and cur
In view of this: total charge density can be separated into 2 parts, In view of this: total charge density can be separated into 2 parts,
{\it free} and {\it bound}: {\it free} and {\it bound}:
</p> </p>
<div class="main div" id="org3b2083c"> <div class="main div" id="orgf8c82b2">
<p> <p>
\[ \[
\rho = \rho_f + \rho_b = \rho_f - {\boldsymbol \nabla} \cdot {\bf P} \rho = \rho_f + \rho_b = \rho_f - {\boldsymbol \nabla} \cdot {\bf P}
@ -1964,10 +1708,10 @@ In view of this: total charge density can be separated into 2 parts,
and current can be separated into three parts, {\it free}, {\it bound} and and current can be separated into three parts, {\it free}, {\it bound} and
{\it polarization}: {\it polarization}:
</p> </p>
<div class="main div" id="org09ed727"> <div class="main div" id="org4054380">
<p> <p>
\[ \[
{\bf J} = {\bf J}<sub>f</sub> + {\bf J}<sub>b</sub> + {\bf J}<sub>p</sub> = {\bf J}<sub>f</sub> + {\boldsymbol ∇} × {\bf M} {\bf J} = {\bf J}_f + {\bf J}_b + {\bf J}_p = {\bf J}_f + {\boldsymbol ∇} × {\bf M}
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>\frac{∂ {\bf P}}{∂ t}.</li> <li>\frac{∂ {\bf P}}{∂ t}.</li>
@ -1988,7 +1732,7 @@ Gauss's law: can be rewritten
\] \]
where (as in static case) where (as in static case)
</p> </p>
<div class="core div" id="org508fb0a"> <div class="core div" id="orgf78b92c">
<p> <p>
\[ \[
{\bf D} \equiv \varepsilon_0 {\bf E} + {\bf P} {\bf D} \equiv \varepsilon_0 {\bf E} + {\bf P}
@ -2000,10 +1744,10 @@ where (as in static case)
<p> <p>
Ampère's law including Maxwell's term: Ampère's law including Maxwell's term:
\[ \[
{\boldsymbol ∇} × {\bf B} = μ<sub>0</sub> \left( {\bf J}<sub>f</sub> + {\boldsymbol ∇} × {\bf M} {\boldsymbol ∇} × {\bf B} = μ_0 \left( {\bf J}_f + {\boldsymbol ∇} × {\bf M}
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>\frac{∂ {\bf P}}{∂ t} \right) + μ<sub>0</sub> ε<sub>0</sub> \frac{∂ {\bf E}}{∂ t},</li> <li>\frac{∂ {\bf P}}{∂ t} \right) + μ_0 ε_0 \frac{∂ {\bf E}}{∂ t},</li>
</ul> </ul>
<p> <p>
\] \]
@ -2014,7 +1758,7 @@ or
\] \]
where as before where as before
</p> </p>
<div class="core div" id="org6879249"> <div class="core div" id="org513c514">
<p> <p>
\[ \[
{\bf H} \equiv \frac{1}{\mu_0} {\bf B} - {\bf M} {\bf H} \equiv \frac{1}{\mu_0} {\bf B} - {\bf M}
@ -2032,7 +1776,7 @@ bound parts, since they don't involve \(\rho\) or \({\bf J}\).
<p> <p>
In terms of free charges and currents, we thus get In terms of free charges and currents, we thus get
</p> </p>
<div class="core div" id="orgb7d4703"> <div class="core div" id="org686ea33">
<p> <p>
{\bf Maxwell's equations {\it (in matter)}} {\bf Maxwell's equations {\it (in matter)}}
</p> </p>
@ -2058,7 +1802,7 @@ Must be complemented by the {\bf constitutive relations} giving \({\bf D}\) and
in terms of \({\bf E}\) and \({\bf B}\). in terms of \({\bf E}\) and \({\bf B}\).
