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Update 2022-02-09 22:41

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Jean-Sébastien
2022-02-09 22:41:42 +01:00
parent 3c40f5bfe8
commit f3c2446d19
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build/ems_ca_sv_sph.html
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@@ -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>
@@ -1625,7 +1600,7 @@ Table of contents
<p>
In spherical coordinates, the Laplace equation takes the following form:
</p>
<div class="main div" id="org22e7f15">
<div class="main div" id="org8d28442">
<p>
</p>
@@ -1786,7 +1761,7 @@ Ex.: second solution for \(l = 0\) is
<p>
General solution to problem with azimuthal symmetry:
</p>
<div class="main div" id="org1447aa6">
<div class="main div" id="org56120f8">
<p>
\[
V(r,\theta) = \sum_{l=0}^{\infty} \left( A_l r^l + \frac{B_l}{r^{l+1}} \right) P_l (\cos \theta)
@@ -1798,7 +1773,7 @@ General solution to problem with azimuthal symmetry:
<div class="example div" id="orgfbd5cb1">
<div class="example div" id="orgc839e25">
<p>
<b>Example: separation of variables (spherical coordinates)</b>
</p>
@@ -1890,7 +1865,7 @@ V(r, \theta) = \frac{k}{2} (1 - \frac{r}{R} \cos \theta).
</p>
<div class="example div" id="orgc4263f1">
<div class="example div" id="orgbd87df3">
<p>
<b>Example: surface charge density on sphere</b>
</p>
@@ -1935,7 +1910,7 @@ Since Legendre polynomials are orthogonal,
B_l^&gt; = A_l^&lt; R^{2l + 1}.
\label{Gr(3.81)}
\]
Surface charge induces discontinuity in derivative of \(V\) from (\ref{Gr(2.36)}):
Surface charge induces discontinuity in derivative of \(V\) from <a href="./ems_es_ep_bc.html#dpdisc">dpdisc</a>:
</p>
<p>
@@ -2019,7 +1994,7 @@ 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>