Update 2022-02-08 07:07
This commit is contained in:
Jean-Sébastien
+11
-267
@@ -1,7 +1,7 @@
|
||||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-07 Mon 08:02 -->
|
||||
<!-- 2022-02-08 Tue 06:55 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
@@ -348,58 +348,12 @@ Table of contents
|
||||
|
||||
</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>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="#org788e483">Before Coulomb</a>
|
||||
|
||||
</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>
|
||||
|
||||
|
||||
</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>
|
||||
|
||||
</ul>
|
||||
@@ -427,25 +381,8 @@ Table of contents
|
||||
|
||||
</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>
|
||||
|
||||
|
||||
</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>
|
||||
|
||||
</ul>
|
||||
@@ -455,7 +392,7 @@ Table of contents
|
||||
|
||||
<details>
|
||||
<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>
|
||||
@@ -492,7 +429,7 @@ Table of contents
|
||||
|
||||
<details>
|
||||
<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>
|
||||
@@ -565,29 +502,8 @@ Table of contents
|
||||
</summary>
|
||||
<ul>
|
||||
<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>
|
||||
|
||||
|
||||
</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>
|
||||
<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>
|
||||
<ul>
|
||||
<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>
|
||||
|
||||
|
||||
</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>
|
||||
|
||||
</ul>
|
||||
@@ -926,21 +817,8 @@ Table of contents
|
||||
</summary>
|
||||
<ul>
|
||||
<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>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</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>
|
||||
@@ -989,25 +867,8 @@ Table of contents
|
||||
</summary>
|
||||
<ul>
|
||||
<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>
|
||||
|
||||
|
||||
</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>
|
||||
|
||||
</ul>
|
||||
@@ -1599,37 +1460,8 @@ Table of contents
|
||||
|
||||
</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>
|
||||
|
||||
|
||||
</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>
|
||||
|
||||
</ul>
|
||||
@@ -1645,29 +1477,8 @@ Table of contents
|
||||
</summary>
|
||||
<ul>
|
||||
<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>
|
||||
|
||||
|
||||
</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>
|
||||
<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>
|
||||
<ul>
|
||||
<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>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="#c_m_cs_sph_grad">Gradient</a>
|
||||
|
||||
</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>
|
||||
|
||||
|
||||
</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>
|
||||
<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>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
<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>
|
||||
|
||||
</ul>
|
||||
@@ -1902,7 +1646,7 @@ we get
|
||||
But \({\bf J}\) depends only on \({\bf r}'\) so \({\boldsymbol \nabla} \times {\bf J} ({\bf r}') = 0\), and since
|
||||
the curl of a gradient always vanishes, we obtain
|
||||
</p>
|
||||
<div class="core div" id="org6040235">
|
||||
<div class="core div" id="orgdf5fc3e">
|
||||
<p>
|
||||
\[
|
||||
{\boldsymbol \nabla} \cdot {\bf B} = 0
|
||||
@@ -1970,7 +1714,7 @@ at infinity), and in the third step we have used the assumption of steady-state
|
||||
<p>
|
||||
We thus obtain in total
|
||||
</p>
|
||||
<div class="core div" id="org5910098">
|
||||
<div class="core div" id="org3da2f25">
|
||||
<p>
|
||||
<b>Ampère's law</b>
|
||||
\[
|
||||
@@ -1987,7 +1731,7 @@ We thus obtain in total
|
||||
\]
|
||||
so
|
||||
</p>
|
||||
<div class="core div" id="org797a8ba">
|
||||
<div class="core div" id="org5aa5f70">
|
||||
<p>
|
||||
\[
|
||||
\oint_{\cal P} {\bf B} \cdot d{\bf l} = \mu_0 I_{enc} \hspace{2cm}
|
||||
@@ -2009,7 +1753,7 @@ Sign ambiguity: resolved by right-hand rule as usual.
|
||||
Ampère's law in magnetostatics takes a parallel role to Gauss's law in electrostatics.
|
||||
</p>
|
||||
|
||||
<div class="example div" id="org727441a">
|
||||
<div class="example div" id="orgc846872">
|
||||
<p>
|
||||
\paragraph{Example 5.7:} same as Example 5.5, but now with Ampère.
|
||||
\paragraph{Solution:} by symmetry, \({\bf B}\) is circumferential and can only depend on \(s\). Then,
|
||||
@@ -2021,7 +1765,7 @@ choosing an amperian loop at a fixed radius \(s\), we get
|
||||
|
||||
</div>
|
||||
|
||||
<div class="example div" id="org2c88441">
|
||||
<div class="example div" id="org1c375de">
|
||||
<p>
|
||||
\paragraph{Example 5.8:} uniform surface current \({\bf K} = K \hat{\bf x}\) flowing in \(xy\) plane.
|
||||
\paragraph{Solution:} Biot-Savart: \({\bf B}\) must be perpendicular to \({\bf K}\). Intuition:
|
||||
@@ -2038,7 +1782,7 @@ and along \(\hat{\bf y}\) for \(z < 0\). Amperian loop of width \(l\) punchi
|
||||
|
||||
</div>
|
||||
|
||||
<div class="example div" id="org351bb6d">
|
||||
<div class="example div" id="orgc3e6b98">
|
||||
<p>
|
||||
\paragraph{Example 5.9:} solenoid along \(\hat{\bf z}\), wire carrying current \(I\) doing \(n\) turns per unit length on cylinder of radius \(R\).
|
||||
\paragraph{Solution:} by symmetry, \({\bf B}\) must be along axis of solenoid. Outside: infinitely far away, \({\bf B}\) must vanish.
|
||||
@@ -2059,7 +1803,7 @@ Amperian loop of length \(l\), half-inside and half-outside:
|
||||
i) infinite straight lines, ii) infinite planes, iii) infinite solenoids, iv) toroids.
|
||||
</p>
|
||||
|
||||
<div class="example div" id="orgb0ff555">
|
||||
<div class="example div" id="orgb302b1e">
|
||||
<p>
|
||||
\paragraph{Example 5.10:} toroidal coil (no matter the shape, as long as it is rotationally symmetric).
|
||||
\paragraph{Solution:} magnetic field is circumferential everywhere. Outside coil, field again zero.
|
||||
@@ -2079,7 +1823,7 @@ Amperian loop half inside, half outside:
|
||||
|
||||
<hr><div id="postamble" class="status">
|
||||
<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>
|
||||
</div>
|
||||
|
||||
|
||||
Reference in New Issue
Block a user