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Update 2022-02-15 10:32

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Jean-Sébastien
2022-02-15 10:32:42 +01:00
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commit 6874e66024
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-14 Mon 20:35 -->
<!-- 2022-02-15 Tue 10:14 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1597,11 +1597,11 @@ Table of contents
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a><span class="headline-id">ems.ca.fe.g</span></h5>
<div class="outline-text-5" id="text-ems_ca_fe_g">
<div class="info div" id="org9c72286">
<div class="info div" id="org99000c7">
<p>
<b>George Green</b>
</p>
<aside id="org6a5deaa">
<aside id="orga8c84e7">
<p>
See a <a href="https://en.wikipedia.org/wiki/George%5C_Green%5C_(mathematician)">short bio on wikipedia</a>
</p>
@@ -1621,7 +1621,7 @@ be found. He was later admitted, at the young age of
We can provide a very precise statement about uniqueness of solutions to Poisson's (or Laplace's)
equation with some very basic considerations starting from the divergence theorem
\[
\int_{\cal V} d\tau {\boldsymbol \nabla} \cdot {\bf F} = \oint_{\cal S} da ~{\bf F} \cdot {\bf n}
\int_{\cal V} d\tau ~{\boldsymbol \nabla} \cdot {\bf F} = \oint_{\cal S} da ~{\bf F} \cdot {\bf n}
\]
Let \({\bf F} = \phi {\boldsymbol \nabla} \psi\), where \(\phi\) and \(\psi\) are scalar fields. We
can then write
@@ -1634,14 +1634,14 @@ and
\]
Substituting this in the divergence theorem gives <b>Green's first identity</b>
</p>
<div class="eqlabel" id="orgc80fef9">
<div class="eqlabel" id="org6de2e63">
<p>
<a id="Green1"></a><a href="./ems_ca_fe_g.html#Green1"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a>
</p>
<div class="alteqlabels" id="org985f604">
<div class="alteqlabels" id="org6c786de">
<ul class="org-ul">
<li>J (1.34)</li>
</ul>
@@ -1659,14 +1659,14 @@ As an aside for now, for completeness, if we do the same thing again but with \(
interchanged, and subtract the result, we obtain another useful result known as
<b>Green's second identity</b> or <b>Green's theorem</b>
</p>
<div class="eqlabel" id="org55daee4">
<div class="eqlabel" id="org0307c8b">
<p>
<a id="Green2"></a><a href="./ems_ca_fe_g.html#Green2"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a>
</p>
<div class="alteqlabels" id="orgd7df7dc">
<div class="alteqlabels" id="org3cf622d">
<ul class="org-ul">
<li>J (1.35)</li>
</ul>
@@ -1702,7 +1702,7 @@ 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: 2022-02-14 Mon 20:35</p>
<p class="date">Created: 2022-02-15 Tue 10:14</p>
<p class="validation"></p>
</div>