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Update 2022-03-24 08:43

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Jean-Sébastien
2022-03-24 08:43:21 +01:00
parent 1d852e7213
commit 50704eba07
211 changed files with 1506 additions and 3143 deletions
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build/ems_ca_me_h.html
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-03-22 Tue 10:52 -->
<!-- 2022-03-24 Thu 08:42 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
</summary>
<ul>
<li>
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
</li>
@@ -1621,19 +1621,19 @@ The next terms in the expansion are obtained similarly: the <b>quadrupole</b> te
\]
and can be rewritten as
</p>
<div class="eqlabel" id="org9893011">
<div class="eqlabel" id="org51d4992">
<p>
<a id="p_quad"></a><a href="./ems_ca_me_h.html#p_quad"><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="org8d2b01e">
<div class="alteqlabels" id="org810939b">
</div>
</div>
<div class="main div" id="org3dd96b8">
<div class="main div" id="org72b3bb3">
<p>
\[
\phi_q ({\bf r}) = \frac{1}{4\pi \varepsilon_0} \frac{1}{2} \sum_{a,b} \frac{r_a r_b}{r^5} Q_{ab}
@@ -1645,19 +1645,19 @@ and can be rewritten as
<p>
in terms of the <b>quadrupole moment</b>
</p>
<div class="eqlabel" id="org476da28">
<div class="eqlabel" id="orgfda7b59">
<p>
<a id="quadmom"></a><a href="./ems_ca_me_h.html#quadmom"><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="org3a377ca">
<div class="alteqlabels" id="orgef3c526">
</div>
</div>
<div class="main div" id="orgf571492">
<div class="main div" id="orgff250a4">
<p>
\[
Q_{ab} = \int_{\cal V} d\tau_s (3 r_{s,a} r_{s,b} - r_s^2 \delta_{a,b}) \rho ({\bf r}_s).
@@ -1676,19 +1676,19 @@ This is a symmetric, traceless rank \(2\) tensor: \(Q_{ab} = Q_{ba}\) and
<p>
Our expansion for the potential, with terms up to quadrupole ones, thus looks like
</p>
<div class="eqlabel" id="org2f1183a">
<div class="eqlabel" id="org528a861">
<p>
<a id="p_mdq"></a><a href="./ems_ca_me_h.html#p_mdq"><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="orgae17c12">
<div class="alteqlabels" id="org4e6d3ec">
</div>
</div>
<div class="main div" id="org3db4f46">
<div class="main div" id="org934568d">
<p>
\[
\phi({\bf r}) = \frac{1}{4\pi \varepsilon_0} \left( \frac{Q}{r} + \sum_a \frac{r_a}{r^3} p_a + \frac{1}{2} \sum_{a,b} \frac{r_a r_b}{r^5} Q_{ab} + ... \right)
@@ -1709,7 +1709,7 @@ the leading nonvanishing multipole moment is independent of the chosen location
the origin of the coordinate system (see Jackson Prob. 4.4).
</p>
<div class="info div" id="org6c4c92f">
<div class="info div" id="org4f925ea">
<p>
<b>A consistent nomenclature for the multipole expansion?</b>
</p>
@@ -1858,7 +1858,7 @@ 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: 2022-03-22 Tue 10:52</p>
<p class="date">Created: 2022-03-24 Thu 08:42</p>
<p class="validation"></p>
</div>