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Update 2022-02-14 06:33

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Jean-Sébastien
2022-02-14 06:33:37 +01:00
parent f8446c1405
commit 4cfe8cef59
204 changed files with 1839 additions and 941 deletions
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build/emdm_Me_Mem.html
+12 -10
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-10 Thu 08:32 -->
<!-- 2022-02-13 Sun 21:20 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1633,7 +1633,7 @@ dI = \frac{\partial \sigma_b}{\partial t} da_{\perp} = \frac{\partial P}{\partia
\]
We therefore have the
</p>
<div class="core div" id="orga19bc43">
<div class="core div" id="orgc16990f">
<p>
{\bf Polarization current density}
\[
@@ -1651,7 +1651,7 @@ 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="org7492618">
<aside id="orgbe14b68">
<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.
@@ -1674,7 +1674,7 @@ 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="org6458291">
<div class="main div" id="org27840ee">
<p>
\[
\rho = \rho_f + \rho_b = \rho_f - {\boldsymbol \nabla} \cdot {\bf P}
@@ -1687,7 +1687,7 @@ 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="org79300fd">
<div class="main div" id="orge8444d0">
<p>
\[
{\bf J} = {\bf J}_f + {\bf J}_b + {\bf J}_p = {\bf J}_f + {\boldsymbol ∇} × {\bf M}
@@ -1711,7 +1711,7 @@ Gauss's law: can be rewritten
\]
where (as in static case)
</p>
<div class="core div" id="org0cf7843">
<div class="core div" id="org3e52dc6">
<p>
\[
{\bf D} \equiv \varepsilon_0 {\bf E} + {\bf P}
@@ -1737,7 +1737,7 @@ or
\]
where as before
</p>
<div class="core div" id="org4d58c35">
<div class="core div" id="org5550f7c">
<p>
\[
{\bf H} \equiv \frac{1}{\mu_0} {\bf B} - {\bf M}
@@ -1755,7 +1755,7 @@ 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="org4ca5e56">
<div class="core div" id="orge1d07ac">
<p>
{\bf Maxwell's equations {\it (in matter)}}
</p>
@@ -1781,7 +1781,7 @@ 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="orgac29d47">
<div class="main div" id="org83b4dbd">
<p>
\[
{\bf P} = \varepsilon_0 \chi_e {\bf E}, \hspace{1cm}
@@ -1803,6 +1803,8 @@ where \(\varepsilon \equiv \varepsilon_0(1 + \chi_e)\) and \(\mu \equiv \mu_0 (1
<br><ul class="navigation-links"><li>Prev:&nbsp;<a href="emdm_Me.html">Maxwell's Equations in Matter&emsp;<small>[emdm.Me]</small></a></li><li>Next:&nbsp;<a href="emdm_Me_bc.html">Boundary Conditions&emsp;<small>[emdm.Me.bc]</small></a></li><li>Up:&nbsp;<a href="emdm_Me.html">Maxwell's Equations in Matter&emsp;<small>[emdm.Me]</small></a></li></ul>
<br>
<hr>
<div class="license">
<a rel="license noopener" href="https://creativecommons.org/licenses/by/4.0/"
@@ -1816,7 +1818,7 @@ 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: 2022-02-10 Thu 08:32</p>
<p class="date">Created: 2022-02-13 Sun 21:20</p>
<p class="validation"></p>
</div>