For the restricted case of linear media: For the restricted case of linear media:
</p> </p>
<div class="main div" id="org30a7942"> <div class="main div" id="org6accc1d">
<p> <p>
\[ \[
{\bf P} = \varepsilon_0 \chi_e {\bf E}, \hspace{1cm} {\bf P} = \varepsilon_0 \chi_e {\bf E}, \hspace{1cm}
@ -2082,7 +1826,7 @@ where \(\varepsilon \equiv \varepsilon_0(1 + \chi_e)\) and \(\mu \equiv \mu_0 (1
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1877,7 +1621,7 @@ Table of contents
<p> <p>
Discontinuities between different media, deduced from Discontinuities between different media, deduced from
</p> </p>
<div class="core div" id="orgb5cfb31"> <div class="core div" id="org18c9c85">
<p> <p>
{\bf Maxwell's equations {\it (in matter)}, integral form} {\bf Maxwell's equations {\it (in matter)}, integral form}
</p> </p>
@ -1955,7 +1699,7 @@ These are basis of theory of reflection and refraction.
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1889,7 +1633,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1885,7 +1629,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1981,7 +1725,7 @@ so the final form of the fields is
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1912,7 +1656,7 @@ v = \frac{1}{\sqrt{\mu \varepsilon}} = \frac{c}{n}
\] \]
where the index of refraction of the material is defined as where the index of refraction of the material is defined as
</p> </p>
<div class="main div" id="org4e4a2f7"> <div class="main div" id="orgc00345d">
<p> <p>
{\bf Index of refraction} {\bf Index of refraction}
\[ \[
@ -1956,7 +1700,7 @@ I = \frac{1}{2} \varepsilon v E_0^2
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1900,7 +1644,7 @@ Detailed study: starts from boundary conditions \ref{Gr(7.64)},
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1880,7 +1624,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1881,7 +1625,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1972,7 +1716,7 @@ R + T = 1.
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1912,7 +1656,7 @@ These forms for incident, reflected and transmitted wave can be substituted in t
<p> <p>
From now on we will orient the axes so that \({\boldsymbol k}_I\) lies in the \(xz\) plane. This means that \({\boldsymbol k}_R\) and \({\boldsymbol k}_T\) also lie in that plane. This is the From now on we will orient the axes so that \({\boldsymbol k}_I\) lies in the \(xz\) plane. This means that \({\boldsymbol k}_R\) and \({\boldsymbol k}_T\) also lie in that plane. This is the
</p> </p>
<div class="core div" id="org5b0d3cd"> <div class="core div" id="orgefbfc7d">
<p> <p>
{\bf First law of reflection:} {\bf First law of reflection:}
the incident, reflected and transmitted wave vectors form a plane (called the plane of incidence) which also includes the normal to the surface. the incident, reflected and transmitted wave vectors form a plane (called the plane of incidence) which also includes the normal to the surface.
@ -1927,7 +1671,7 @@ Specializing (\ref{eq:RTObliquek}) to our notations, we have
with the incidence (\(\theta_I\)) and reflection (\(\theta_R\)) angles with the incidence (\(\theta_I\)) and reflection (\(\theta_R\)) angles
and the angle of refraction (\(\theta_T\)) obey the following laws: and the angle of refraction (\(\theta_T\)) obey the following laws:
</p> </p>
<div class="core div" id="orgad4f6b0"> <div class="core div" id="org13fc947">
<p> <p>
{\bf Law of reflection} {\bf Law of reflection}
\[ \[
@ -1985,7 +1729,7 @@ while the third equation becomes
\] \]
Writing everything in terms of the incident amplitude, we get Writing everything in terms of the incident amplitude, we get
</p> </p>
<div class="main div" id="org969c30d"> <div class="main div" id="orgd7a540b">
<p> <p>
{\bf Fresnel's equations for reflection and transmission amplitudes (parallel case)} {\bf Fresnel's equations for reflection and transmission amplitudes (parallel case)}
\[ \[
@ -2005,7 +1749,7 @@ Amplitudes for transmitted and reflected wave: depend on angle of incidence:
Behaviour: for \(\theta_I = 0\) we recover (\ref{Gr(9.82)}). Behaviour: for \(\theta_I = 0\) we recover (\ref{Gr(9.82)}).
