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Update 2022-02-21 10:35

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Jean-Sébastien
2022-02-21 10:35:02 +01:00
parent ec8a4ca406
commit 40679d39bc
204 changed files with 4807 additions and 13916 deletions
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-17 Thu 08:42 -->
<!-- 2022-02-21 Mon 10:33 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -602,11 +602,11 @@ Table of contents
</summary>
<ul>
<li>
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
</li>
<li>
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
</li>
@@ -614,21 +614,12 @@ Table of contents
</details>
</li>
<li>
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
<details>
<summary>
</li>
<li>
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
</summary>
<ul>
<li>
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
</li>
</ul>
</details>
</li>
<li>
@@ -640,11 +631,15 @@ Table of contents
</summary>
<ul>
<li>
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
</li>
<li>
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
</li>
<li>
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
</li>
@@ -661,6 +656,10 @@ Table of contents
</summary>
<ul>
<li>
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
</li>
<li>
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
</li>
@@ -698,10 +697,6 @@ Table of contents
</summary>
<ul>
<li>
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
</li>
<li>
<details open="">
<summary class="toc-open">
@@ -1435,7 +1430,7 @@ Table of contents
</li>
<li>
<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 arguments</a><span class="headline-id">c.m.dc.pr</span>
</li>
<li>
@@ -1605,7 +1600,7 @@ Table of contents
<p>
For many substances: polarization is proportional to field, if the latter isn't too strong:
</p>
<div class="main div" id="org19b6c6b">
<div class="main div" id="org8261509">
<p>
\[
{\bf P} = \varepsilon_0 \chi_e {\bf E}
@@ -1635,7 +1630,7 @@ In linear dielectrics:
\]
so
</p>
<div class="main div" id="orgbcecf63">
<div class="main div" id="org541d013">
<p>
\[
{\bf D} = \varepsilon {\bf E}
@@ -1657,7 +1652,7 @@ This is all just nomenclature, everything is already in \ref{Gr(4.30)}.
<div class="example div" id="org053a13e">
<div class="example div" id="org68a0528">
<p>
\paragraph{Example 4.5:} metal sphere of radius \(a\) carrying charge \(Q\), surrounded out to radius \(b\) by
a linear dielectric material of permittivity \(\varepsilon\). Find potential at center (relative to infinity).
@@ -1713,7 +1708,7 @@ of {\it e.g.} \({\bf P}\) would not vanish.
Only case where parallel works: space entirely filled with homogeneous linear dielectric.
</p>
<div class="example div" id="orga6e236b">
<div class="example div" id="org35c8add">
<p>
\paragraph{Example 4.6:} parallel-plate capacitor filled with insulating material of
dielectric constant \(\varepsilon_r\). What is the effect on the capacitance ?
@@ -1748,7 +1743,7 @@ If \(\rho = 0\), any net charge is on surface, potential then obeys Laplace.
<p>
Convenient to rewrite boundary conditions in terms of free charge: from \ref{Gr(4.26)},
</p>
<div class="main div" id="orgf6c2f6b">
<div class="main div" id="org534154f">
<p>
\[
\varepsilon_{above} E^{\perp}_{above} - \varepsilon_{below} E^{\perp}_{below} = \sigma_f
@@ -1760,7 +1755,7 @@ Convenient to rewrite boundary conditions in terms of free charge: from \ref{Gr
<p>
or in terms of the potential,
</p>
<div class="main div" id="org555861c">
<div class="main div" id="orgce8bba1">
<p>
\[
\varepsilon_{above} \frac{\partial V_{above}}{\partial n} -
@@ -1773,7 +1768,7 @@ or in terms of the potential,
<p>
Potential itself is continuous,
</p>
<div class="main div" id="orgad5f974">
<div class="main div" id="orgc3f3f8a">
<p>
\[
V_{above} = V_{below}
@@ -1785,7 +1780,7 @@ Potential itself is continuous,
<div class="example div" id="org83cb9f1">
<div class="example div" id="orga7c350b">
<p>
\paragraph{Example 4.7:} sphere of homogeneous dielectric material in uniform electric field \({\bf E}_0\).
Find electric field inside sphere.
@@ -1843,7 +1838,7 @@ Thus,
<div class="example div" id="org9d43c5a">
<div class="example div" id="org2cd48ac">
<p>
\paragraph{Example 4.8:} suppose region below \(z = 0\) is filled with uniform linear dielectric with susceptibility \(\chi_e\).
Calculate force on point charge \(q\) situated a distance \(d\) above origin.
@@ -1947,7 +1942,7 @@ Special case of linear isotropic dielectric: \({\bf D} = \varepsilon {\bf E}\),
\]
Total work done:
</p>
<div class="main div" id="org7d8e5ae">
<div class="main div" id="org9699879">
<p>
\[
W = \frac{1}{2} \int d\tau {\bf D} \cdot {\bf E}
@@ -2051,7 +2046,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
</div>
<div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-17 Thu 08:42</p>
<p class="date">Created: 2022-02-21 Mon 10:33</p>
<p class="validation"></p>
</div>