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Update 2022-02-08 17:21

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Jean-Sébastien
2022-02-08 17:21:33 +01:00
parent 077433c40a
commit 3454aba504
207 changed files with 1882 additions and 1097 deletions
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build/emdm_Me_Mem.html
+15 -11
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-08 Tue 06:55 -->
<!-- 2022-02-08 Tue 17:21 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -272,6 +272,10 @@ Table of contents
</summary>
<ul>
<li>
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
</li>
<li>
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
</li>
@@ -736,7 +740,7 @@ Table of contents
</li>
<li>
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
</li>
<li>
@@ -1654,7 +1658,7 @@ dI = \frac{\partial \sigma_b}{\partial t} da_{\perp} = \frac{\partial P}{\partia
\]
We therefore have the
</p>
<div class="core div" id="orgb555ebf">
<div class="core div" id="orgff46cb4">
<p>
{\bf Polarization current density}
\[
@@ -1672,7 +1676,7 @@ the polarization current is the result of linear motion of charge when
polarization changes). We can check consistency with the continuity equation
associated to the conservation of bound charges:
</p>
<aside id="org86c5ff2">
<aside id="orgbce7d73">
<p>
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.
@@ -1695,7 +1699,7 @@ 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,
{\it free} and {\it bound}:
</p>
<div class="main div" id="orgf8c82b2">
<div class="main div" id="org4df7865">
<p>
\[
\rho = \rho_f + \rho_b = \rho_f - {\boldsymbol \nabla} \cdot {\bf P}
@@ -1708,7 +1712,7 @@ 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
{\it polarization}:
</p>
<div class="main div" id="org4054380">
<div class="main div" id="orgcc32502">
<p>
\[
{\bf J} = {\bf J}_f + {\bf J}_b + {\bf J}_p = {\bf J}_f + {\boldsymbol ∇} × {\bf M}
@@ -1732,7 +1736,7 @@ Gauss's law: can be rewritten
\]
where (as in static case)
</p>
<div class="core div" id="orgf78b92c">
<div class="core div" id="org7600f00">
<p>
\[
{\bf D} \equiv \varepsilon_0 {\bf E} + {\bf P}
@@ -1758,7 +1762,7 @@ or
\]
where as before
</p>
<div class="core div" id="org513c514">
<div class="core div" id="orgb942ad8">
<p>
\[
{\bf H} \equiv \frac{1}{\mu_0} {\bf B} - {\bf M}
@@ -1776,7 +1780,7 @@ bound parts, since they don't involve \(\rho\) or \({\bf J}\).
<p>
In terms of free charges and currents, we thus get
</p>
<div class="core div" id="org686ea33">
<div class="core div" id="orgd9d30d5">
<p>
{\bf Maxwell's equations {\it (in matter)}}
</p>
@@ -1802,7 +1806,7 @@ Must be complemented by the {\bf constitutive relations} giving \({\bf D}\) and
in terms of \({\bf E}\) and \({\bf B}\).
For the restricted case of linear media:
</p>
<div class="main div" id="org6accc1d">
<div class="main div" id="orge1df28e">
<p>
\[
{\bf P} = \varepsilon_0 \chi_e {\bf E}, \hspace{1cm}
@@ -1826,7 +1830,7 @@ where \(\varepsilon \equiv \varepsilon_0(1 + \chi_e)\) and \(\mu \equiv \mu_0 (1
<hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div>