For grazing waves \(\theta_I \rightarrow \pi/2\) we have that \(\alpha \rightarrow \infty\) and the wave is totally reflected. The most interesting angle is the one at which \(\alpha = \beta\) and the reflected wave has zero amplitude. This is known as For grazing waves \(\theta_I \rightarrow \pi/2\) we have that \(\alpha \rightarrow \infty\) and the wave is totally reflected. The most interesting angle is the one at which \(\alpha = \beta\) and the reflected wave has zero amplitude. This is known as
</p> </p>
<div class="main div" id="orgd0455e3"> <div class="main div" id="orgdb6468b">
<p> <p>
{\bf Brewster's angle {\it (at which the reflected wave amplitude vanishes)}} {\bf Brewster's angle {\it (at which the reflected wave amplitude vanishes)}}
\[ \[
@ -2042,7 +1786,7 @@ Of course, we get \(R + T = 1\) as expected.
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1881,7 +1625,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1887,7 +1631,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1907,7 +1651,7 @@ where \(A\) is a constant amplitude. Substituting and taking the real part,
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1931,7 +1675,7 @@ with an identical equation for \(B_z\). If \(E_z = 0\) the waves are called {\bf
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
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<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1940,7 +1684,7 @@ which is {\it greater} than \(c\). The energy of the wave however propagates at
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1875,8 +1619,8 @@ Table of contents
</svg></a><span class="headline-id">emf</span></h2> </svg></a><span class="headline-id">emf</span></h2>
<div class="outline-text-2" id="text-emf"> <div class="outline-text-2" id="text-emf">
<details class="prereq" id="org720fb76"> <details class="prereq" id="org0b4147b">
<summary id="org8fa28e8"> <summary id="orgaa9a8c2">
Prerequisites Prerequisites
</summary> </summary>
<ul class="org-ul"> <ul class="org-ul">
@ -1884,8 +1628,8 @@ Prerequisites
</ul> </ul>
</details> </details>
<details class="objectives" id="orgb2961ae"> <details class="objectives" id="orgd0127b4">
<summary id="orga6c8829"> <summary id="orgf210d58">
Objectives Objectives
</summary> </summary>
<ul class="org-ul"> <ul class="org-ul">
@ -1908,7 +1652,7 @@ Objectives
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1905,7 +1649,7 @@ implementing a <b>gauge transformation</b>.
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1904,7 +1648,7 @@ Although Gauss's law looks nice in the Coulomb gauge, Amp{\`e}re-Maxwell does no
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1890,7 +1634,7 @@ while the equation for \(V\) becomes
\] \]
These can be written compactly upon introducing a new operator: the These can be written compactly upon introducing a new operator: the
</p> </p>
<div class="core div" id="org07a44ab"> <div class="core div" id="orgd5ba96e">
<p> <p>
{\bf d'Alembertian operator} {\bf d'Alembertian operator}
\[ \[
@ -1903,7 +1647,7 @@ These can be written compactly upon introducing a new operator: the
<p> <p>
so we get the so we get the
</p> </p>
<div class="core div" id="orgc7c0452"> <div class="core div" id="org15005e7">
<p> <p>
{\bf Inhomogeneous Maxwell equations (Lorenz gauge)} {\bf Inhomogeneous Maxwell equations (Lorenz gauge)}
\[ \[
@ -1940,7 +1684,7 @@ we have by direct inspection
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1891,7 +1635,7 @@ Useful strategy: represent fields in terms of potentials.
