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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/ems_ms_vp_LC.html
+9 -9
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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>
@@ -1626,18 +1626,18 @@ Similarly to the electrostatic dipole,
the magnetic field of a dipole can be written in coordinate-free form.
For this: we define a useful object, the <br>
</p>
<div class="info div" id="org55b6db0">
<div class="info div" id="org98157b0">
<p>
<b>Levi-Civita symbol</b>
</p>
<div class="eqlabel" id="org9e576ba">
<div class="eqlabel" id="org535778a">
<p>
<a id="LeviCivita"></a><a href="./ems_ms_vp_LC.html#LeviCivita"><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="org77f08c0">
<div class="alteqlabels" id="org0f52644">
</div>
@@ -1660,14 +1660,14 @@ Using this: we can for example rewrite the cross product as
\]
Important identity:
</p>
<div class="eqlabel" id="org07de3ba">
<div class="eqlabel" id="org6ea221e">
<p>
<a id="sumLeviCivita"></a><a href="./ems_ms_vp_LC.html#sumLeviCivita"><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="org861cb1f">
<div class="alteqlabels" id="org7cc6ac8">
</div>
@@ -1706,14 +1706,14 @@ and \(\epsilon_{ijk} \epsilon_{klm} = \epsilon_{ijk} \epsilon_{lmk} = \delta_{il
<p>
Putting back the vector notation, and the \(m\) notation for the magnetic dipole (instead of \(M\)), we obtain
</p>
<div class="eqlabel" id="orgfe40c46">
<div class="eqlabel" id="orgda07de3">
<p>
<a id="B_di"></a><a href="./ems_ms_vp_LC.html#B_di"><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="org6c5c93e">
<div class="alteqlabels" id="org07c640d">
<ul class="org-ul">
<li>Gr (5.89)</li>
</ul>
@@ -1751,7 +1751,7 @@ 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>