Update 2022-03-07 20:40
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-24
@@ -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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<!-- 2022-03-02 Wed 15:45 -->
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<!-- 2022-03-07 Mon 20:38 -->
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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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@@ -1098,14 +1098,6 @@ Table of contents
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<li>
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<a href="./emdm_emwm_refl_oi.html#emdm_emwm_refl_oi">Oblique Incidence</a><span class="headline-id">emdm.emwm.refl.oi</span>
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</li>
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<li>
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<a href="./emdm_emwm_refl_Fe.html#emdm_emwm_refl_Fe">Fresnel's Equations</a><span class="headline-id">emdm.emwm.refl.Fe</span>
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</li>
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<li>
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<a href="./emdm_emwm_refl_Ba.html#emdm_emwm_refl_Ba">Brewster's Angle</a><span class="headline-id">emdm.emwm.refl.Ba</span>
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</li>
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</ul>
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@@ -1637,14 +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="org27484f4">
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<div class="eqlabel" id="orgb783834">
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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="org9ff401f">
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<div class="alteqlabels" id="org7cfeed1">
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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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@@ -1671,14 +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="org9199b17">
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<div class="eqlabel" id="org3177483">
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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="org78a790f">
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<div class="alteqlabels" id="orge720d21">
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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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@@ -1693,14 +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="org2901c54">
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<div class="eqlabel" id="orgeec59ec">
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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="orgfc7ceb9">
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<div class="alteqlabels" id="org72f674e">
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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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@@ -1717,7 +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="orgebd6f00">
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<div class="info div" id="orgf235098">
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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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@@ -1760,18 +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="org5ecb13e">
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<div class="core div" id="org98ff1a4">
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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="org8cc3cc2">
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<div class="eqlabel" id="org5f9bf60">
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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="orga962094">
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<div class="alteqlabels" id="org61dc942">
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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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@@ -1790,18 +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="org1da60f6">
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<div class="main div" id="org335e87a">
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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="orgc2cee5c">
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<div class="eqlabel" id="org211bc41">
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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="org4142575">
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<div class="alteqlabels" id="org12c378d">
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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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@@ -1818,7 +1810,7 @@ we obtain the convenient expression for the
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</div>
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<div class="example div" id="org626c6c5">
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<div class="example div" id="org3da15bb">
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<p>
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<b>Example: bookend shape</b>
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</p>
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@@ -1872,7 +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: 2022-03-02 Wed 15:45</p>
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<p class="date">Created: 2022-03-07 Mon 20:38</p>
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<p class="validation"></p>
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</div>
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