<p> <p>
Easiest: Easiest:
</p> </p>
<div class="core div" id="org2047afa"> <div class="core div" id="org389d31f">
<p> <p>
\[ \[
{\boldsymbol B} = {\boldsymbol \nabla} \times {\boldsymbol A} {\boldsymbol B} = {\boldsymbol \nabla} \times {\boldsymbol A}
@ -1907,7 +1651,7 @@ Putting this into Faraday's law gives
\] \]
so this can be written as the gradient of a scalar (by choice: \(-{\boldsymbol \nabla} V\)) so we get so this can be written as the gradient of a scalar (by choice: \(-{\boldsymbol \nabla} V\)) so we get
</p> </p>
<div class="core div" id="org135e92c"> <div class="core div" id="orgbbcf54f">
<p> <p>
\[ \[
{\boldsymbol E} = -{\boldsymbol \nabla} V - \frac{\partial {\boldsymbol A}}{\partial t} {\boldsymbol E} = -{\boldsymbol \nabla} V - \frac{\partial {\boldsymbol A}}{\partial t}
@ -1920,7 +1664,7 @@ so this can be written as the gradient of a scalar (by choice: \(-{\boldsymbol \
<p> <p>
Using this potential representation for \({\boldsymbol E}\) and \({\boldsymbol B}\) automatically fulfills the two homogeneous Maxwell equations. For the inhomogeneous equations, substituting (\ref{eq:E_from_Potentials}) into Gauss's law gives Using this potential representation for \({\boldsymbol E}\) and \({\boldsymbol B}\) automatically fulfills the two homogeneous Maxwell equations. For the inhomogeneous equations, substituting (\ref{eq:E_from_Potentials}) into Gauss's law gives
</p> </p>
<div class="main div" id="org020a783"> <div class="main div" id="org2d36baf">
<p> <p>
\[ \[
{\boldsymbol \nabla}^2 V + \frac{\partial}{\partial t} {\boldsymbol \nabla} \cdot {\boldsymbol A} = -\frac{\rho}{\varepsilon_0} {\boldsymbol \nabla}^2 V + \frac{\partial}{\partial t} {\boldsymbol \nabla} \cdot {\boldsymbol A} = -\frac{\rho}{\varepsilon_0}
@ -1936,13 +1680,13 @@ whereas Amp{\`ere}-Maxwell becomes
\] \]
which becomes after simple rearrangement and use of the identity \({\boldsymbol \nabla} \times \left({\boldsymbol \nabla} \times {\boldsymbol A}\right) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\boldsymbol A}) - {\boldsymbol \nabla}^2 {\boldsymbol A}\), which becomes after simple rearrangement and use of the identity \({\boldsymbol \nabla} \times \left({\boldsymbol \nabla} \times {\boldsymbol A}\right) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\boldsymbol A}) - {\boldsymbol \nabla}^2 {\boldsymbol A}\),
</p> </p>
<div class="main div" id="orga9e7111"> <div class="main div" id="orga7cdd8b">
<p> <p>
\[ \[
\left( {\boldsymbol ∇}<sup>2</sup> {\boldsymbol A} - μ<sub>0</sub> ε<sub>0</sub> \frac{∂<sup>2</sup> {\boldsymbol A}}{∂ t<sup>2</sup>} \right) \left( {\boldsymbol ∇}^2 {\boldsymbol A} - μ_0 ε_0 \frac{∂^2 {\boldsymbol A}}{∂ t^2} \right)
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>{\boldsymbol ∇} \left({\boldsymbol ∇} ⋅ {\boldsymbol A} + μ<sub>0</sub> ε<sub>0</sub> \frac{\partial V}{\partial t} \right) = -μ<sub>0</sub> {\boldsymbol J}</li> <li>{\boldsymbol ∇} \left({\boldsymbol ∇} ⋅ {\boldsymbol A} + μ_0 ε_0 \frac{\partial V}{\partial t} \right) = -μ_0 {\boldsymbol J}</li>
</ul> </ul>
<p> <p>
\label{eq:LaplacianA} \label{eq:LaplacianA}
@ -1959,7 +1703,7 @@ which becomes after simple rearrangement and use of the identity \({\boldsymbol
