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Update 2022-02-15 10:32

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Jean-Sébastien
2022-02-15 10:32:42 +01:00
parent 09a8ba5fb6
commit 6874e66024
204 changed files with 1019 additions and 937 deletions
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build/ems_ca_mi_isc.html
+13 -7
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-14 Mon 20:35 -->
<!-- 2022-02-15 Tue 10:14 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1601,14 +1601,14 @@ Table of contents
Use <a href="./ems_es_c_sc.html#scd_cond">scd_cond</a>, with the normal direction now
being \(\hat{\bf z}\):
</p>
<div class="eqlabel" id="orgb4f8d95">
<div class="eqlabel" id="orgbe59100">
<p>
<a id="scd_dip_z"></a><a href="./ems_ca_mi_isc.html#scd_dip_z"><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="org8e494f1">
<div class="alteqlabels" id="org69dd517">
<ul class="org-ul">
<li>Gr (3.10)</li>
</ul>
@@ -1625,18 +1625,18 @@ being \(\hat{\bf z}\):
<p>
The total induced charge can be obtained by simple integration as
\(Q = \int \sigma da\).
\(Q = \int da ~\sigma\).
Using planar coordinates,
\(\sigma(r) = \frac{-qd}{4\pi (r^2 + (d/2)^2)^{3/2}}\), so
</p>
<div class="eqlabel" id="orgb80bd55">
<div class="eqlabel" id="orgecbeb84">
<p>
<a id="sc_dip_z"></a><a href="./ems_ca_mi_isc.html#sc_dip_z"><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="orgc27b3da">
<div class="alteqlabels" id="org6672793">
<ul class="org-ul">
<li>Gr (3.11)</li>
</ul>
@@ -1651,6 +1651,12 @@ Q = \int_0^{2\pi} d\varphi \int_0^{\infty} dr r \frac{-qd}{4\pi (r^2 + (d/2)^2)^
\tag{sc_dip_z}\label{sc_dip_z}
\]
</p>
<p>
This is precisely what we expected, namely that the total charge induced on
the surface of the conductor at \(z=0\) precisely compensates the point charge \(q\)
above it.
</p>
</div>
</div>
@@ -1671,7 +1677,7 @@ 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: 2022-02-14 Mon 20:35</p>
<p class="date">Created: 2022-02-15 Tue 10:14</p>
<p class="validation"></p>
</div>