jscaux/pqed_html
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Update 2022-02-09 22:41

Browse Source
This commit is contained in:
Jean-Sébastien
2022-02-09 22:41:42 +01:00
parent 3c40f5bfe8
commit f3c2446d19
208 changed files with 1583 additions and 12916 deletions
Download Patch File Download Diff File Expand all files Collapse all files
build/ems_ms_vp.html
+10 -35
View File
@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-09 Wed 07:31 -->
<!-- 2022-02-09 Wed 22:40 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -408,17 +408,13 @@ Table of contents
<li>
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
</li>
<li>
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
</li>
<li>
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
</li>
<li>
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
</li>
<li>
@@ -430,29 +426,8 @@ Table of contents
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary>
<ul>
<li>
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
</li>
<li>
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
</li>
<li>
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
</li>
</ul>
</details>
</li>
<li>
@@ -1626,7 +1601,7 @@ 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="orgb824ded">
<div class="core div" id="org9b91637">
<p>
\[
{\bf B} = {\boldsymbol \nabla} \times {\bf A}
@@ -1648,7 +1623,7 @@ 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="org40f92f3">
<div class="main div" id="org96acd55">
<p>
{\bf Example gauge choice:}
\[
@@ -1679,7 +1654,7 @@ zero at infinity,
<p>
Under this gauge choice, Ampère's law becomes
</p>
<div class="main div" id="orgba366e5">
<div class="main div" id="org2bbba61">
<p>
\[
{\boldsymbol \nabla}^2 {\bf A} = -\mu_0 {\bf J}
@@ -1692,7 +1667,7 @@ 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="org576a84c">
<div class="core div" id="org70b82cc">
<p>
\[
{\bf A} ({\bf r}) = \frac{\mu_0}{4\pi} \int d\tau' \frac{J({\bf r}')}{|{\bf r} - {\bf r}'|}
@@ -1704,7 +1679,7 @@ 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="orgd64eded">
<div class="main div" id="org4a28168">
<p>
\[
{\bf A}({\bf r}) = \frac{\mu_0}{4\pi} \int dl' \frac{{\bf I ({\bf r}')}}{|{\bf r} - {\bf r}'|},
@@ -1718,7 +1693,7 @@ For line and surface currents, <i>(beware Griffiths' <b>horrendous</b> notation)
<div class="example div" id="orgfd862d3">
<div class="example div" id="orgc3d19f2">
<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 \({\bf r}\).
@@ -1732,7 +1707,7 @@ the sphere is uniform !
</div>
<div class="example div" id="org78723ad">
<div class="example div" id="org879c4a2">
<p>
\paragraph{Example 5.12:} find the vector potential of an infinite solenoid with \(n\) turns
pet unit length, radius \(R\) and current \(I\).
@@ -1803,7 +1778,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
</div>
<div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="date">Created: 2022-02-09 Wed 22:40</p>
<p class="validation"></p>
</div>