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Update 2022-03-02 15:47

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Jean-Sébastien
2022-03-02 15:47:54 +01:00
parent ac1e628013
commit 21bf9fdba5
194 changed files with 1653 additions and 1216 deletions
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build/emdm_Me_Mem.html
+10 -10
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-03-01 Tue 08:14 -->
<!-- 2022-03-02 Wed 15:45 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1657,7 +1657,7 @@ dI = \frac{\partial \sigma_b}{\partial t} da_{\perp} = \frac{\partial P}{\partia
\]
We therefore have the
</p>
<div class="core div" id="org9606db6">
<div class="core div" id="org0421a72">
<p>
{\bf Polarization current density}
\[
@@ -1675,7 +1675,7 @@ 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="orge1ae7f1">
<aside id="org642846e">
<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.
@@ -1698,7 +1698,7 @@ 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="orgb0d00db">
<div class="main div" id="orgba471ef">
<p>
\[
\rho = \rho_f + \rho_b = \rho_f - {\boldsymbol \nabla} \cdot {\bf P}
@@ -1711,7 +1711,7 @@ 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="org89c562c">
<div class="main div" id="org2ffd81b">
<p>
\[
{\bf J} = {\bf J}_f + {\bf J}_b + {\bf J}_p = {\bf J}_f + {\boldsymbol ∇} × {\bf M}
@@ -1735,7 +1735,7 @@ Gauss's law: can be rewritten
\]
where (as in static case)
</p>
<div class="core div" id="org0196779">
<div class="core div" id="org88bb3c5">
<p>
\[
{\bf D} \equiv \varepsilon_0 {\bf E} + {\bf P}
@@ -1761,7 +1761,7 @@ or
\]
where as before
</p>
<div class="core div" id="org2b5f6d5">
<div class="core div" id="org90cea20">
<p>
\[
{\bf H} \equiv \frac{1}{\mu_0} {\bf B} - {\bf M}
@@ -1779,7 +1779,7 @@ 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="org2c2cd2a">
<div class="core div" id="orgd6526ab">
<p>
{\bf Maxwell's equations {\it (in matter)}}
</p>
@@ -1805,7 +1805,7 @@ 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="orgcaf59d5">
<div class="main div" id="orgd345cd6">
<p>
\[
{\bf P} = \varepsilon_0 \chi_e {\bf E}, \hspace{1cm}
@@ -1842,7 +1842,7 @@ 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: 2022-03-01 Tue 08:14</p>
<p class="date">Created: 2022-03-02 Wed 15:45</p>
<p class="validation"></p>
</div>