Update 2022-02-08 07:07
This commit is contained in:
Jean-Sébastien
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-267
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<!DOCTYPE html>
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<html lang="en">
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<head>
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<!-- 2022-02-07 Mon 08:02 -->
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<!-- 2022-02-08 Tue 06:55 -->
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<meta charset="utf-8">
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<meta name="viewport" content="width=device-width, initial-scale=1">
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<title>Pre-Quantum Electrodynamics</title>
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@@ -348,58 +348,12 @@ Table of contents
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</li>
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<li>
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<details>
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<summary>
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<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
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</summary>
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<ul>
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<li>
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<a href="#org788e483">Before Coulomb</a>
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</li>
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<li>
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<a href="#org8b037d5">Cavendish's experiment</a>
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</li>
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<li>
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<a href="#org1f82edc">Coulomb</a>
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</li>
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<li>
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<a href="#org359fd13">Current status</a>
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</li>
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</ul>
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</details>
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</li>
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<li>
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<details>
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<summary>
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<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>
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</summary>
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<ul>
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<li>
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<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
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</li>
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<li>
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<a href="#ems_es_efo_e_ga">Generic assembly</a>
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</li>
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<li>
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<a href="#ems_es_efo_e_cl">Crystal lattices</a>
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</li>
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</ul>
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</details>
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</li>
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</ul>
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@@ -427,25 +381,8 @@ Table of contents
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</li>
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<li>
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<details>
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<summary>
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<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>
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</summary>
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<ul>
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<li>
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<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
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</li>
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<li>
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<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
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</li>
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</ul>
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</details>
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</li>
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</ul>
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@@ -455,7 +392,7 @@ Table of contents
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<details>
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<summary>
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<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
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<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
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</summary>
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@@ -492,7 +429,7 @@ Table of contents
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<details>
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<summary>
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<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
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<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
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</summary>
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@@ -565,29 +502,8 @@ Table of contents
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</summary>
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<ul>
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<li>
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<details>
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<summary>
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<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
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</summary>
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<ul>
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<li>
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<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
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</li>
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<li>
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<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
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</li>
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<li>
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<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
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</li>
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</ul>
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</details>
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</li>
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<li>
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<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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@@ -871,33 +787,8 @@ Table of contents
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</summary>
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<ul>
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<li>
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<details>
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<summary>
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<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
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</summary>
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<ul>
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<li>
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<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
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</li>
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<li>
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<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
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</li>
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<li>
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<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
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</li>
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<li>
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<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
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</li>
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</ul>
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</details>
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</li>
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</ul>
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@@ -926,21 +817,8 @@ Table of contents
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</summary>
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<ul>
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<li>
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<details>
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<summary>
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<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
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</summary>
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<ul>
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<li>
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<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
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</li>
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</ul>
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</details>
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</li>
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<li>
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<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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@@ -989,25 +867,8 @@ Table of contents
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</summary>
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<ul>
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<li>
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<details>
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<summary>
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<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>
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</summary>
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<ul>
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<li>
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<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
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</li>
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<li>
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<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
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</li>
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</ul>
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</details>
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</li>
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</ul>
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@@ -1599,37 +1460,8 @@ Table of contents
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</li>
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<li>
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<details>
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<summary>
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<a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
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</summary>
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<ul>
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<li>
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<a href="#orge025182">Divergence of gradient</a>
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</li>
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<li>