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
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<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1888,7 +1632,7 @@ Table of contents
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1875,8 +1619,8 @@ Table of contents
</svg></a><span class="headline-id">ems.ca</span></h3> </svg></a><span class="headline-id">ems.ca</span></h3>
<div class="outline-text-3" id="text-ems_ca"> <div class="outline-text-3" id="text-ems_ca">
<details class="prereq" id="orga9b4667"> <details class="prereq" id="org9f1c7db">
<summary id="org6a495fc"> <summary id="orgbf053b0">
Prerequisites Prerequisites
</summary> </summary>
<ul class="org-ul"> <ul class="org-ul">
@ -1884,8 +1628,8 @@ Prerequisites
</ul> </ul>
</details> </details>
<details class="objectives" id="org20c94d0"> <details class="objectives" id="org06b35e7">
<summary id="org981132c"> <summary id="org6416a57">
Objectives Objectives
</summary> </summary>
<ul class="org-ul"> <ul class="org-ul">
@ -1910,7 +1654,7 @@ Objectives
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -565,29 +502,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1878,22 +1622,19 @@ Table of contents
<p> <p>
A generic configuration of static charges coupled via the Coulomb interaction A generic configuration of static charges coupled via the Coulomb interaction
defines an electrostatic problem, whose solution is in principle obtained defines an electrostatic problem, whose solution is in principle obtained
from calculating either the field according to (\ref{eq:E_from_rho}), from calculating either the field according to <a href="./ems_es_ef_ccd.html#E_vcd">E_vcd</a>
</p>
<div class="main div" id="orgd9c6ec8">
<p>
\[
{\bf E} ({\bf r}) = \frac{1}{4\pi\varepsilon_0} \int_{\mathbb{R}^3} d\tau' \rho({\bf r}') \frac{{\bf r} - {\bf r}'}{|{\bf r} - {\bf r}'|^3}
\tag{\ref{eq:E_from_rho}}
\]
</p> </p>
<div class="main div" id="orgb912407">
\begin{equation*}
{\bf E} ({\bf r}) = \frac{1}{4\pi\varepsilon_0} \int_{\mathbb{R}^3} d\tau' \rho({\bf r}') \frac{{\bf r} - {\bf r}'}{|{\bf r} - {\bf r}'|^3}
\end{equation*}
</div> </div>
<p> <p>
or (often simpler) by calculating the electrostatic potential, using either the or (often simpler) by calculating the electrostatic potential, using either the
explicit construction (\ref{eq:V_from_rho}) explicit construction (\ref{eq:V_from_rho})
</p> </p>
<div class="main div" id="orgabd23e7"> <div class="main div" id="orgc09a05f">
<p> <p>
\[ \[
V({\bf r}) = \frac{1}{4\pi \varepsilon_0} \int_{\mathbb{R}^3} d\tau' \frac{\rho({\bf r}')}{|{\bf r} - {\bf r}'|}. V({\bf r}) = \frac{1}{4\pi \varepsilon_0} \int_{\mathbb{R}^3} d\tau' \frac{\rho({\bf r}')}{|{\bf r} - {\bf r}'|}.
@ -1909,7 +1650,7 @@ condition (\ref{Gr(2.20)}) can be expressed as the single
'local' (differential) condition (Poisson's equation) (\ref{eq:Poisson}) 'local' (differential) condition (Poisson's equation) (\ref{eq:Poisson})
</p> </p>
<div class="core div" id="orgb65e1cf"> <div class="core div" id="orgbe52068">
<p> <p>
\[ \[
{\boldsymbol \nabla}^2 V = -\frac{\rho}{\varepsilon_0}. {\boldsymbol \nabla}^2 V = -\frac{\rho}{\varepsilon_0}.
