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Update 2022-03-15 10:07

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Jean-Sébastien
2022-03-15 10:07:27 +01:00
parent 4808df71e6
commit 55f0de8197
193 changed files with 2416 additions and 2082 deletions
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build/ems_ca_me_h.html
+16 -16
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-03-07 Mon 20:38 -->
<!-- 2022-03-15 Tue 08:10 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1310,10 +1310,6 @@ Table of contents
</summary>
<ul>
<li>
<a href="./d_m.html#d_m">Diagnostics: Mathematical Preliminaries</a><span class="headline-id">d.m</span>
</li>
<li>
<a href="./d_ems.html#d_ems">Diagnostics: Electromagnetostatics</a><span class="headline-id">d.ems</span>
</li>
@@ -1352,6 +1348,10 @@ Table of contents
<li>
<a href="./d_red.html#d_red">Diagnostics: Relativistic Electrodynamics</a><span class="headline-id">d.red</span>
</li>
<li>
<a href="./d_m.html#d_m">Diagnostics: Compendium - Mathematics</a><span class="headline-id">d.m</span>
</li>
</ul>
@@ -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="orga8d81de">
<div class="eqlabel" id="orgc0ad248">
<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="org8432c29">
<div class="alteqlabels" id="orgfb585e2">
</div>
</div>
<div class="main div" id="orga83be58">
<div class="main div" id="org1a7deb8">
<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="org77742da">
<div class="eqlabel" id="orgbc8de26">
<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="orgc910af4">
<div class="alteqlabels" id="orge3da8dd">
</div>
</div>
<div class="main div" id="orgc071af5">
<div class="main div" id="orgbc87048">
<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="orgee515a1">
<div class="eqlabel" id="org2c48c0e">
<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="org1820e34">
<div class="alteqlabels" id="orgfce9466">
</div>
</div>
<div class="main div" id="org579b283">
<div class="main div" id="org930eead">
<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="org9e7c860">
<div class="info div" id="orgf830029">
<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: 2022-03-07 Mon 20:38</p>
<p class="date">Created: 2022-03-15 Tue 08:10</p>
<p class="validation"></p>
</div>