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Update 2022-02-14 06:33

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Jean-Sébastien
2022-02-14 06:33:37 +01:00
parent f8446c1405
commit 4cfe8cef59
204 changed files with 1839 additions and 941 deletions
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build/ems_ca_mi_isc.html
+49 -7
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-10 Thu 08:32 -->
<!-- 2022-02-13 Sun 21:20 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1598,17 +1598,57 @@ Table of contents
</svg></a><span class="headline-id">ems.ca.mi.isc</span></h5>
<div class="outline-text-5" id="text-ems_ca_mi_isc">
<p>
Use (\ref{Gr(2.49)}), where normal direction is now \(\hat{\bf z}\).
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="org06022a8">
<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="orgc9370ec">
<ul class="org-ul">
<li>Gr (3.10)</li>
</ul>
</div>
</div>
<p>
\[
\sigma(x, y) = \frac{-qd}{2\pi (x^2 + y^2 + d^2)^{3/2}}
\label{Gr(3.10)}
\tag{scd_dip_z}\label{scd_dip_z}
\]
Total induced charge: \(Q = \int \sigma da\).
Use planar coordinates: \(\sigma(r) = \frac{-qd}{2\pi (r^2 + d^2)^{3/2}}\), so
</p>
<p>
The total induced charge can be obtained by simple integration as
\(Q = \int \sigma da\).
Using planar coordinates,
\(\sigma(r) = \frac{-qd}{2\pi (r^2 + d^2)^{3/2}}\), so
</p>
<div class="eqlabel" id="orgfe9d97c">
<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="org95f2a87">
<ul class="org-ul">
<li>Gr (3.11)</li>
</ul>
</div>
</div>
<p>
\[
Q = \int_0^{2\pi} d\phi \int_0^{\infty} dr r \frac{-qd}{2\pi (r^2 + d^2)^{3/2}}
= \frac{qd}{\sqrt{r^2 + d^2}}|_0^{\infty} = -q
\label{Gr(3.11)}
\tag{sc_dip_z}\label{sc_dip_z}
\]
</p>
</div>
@@ -1616,6 +1656,8 @@ Q = \int_0^{2\pi} d\phi \int_0^{\infty} dr r \frac{-qd}{2\pi (r^2 + d^2)^{3/2}}
<br><ul class="navigation-links"><li>Prev:&nbsp;<a href="ems_ca_mi.html">The Method of Images&emsp;<small>[ems.ca.mi]</small></a></li><li>Next:&nbsp;<a href="ems_ca_mi_fe.html">Force and Energy&emsp;<small>[ems.ca.mi.fe]</small></a></li><li>Up:&nbsp;<a href="ems_ca_mi.html">The Method of Images&emsp;<small>[ems.ca.mi]</small></a></li></ul>
<br>
<hr>
<div class="license">
<a rel="license noopener" href="https://creativecommons.org/licenses/by/4.0/"
@@ -1629,7 +1671,7 @@ 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: 2022-02-10 Thu 08:32</p>
<p class="date">Created: 2022-02-13 Sun 21:20</p>
<p class="validation"></p>
</div>