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Update 2022-03-02 15:47

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Jean-Sébastien
2022-03-02 15:47:54 +01:00
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build/emd_ce_ce.html
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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>
@@ -1622,13 +1622,13 @@ Table of contents
</svg></a><span class="headline-id">emd.ce.ce</span></h4>
<div class="outline-text-4" id="text-emd_ce_ce">
<p>
Very important distinction: {\bf global} versus {\bf local} conservation of charge.
Very important distinction: <b>global</b> versus <b>local</b> conservation of charge.
</p>
<p>
Charge in a volume {\cal V}:
Charge in a volume \({\cal V}\):
\[
Q_{\cal V} (t) = \int_{\cal V} d\tau \rho ({\bf r}, t)
Q_{\cal V} (t) = \int_{\cal V} d\tau~ \rho ({\bf r}, t)
\label{Gr(8.1)}
\]
Current \({\bf J}\) flowing out through boundary \({\cal S}\) of \({\cal V}\): conservation of charge means
@@ -1643,13 +1643,12 @@ This means that
\]
Since this is true for any volume, we have (re)derived the
</p>
<div class="core div" id="orgfb5850b">
<div class="core div" id="orgf1c2b2a">
<p>
{\bf Continuity equation}
<b>Continuity equation</b> <a href="./ems_ms_ce.html#conteq">conteq</a>
\[
\frac{\partial \rho}{\partial t} + {\boldsymbol \nabla} \cdot {\bf J} = 0
\label{Gr(8.4)}
\]
\frac{\partial \rho}{\partial t} + {\boldsymbol \nabla} \cdot {\bf J} = 0
\]
</p>
</div>
@@ -1660,7 +1659,7 @@ Therefore, conservation of charge is a direct consequence of Maxwell's equations
<p>
One thing to note: we have viewed \(\rho\) and \({\boldsymbol J}\) as sources
(the ''right-hand side'') of Maxwell's equations. The continuity equation thus
imposes a functional constraint on these sources: not {\it any} \(\rho\) and
imposes a functional constraint on these sources: not <i>any</i> \(\rho\) and
\({\boldsymbol J}\) will do the trick, only the ones what obey it.
</p>
</div>
@@ -1684,7 +1683,7 @@ 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>