Update 2022-03-15 10:07
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Jean-Sébastien
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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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@@ -1658,14 +1658,14 @@ sphere of radius \(r\) around the charge,
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<p>
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so by superposition, we obtain
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</p>
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<div class="eqlabel" id="orgbd405a4">
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<div class="eqlabel" id="orgdb1b683">
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<p>
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<a id="Gl_i"></a><a href="./ems_es_ef_Gl.html#Gl_i"><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="org003a349">
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<div class="alteqlabels" id="orgce2000b">
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<ul class="org-ul">
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<li>Gr (2.13)</li>
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</ul>
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@@ -1673,7 +1673,7 @@ so by superposition, we obtain
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</div>
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</div>
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<div class="core div" id="org1a75708">
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<div class="core div" id="org2a79f58">
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<p>
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<b>Gauss' law (in integral form)</b>
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</p>
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@@ -1705,14 +1705,14 @@ By applying the divergence theorem,
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and using \(Q_{\mbox{enc}} = \int_{\cal V} \rho d\tau\), and using the fact the the choice of volume
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is arbitrary, we get
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</p>
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<div class="eqlabel" id="org0aedc78">
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<div class="eqlabel" id="org8cb0bb4">
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<p>
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<a id="Gl_d"></a><a href="./ems_es_ef_Gl.html#Gl_d"><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="org52e4892">
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<div class="alteqlabels" id="org0bf7bc4">
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<ul class="org-ul">
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<li>Gr (2.14)</li>
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</ul>
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@@ -1720,7 +1720,7 @@ is arbitrary, we get
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</div>
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</div>
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<div class="core div" id="orgd3769c9">
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<div class="core div" id="org03bfea1">
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<p>
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<b>Gauss' law in differential form</b>
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</p>
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@@ -1779,7 +1779,7 @@ cylindrical or plane symmetry.
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Gaussian surfaces: respectively, concentric sphere, coaxial cylinder, pillbox.
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</p>
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<div class="example div" id="orgf56f79b">
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<div class="example div" id="org86862f2">
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<p>
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<a id="E_uni_sph"></a><a href="./ems_es_ef_Gl.html#E_uni_sph"><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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@@ -1814,7 +1814,7 @@ Same as point charge at origin!
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</div>
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<div class="example div" id="org5f80c2b">
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<div class="example div" id="orge7c3996">
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<p>
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<b>Example 2.3</b>: infinitely long cylinder carrying charge density \(\rho = k s\) for some constant \(k\). Find \({\bf E}\) within the cylinder.
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</p>
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@@ -1853,7 +1853,7 @@ Therefore,
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</div>
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<div class="example div" id="org57e730d">
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<div class="example div" id="org2465dd4">
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<p>
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<b>Example 2.4</b>: infinite plane (defined by \(z = 0\)) with uniform surface charge density \(\sigma\). Find \({\bf E}\).
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</p>
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@@ -1879,7 +1879,7 @@ where \(\hat{\bf n}\) is a unit vector extending away from the plane. Independe
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</div>
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<div class="example div" id="org4dbf2ef">
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<div class="example div" id="org2090e4b">
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<p>
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<b>Example 2.5</b>: two infinite planes (put them vertical) carrying equal but opposite uniform surface charge densities \(\pm \sigma\).
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</p>
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@@ -1909,7 +1909,7 @@ 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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