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<a href="#orgacb930d">Curl of a gradient</a>
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</li>
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<li>
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<a href="#org6caee98">Gradient of the divergence</a>
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</li>
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<li>
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<a href="#orgb5da747">Divergence of a curl</a>
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</li>
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<li>
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<a href="#orgebcbadc">Curl of curl</a>
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</li>
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</ul>
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</details>
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</li>
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</ul>
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@@ -1645,29 +1477,8 @@ Table of contents
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</summary>
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<ul>
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<li>
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<details>
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<summary>
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<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>
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</summary>
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<ul>
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<li>
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<a href="#org638a76f">Line Integrals</a>
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</li>
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<li>
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<a href="#orgd8e925a">Surface Integrals</a>
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</li>
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<li>
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<a href="#org5c24b4a">Volume Integrals</a>
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</li>
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</ul>
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</details>
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</li>
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<li>
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<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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@@ -1703,62 +1514,12 @@ Table of contents
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</summary>
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<ul>
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<li>
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<details>
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<summary>
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<a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
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</summary>
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<ul>
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<li>
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<a href="#c_m_cs_sph_grad">Gradient</a>
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</li>
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<li>
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<a href="#c_m_cs_sph_div">Divergence</a>
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</li>
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<li>
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<a href="#c_m_cs_sph_curl">Curl</a>
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</li>
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<li>
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<a href="#c_m_cs_sph_lap">Laplacian</a>
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</li>
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</ul>
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</details>
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</li>
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<li>
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<details>
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<summary>
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<a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
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</summary>
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<ul>
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<li>
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<a href="#c_m_cs_cyl_grad">Gradient</a>
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</li>
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<li>
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<a href="#c_m_cs_cyl_div">Divergence</a>
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</li>
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<li>
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<a href="#c_m_cs_cyl_curl">Curl</a>
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</li>
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<li>
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<a href="#c_m_cs_cyl_lap">Laplacian</a>
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</li>
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</ul>
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</details>
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</li>
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<li>
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<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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@@ -1807,25 +1568,8 @@ Table of contents
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</li>
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<li>
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<details>
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<summary>
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<a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
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</summary>
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<ul>
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<li>
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<a href="#c_m_vf_pot_irrot">Theorem 1: Curl-less (irrotational) fields</a>
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</li>
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<li>
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<a href="#c_m_vf_pot_solen">Theorem 2: Divergence-less (solenoidal) fields</a>
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</li>
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</ul>
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</details>
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</li>
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</ul>
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@@ -1896,11 +1640,11 @@ or (in my notations)
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\]
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Explicitly, the first few terms are
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\[
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{\bf A}({\bf r}) = \frac{\mu_0 I}{4\pi} \left[ \frac{1}{r} \oint<sub>\cal P</sub> d{\bf l}'
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{\bf A}({\bf r}) = \frac{\mu_0 I}{4\pi} \left[ \frac{1}{r} \oint_{\cal P} d{\bf l}'
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</p>
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<ul class="org-ul">
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<li>\frac{1}{r^2} \oint d{\bf l}' r' cos θ'</li>
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<li>\frac{1}{r^3} \oint d{\bf l}' (r')<sup>2</sup> \left( \frac{3}{2} cos<sup>2</sup> θ' - \frac{1}{2} \right) + … \right]</li>
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<li>\frac{1}{r^3} \oint d{\bf l}' (r')^2 \left( \frac{3}{2} cos^2 θ' - \frac{1}{2} \right) + … \right]</li>
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</ul>
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<p>
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\label{Gr(5.79)}
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@@ -1929,7 +1673,7 @@ Using equation \ref{Gr(1.108)} from Problem 1.61,
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with \({\bf c} = \hat {\bf r}\),
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</p>
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<div class="info div" id="org87ac3e2">
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<div class="info div" id="org5d7df6b">
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<p>
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\paragraph{Parenthesis: Problem 1.61 (e)} Start from Stokes' theorem,
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\[
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@@ -1946,7 +1690,7 @@ term thus becomes
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\[
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</p>
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<ul class="org-ul">
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<li>∫<sub>\cal S</sub> {\bf c} × ({\boldsymbol ∇} T) ⋅ d{\bf a} = -{\bf c} ⋅ ∫<sub>\cal S</sub> {\boldsymbol ∇}T × d{\bf a}</li>
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<li>∫_{\cal S} {\bf c} × ({\boldsymbol ∇} T) ⋅ d{\bf a} = -{\bf c} ⋅ ∫_{\cal S} {\boldsymbol ∇}T × d{\bf a}</li>
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</ul>
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<p>
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\]
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@@ -1971,7 +1715,7 @@ Back to our problem:
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\]
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and defining the
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</p>
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<div class="core div" id="org8aeada9">
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<div class="core div" id="org21dd473">
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<p>
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<b>magnetic dipole moment</b>
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\[
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@@ -1984,7 +1728,7 @@ and defining the
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<p>
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we obtain the convenient expression for the
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</p>
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<div class="main div" id="org3a7148b">
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<div class="main div" id="orgf135519">
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<p>
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{\bf dipole term of the vector potential}
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\[
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@@ -1995,7 +1739,7 @@ we obtain the convenient expression for the
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</div>
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<div class="example div" id="org474d3c1">
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<div class="example div" id="org2824494">
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<p>
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\paragraph{Example 5.13:} find magnetic dipole moment of bookend shape of Gr. Fig. 5.52.
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All sides have length \(w\) and carry current \(I\).
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@@ -2029,7 +1773,7 @@ scale of the source's current loops.
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<hr><div id="postamble" class="status">
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<p class="author">Author: Jean-Sébastien Caux</p>
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<p class="date">Created: 2022-02-07 Mon 08:02</p>
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<p class="date">Created: 2022-02-08 Tue 06:55</p>
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<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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</div>
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