@ -1923,7 +1664,7 @@ condition (\ref{Gr(2.20)}) can be expressed as the single
In the specific case where the charge density vanishes, we fall back onto the simpler In the specific case where the charge density vanishes, we fall back onto the simpler
Laplace equation Laplace equation
</p> </p>
<div class="core div" id="org0f820c6"> <div class="core div" id="orgb4303af">
<p> <p>
\[ \[
{\boldsymbol \nabla}^2 V = 0 {\boldsymbol \nabla}^2 V = 0
@ -1945,7 +1686,7 @@ Laplace equation
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>

View File

@ -1,7 +1,7 @@
<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<!-- 2022-02-07 Mon 08:02 --> <!-- 2022-02-08 Tue 06:55 -->
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
@ -348,58 +348,12 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -427,25 +381,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -455,7 +392,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
@ -492,7 +429,7 @@ Table of contents
<details> <details>
<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
@ -564,30 +501,9 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li class="toc-currentpage">
<details open="">
<summary class="toc-currentpage">
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
@ -871,33 +787,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -926,21 +817,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
@ -989,25 +867,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1599,37 +1460,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1645,29 +1477,8 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
@ -1703,62 +1514,12 @@ Table of contents
</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
@ -1807,25 +1568,8 @@ Table of contents
</li> </li>
<li> <li>
<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
@ -1868,7 +1612,7 @@ Table of contents
</ul> </ul>
</details> </details>
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<h5 id="ems_ca_fe_L">The Laplace Equation<a class="headline-permalink" href="./ems_ca_fe_L.html#ems_ca_fe_L"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16"> <h5 id="ems_ca_fe_L">The Laplace Equation<a class="headline-permalink" href="./ems_ca_fe_L.html#ems_ca_fe_L"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/> <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/> <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
@ -1954,7 +1698,7 @@ are necessarily positive, we thus require \(f_x &gt; 0\), \(f_y &gt; 0\) and \(f
of the \(f_x + f_y + f_z = 0\) condition above. of the \(f_x + f_y + f_z = 0\) condition above.
</p> </p>
<div class="info div" id="org0be6d8d"> <div class="info div" id="orga2b5411">
<p> <p>
<b>Earnshaw's theorem</b> <br> <b>Earnshaw's theorem</b> <br>
Since solutions to Laplace's equation have no local minimum, Since solutions to Laplace's equation have no local minimum,
@ -2044,7 +1788,7 @@ This all feels a bit amateurish and not very systematic. Can we be more precise
<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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<title>Pre-Quantum Electrodynamics</title> <title>Pre-Quantum Electrodynamics</title>
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<details>
<summary>
<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span> <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
</summary>
<ul>
<li>
<a href="#org788e483">Before Coulomb</a>
</li> </li>
<li> <li>
<a href="#org8b037d5">Cavendish's experiment</a>
</li>
<li>
<a href="#org1f82edc">Coulomb</a>
</li>
<li>
<a href="#org359fd13">Current status</a>
</li>
</ul>
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<li>
<details>
<summary>
<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span> <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
</summary>
<ul>
<li>
<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
</li>
<li>
<a href="#ems_es_efo_e_ga">Generic assembly</a>
</li>
<li>
<a href="#ems_es_efo_e_cl">Crystal lattices</a>
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</ul>
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</li> </li>
</ul> </ul>
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<li> <li>
<details>
<summary>
<a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span> <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
</summary>
<ul>
<li>
<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
</li>
<li>
<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
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<summary> <summary>
<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span> <a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
</summary> </summary>
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<summary> <summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span> <a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary> </summary>
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</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span> <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
</summary>
<ul>
<li>
<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
</li>
<li>
<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
</li>
<li>
<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
</li>
</ul>
</details>
</li> </li>
<li class="toc-currentpage"> <li class="toc-currentpage">
<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span> <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
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</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span> <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
