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Update 2022-02-14 20:42

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Jean-Sébastien
2022-02-14 20:42:37 +01:00
parent 4cfe8cef59
commit 09a8ba5fb6
204 changed files with 1968 additions and 1206 deletions
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build/ems_ca_mi_isc.html
+10 -10
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-13 Sun 21:20 -->
<!-- 2022-02-14 Mon 20:35 -->
<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="org06022a8">
<div class="eqlabel" id="orgb4f8d95">
<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">
<div class="alteqlabels" id="org8e494f1">
<ul class="org-ul">
<li>Gr (3.10)</li>
</ul>
@@ -1618,7 +1618,7 @@ being \(\hat{\bf z}\):
</div>
<p>
\[
\sigma(x, y) = \frac{-qd}{2\pi (x^2 + y^2 + d^2)^{3/2}}
\sigma(x, y) = \frac{-qd}{4\pi (x^2 + y^2 + (d/2)^2)^{3/2}}
\tag{scd_dip_z}\label{scd_dip_z}
\]
</p>
@@ -1627,16 +1627,16 @@ being \(\hat{\bf z}\):
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
\(\sigma(r) = \frac{-qd}{4\pi (r^2 + (d/2)^2)^{3/2}}\), so
</p>
<div class="eqlabel" id="orgfe9d97c">
<div class="eqlabel" id="orgb80bd55">
<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">
<div class="alteqlabels" id="orgc27b3da">
<ul class="org-ul">
<li>Gr (3.11)</li>
</ul>
@@ -1646,8 +1646,8 @@ Using planar coordinates,
</div>
<p>
\[
Q = \int_0^{2\pi} d\phi \int_0^{\infty} dr r \frac{-qd}{2\pi (r^2 + d^2)^{3/2}}
= \frac{qd}{\sqrt{r^2 + d^2}}|_0^{\infty} = -q
Q = \int_0^{2\pi} d\varphi \int_0^{\infty} dr r \frac{-qd}{4\pi (r^2 + (d/2)^2)^{3/2}}
= \frac{qd/2}{\sqrt{r^2 + (d/2)^2}}|_0^{\infty} = -q
\tag{sc_dip_z}\label{sc_dip_z}
\]
</p>
@@ -1671,7 +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: 2022-02-13 Sun 21:20</p>
<p class="date">Created: 2022-02-14 Mon 20:35</p>
<p class="validation"></p>
</div>