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Update 2022-02-08 17:21

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Jean-Sébastien
2022-02-08 17:21:33 +01:00
parent 077433c40a
commit 3454aba504
207 changed files with 1882 additions and 1097 deletions
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build/ems_es_ef_Gl.html
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-08 Tue 06:55 -->
<!-- 2022-02-08 Tue 17:21 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -272,6 +272,10 @@ Table of contents
</summary>
<ul>
<li>
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
</li>
<li>
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
</li>
@@ -736,7 +740,7 @@ Table of contents
</li>
<li>
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
</li>
<li>
@@ -1663,14 +1667,14 @@ sphere of radius \(r\) around the charge,
<p>
so by superposition, we obtain
</p>
<div class="eqlabel" id="org567fae3">
<div class="eqlabel" id="org804902c">
<p>
<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">
<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="orgd08d994">
<div class="alteqlabels" id="org04a2212">
<ul class="org-ul">
<li>Gr (2.13)</li>
</ul>
@@ -1678,7 +1682,7 @@ so by superposition, we obtain
</div>
</div>
<div class="core div" id="org107f70e">
<div class="core div" id="orgbbc9bc1">
<p>
<b>Gauss' law (in integral form)</b>
</p>
@@ -1710,14 +1714,14 @@ By applying the divergence theorem,
and using \(Q_{\mbox{enc}} = \int_{\cal V} \rho d\tau\), and using the fact the the choice of volume
is arbitrary, we get
</p>
<div class="eqlabel" id="orgcbc0cba">
<div class="eqlabel" id="org06ff080">
<p>
<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">
<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="org4033327">
<div class="alteqlabels" id="orgcf50b9d">
<ul class="org-ul">
<li>Gr (2.14)</li>
</ul>
@@ -1725,7 +1729,7 @@ is arbitrary, we get
</div>
</div>
<div class="core div" id="orgb66b8f3">
<div class="core div" id="orgf131b44">
<p>
<b>Gauss' law in differential form</b>
</p>
@@ -1755,7 +1759,7 @@ Using <a href="./c_m_dd_3d.html#divdel">divdel</a>,
<p>
\[
{\boldsymbol \nabla} \cdot {\bf E} = \frac{1}{4\pi \varepsilon_0} \int d\tau' \rho({\bf r}') 4\pi \delta ({\bf r} - {\bf r}') = \frac{\rho({\bf r})}{\varepsilon_0}
{\boldsymbol \nabla} \cdot {\bf E} = \frac{1}{4\pi \varepsilon_0} \int d\tau' \rho({\bf r}') ~4\pi \delta ({\bf r} - {\bf r}') = \frac{\rho({\bf r})}{\varepsilon_0}
\label{Gr(2.16)}
\]
</p>
@@ -1784,7 +1788,7 @@ cylindrical or plane symmetry.
Gaussian surfaces: respectively, concentric sphere, coaxial cylinder, pillbox.
</p>
<div class="example div" id="org34f5bc3">
<div class="example div" id="org57bb4a4">
<p>
<b>Example 2.2</b>: Field outside a uniformly charged sphere of radius \(R\) and total charge \(q\).
</p>
@@ -1815,7 +1819,7 @@ Same as point charge at origin!
</div>
<div class="example div" id="org588cdee">
<div class="example div" id="orgc83260f">
<p>
<b>Example 2.3</b>: infinitely long cylinder carrying charge density \(\rho = k s\) for some constant \(k\). Find \({\bf E}\) within the cylinder.
</p>
@@ -1854,7 +1858,7 @@ Therefore,
</div>
<div class="example div" id="orgd319ae5">
<div class="example div" id="orgabb478b">
<p>
<b>Example 2.4</b>: infinite plane (defined by \(z = 0\)) with uniform surface charge density \(\sigma\). Find \({\bf E}\).
</p>
@@ -1880,7 +1884,7 @@ where \(\hat{\bf n}\) is a unit vector extending away from the plane. Independe
</div>
<div class="example div" id="org65c3abd">
<div class="example div" id="orgd7a4c2f">
<p>
<b>Example 2.5</b>: two infinite planes (put them vertical) carrying equal but opposite uniform surface charge densities \(\pm \sigma\).
</p>
@@ -1897,7 +1901,7 @@ where \(\hat{\bf n}\) is a unit vector extending away from the plane. Independe
<hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div>