</summary>
<ul>
<li>
<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
</li>
<li>
<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
</li>
<li>
<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
</li>
<li>
<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
</li>
</ul>
</details>
</li> </li>
</ul> </ul>
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</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span> <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
</summary>
<ul>
<li>
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span> <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
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</summary> </summary>
<ul> <ul>
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<details>
<summary>
<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span> <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
</summary>
<ul>
<li>
<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
</li>
<li>
<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
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</ul>
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</li> </li>
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<summary>
<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span> <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
</summary>
<ul>
<li>
<a href="#orge025182">Divergence of gradient</a>
</li>
<li>
<a href="#orgacb930d">Curl of a gradient</a>
</li>
<li>
<a href="#org6caee98">Gradient of the divergence</a>
</li>
<li>
<a href="#orgb5da747">Divergence of a curl</a>
</li>
<li>
<a href="#orgebcbadc">Curl of curl</a>
</li>
</ul>
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</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span> <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
</summary>
<ul>
<li>
<a href="#org638a76f">Line Integrals</a>
</li>
<li>
<a href="#orgd8e925a">Surface Integrals</a>
</li>
<li>
<a href="#org5c24b4a">Volume Integrals</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span> <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
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</summary> </summary>
<ul> <ul>
<li> <li>
<details>
<summary>
<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span> <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_sph_grad">Gradient</a>
</li> </li>
<li> <li>
<a href="#c_m_cs_sph_div">Divergence</a>
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<li>
<a href="#c_m_cs_sph_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_sph_lap">Laplacian</a>
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<details>
<summary>
<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span> <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
</summary>
<ul>
<li>
<a href="#c_m_cs_cyl_grad">Gradient</a>
</li>
<li>
<a href="#c_m_cs_cyl_div">Divergence</a>
</li>
<li>
<a href="#c_m_cs_cyl_curl">Curl</a>
</li>
<li>
<a href="#c_m_cs_cyl_lap">Laplacian</a>
</li>
</ul>
</details>
</li> </li>
<li> <li>
<a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span> <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
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<details>
<summary>
<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span> <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
</summary>
<ul>
<li>
<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
</li>
<li>
<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
</li>
</ul>
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</ul> </ul>
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<ul class="navigation-links"><li>Prev:&nbsp;<a href="ems_ca_fe_L_3d.html">The Laplace Equation in Three Dimensions&emsp;<small>[ems.ca.fe.L.3d]</small></a></li><li>Next:&nbsp;<a href="ems_ca_fe_uP.html">Uniqueness of Solution to Poisson's Equation&emsp;<small>[ems.ca.fe.uP]</small></a></li><li>Up:&nbsp;<a href="ems_ca_fe.html">Fundamental Equations for the Electrostatic Potential&emsp;<small>[ems.ca.fe]</small></a></li></ul><div id="outline-container-ems_ca_fe_g" class="outline-5"> <ul class="navigation-links"><li>Prev:&nbsp;<a href="ems_ca_fe_L.html">The Laplace Equation&emsp;<small>[ems.ca.fe.L]</small></a></li><li>Next:&nbsp;<a href="ems_ca_fe_uP.html">Uniqueness of Solution to Poisson's Equation&emsp;<small>[ems.ca.fe.uP]</small></a></li><li>Up:&nbsp;<a href="ems_ca_fe.html">Fundamental Equations for the Electrostatic Potential&emsp;<small>[ems.ca.fe]</small></a></li></ul><div id="outline-container-ems_ca_fe_g" class="outline-5">
<h5 id="ems_ca_fe_g">Green's Identities<a class="headline-permalink" href="./ems_ca_fe_g.html#ems_ca_fe_g"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16"> <h5 id="ems_ca_fe_g">Green's Identities<a class="headline-permalink" href="./ems_ca_fe_g.html#ems_ca_fe_g"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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<p> <p>
<b>George Green</b> <b>George Green</b>
</p> </p>
<aside id="org7db95a9"> <aside id="org5513bf5">
<p> <p>
See a \href{short biography of George Green on Wikipedia}{https://en.wikipedia.org/wiki/George\_Green\_(mathematician)}. See a \href{short biography of George Green on Wikipedia}{https://en.wikipedia.org/wiki/George\_Green\_(mathematician)}.
</p> </p>
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<hr><div id="postamble" class="status"> <hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p> <p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-07 Mon 08:02</p> <p class="date">Created: 2022-02-08 Tue 06:55</p>
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