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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_ms_vp.html
+14 -10
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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>
@@ -1622,7 +1626,7 @@ Table of contents
<p>
Since \({\boldsymbol \nabla} \cdot {\bf B} = 0\) in magnetostatics, following Helmholtz's theorem we can write
</p>
<div class="core div" id="org8c7f863">
<div class="core div" id="org8d029d6">
<p>
\[
{\bf B} = {\boldsymbol \nabla} \times {\bf A}
@@ -1644,7 +1648,7 @@ add any curlless function (so gradient of a scalar field) to the vector potentia
without changing the magnetic field. This is called a {\bf gauge choice} in electrodynamics.
For example, we can {\bf always} eliminate the divergence of \({\bf A}\),
</p>
<div class="main div" id="orga7d7df6">
<div class="main div" id="org2f5ec71">
<p>
{\bf Example gauge choice:}
\[
@@ -1675,7 +1679,7 @@ zero at infinity,
<p>
Under this gauge choice, Ampère's law becomes
</p>
<div class="main div" id="org59fd103">
<div class="main div" id="orga1e23e0">
<p>
\[
{\boldsymbol \nabla}^2 {\bf A} = -\mu_0 {\bf J}
@@ -1688,7 +1692,7 @@ Under this gauge choice, Ampère's law becomes
Note: this is a Poisson equation for each component.
For currents falling off sufficiently rapidly at infinity,
</p>
<div class="core div" id="orgb880c5e">
<div class="core div" id="org4174f16">
<p>
\[
{\bf A} ({\bf r}) = \frac{\mu_0}{4\pi} \int d\tau' \frac{J({\bf r}')}{|{\bf r} - {\bf r}'|}
@@ -1700,7 +1704,7 @@ For currents falling off sufficiently rapidly at infinity,
<p>
For line and surface currents, <i>(beware Griffiths' <b>horrendous</b> notation)</i>
</p>
<div class="main div" id="org3d2b3ad">
<div class="main div" id="org712334e">
<p>
\[
{\bf A}({\bf r}) = \frac{\mu_0}{4\pi} \int dl' \frac{{\bf I ({\bf r}')}}{|{\bf r} - {\bf r}'|},
@@ -1714,7 +1718,7 @@ For line and surface currents, <i>(beware Griffiths' <b>horrendous</b> notation)
<div class="example div" id="org05a3ec0">
<div class="example div" id="org0baf51b">
<p>
\paragraph{Example 5.11:} a spherical shell of radius \(R\), carrying a uniform surface charge
\(\sigma\), is set spinning at angular velocity \(\omega\). Find the vector potential at \({\bf r}\).
@@ -1728,7 +1732,7 @@ the sphere is uniform !
</div>
<div class="example div" id="org238fce0">
<div class="example div" id="org1f6ff4e">
<p>
\paragraph{Example 5.12:} find the vector potential of an infinite solenoid with \(n\) turns
pet unit length, radius \(R\) and current \(I\).
@@ -1788,7 +1792,7 @@ For an 'amperian' loop outside, the flux is always \(\mu_0 n I (\pi R^2)\), so
<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>