Update 2022-03-15 10:07
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@@ -1,7 +1,7 @@
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<!DOCTYPE html>
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<html lang="en">
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<head>
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<!-- 2022-03-07 Mon 20:38 -->
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<!-- 2022-03-15 Tue 08:10 -->
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<meta charset="utf-8">
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<meta name="viewport" content="width=device-width, initial-scale=1">
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<title>Pre-Quantum Electrodynamics</title>
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@@ -1310,10 +1310,6 @@ Table of contents
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</summary>
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<ul>
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<li>
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<a href="./d_m.html#d_m">Diagnostics: Mathematical Preliminaries</a><span class="headline-id">d.m</span>
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</li>
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<li>
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<a href="./d_ems.html#d_ems">Diagnostics: Electromagnetostatics</a><span class="headline-id">d.ems</span>
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</li>
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@@ -1352,6 +1348,10 @@ Table of contents
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<li>
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<a href="./d_red.html#d_red">Diagnostics: Relativistic Electrodynamics</a><span class="headline-id">d.red</span>
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</li>
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<li>
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<a href="./d_m.html#d_m">Diagnostics: Compendium - Mathematics</a><span class="headline-id">d.m</span>
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</li>
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</ul>
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@@ -1629,14 +1629,14 @@ can thus be written
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\]
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Explicitly, the first few terms are (letting \(\hat{\bf r} \cdot \hat{\bf r}_s = \cos \theta\))
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</p>
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<div class="eqlabel" id="orgb783834">
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<div class="eqlabel" id="org7ea630d">
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<p>
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<a id="A_Leg"></a><a href="./ems_ms_vp_me.html#A_Leg"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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<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"/>
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<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"/>
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</svg></a>
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</p>
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<div class="alteqlabels" id="org7cfeed1">
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<div class="alteqlabels" id="orgf544c92">
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<ul class="org-ul">
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<li>Gr (5.80)</li>
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</ul>
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@@ -1663,14 +1663,14 @@ monopoles (also from Maxwell's equation <a href="./ems_ms_dcB_d.html#divB0">divB
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<p>
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The dominant term is thus the dipole,
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</p>
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<div class="eqlabel" id="org3177483">
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<div class="eqlabel" id="org1d49e4f">
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<p>
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<a id="A_di1"></a><a href="./ems_ms_vp_me.html#A_di1"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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<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"/>
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<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"/>
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</svg></a>
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</p>
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<div class="alteqlabels" id="orge720d21">
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<div class="alteqlabels" id="org0f2e926">
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<ul class="org-ul">
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<li>Gr (5.85)</li>
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</ul>
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@@ -1685,14 +1685,14 @@ The dominant term is thus the dipole,
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\]
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Using the identity (see Gr Problem 1.62),
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</p>
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<div class="eqlabel" id="orgeec59ec">
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<div class="eqlabel" id="org62a7346">
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<p>
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<a id="intcr"></a><a href="./ems_ms_vp_me.html#intcr"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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<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"/>
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<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"/>
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</svg></a>
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</p>
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<div class="alteqlabels" id="org72f674e">
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<div class="alteqlabels" id="orga73669a">
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<ul class="org-ul">
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<li>Gr (1.108)</li>
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</ul>
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@@ -1709,7 +1709,7 @@ Using the identity (see Gr Problem 1.62),
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with \({\bf c} = \hat {\bf r}\),
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</p>
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<div class="info div" id="orgf235098">
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<div class="info div" id="orgd9261d2">
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<p>
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<b>Parenthesis: derivation of</b> <a href="./ems_ms_vp_me.html#intcr">intcr</a>
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</p>
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@@ -1752,18 +1752,18 @@ Back to our problem:
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\]
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and defining the
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</p>
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<div class="core div" id="org98ff1a4">
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<div class="core div" id="org252bb34">
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<p>
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<b>magnetic dipole moment</b>
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</p>
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<div class="eqlabel" id="org5f9bf60">
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<div class="eqlabel" id="org52e910f">
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<p>
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<a id="magdim"></a><a href="./ems_ms_vp_me.html#magdim"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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<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"/>
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<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"/>
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</svg></a>
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</p>
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<div class="alteqlabels" id="org61dc942">
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<div class="alteqlabels" id="org521ff8a">
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<ul class="org-ul">
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<li>Gr (5.86)</li>
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</ul>
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@@ -1782,18 +1782,18 @@ and defining the
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<p>
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we obtain the convenient expression for the
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</p>
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<div class="main div" id="org335e87a">
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<div class="main div" id="org919de64">
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<p>
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<b>dipole term of the vector potential</b>
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</p>
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<div class="eqlabel" id="org211bc41">
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<div class="eqlabel" id="orga93a621">
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<p>
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<a id="A_di"></a><a href="./ems_ms_vp_me.html#A_di"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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<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"/>
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<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"/>
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</svg></a>
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</p>
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<div class="alteqlabels" id="org12c378d">
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<div class="alteqlabels" id="orgc5bc8d7">
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<ul class="org-ul">
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<li>Gr (5.85)</li>
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</ul>
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@@ -1810,7 +1810,7 @@ we obtain the convenient expression for the
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</div>
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<div class="example div" id="org3da15bb">
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<div class="example div" id="org6a86d5a">
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<p>
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<b>Example: bookend shape</b>
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</p>
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@@ -1864,7 +1864,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
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</div>
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<div id="postamble" class="status">
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<p class="author">Author: Jean-Sébastien Caux</p>
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<p class="date">Created: 2022-03-07 Mon 20:38</p>
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<p class="date">Created: 2022-03-15 Tue 08:10</p>
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<p class="validation"></p>
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</div>
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