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

Update 2022-02-14 20:42

Browse Source
This commit is contained in:
Jean-Sébastien
2022-02-14 20:42:37 +01:00
parent 4cfe8cef59
commit 09a8ba5fb6
204 changed files with 1968 additions and 1206 deletions
Download Patch File Download Diff File Expand all files Collapse all files
build/ems_ca_mi.html
+16 -9
View File
@@ -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>
@@ -1598,6 +1598,11 @@ Table of contents
</svg></a><span class="headline-id">ems.ca.mi</span></h4>
<div class="outline-text-4" id="text-ems_ca_mi">
<ul class="org-ul altsecnrs">
<li>Gr 3.2</li>
</ul>
<p>
The fact that conductors are equipotentials means that we can fomally solve
loads of electrostatic problems involving conductors of various shapes, by
@@ -1606,22 +1611,24 @@ looking at combinations of point charges.
<p>
Let's consider the simplest electrostatic problem above a single point charge:
a system of two point charges. For definiteness, we put a charge \(q\) at coordinate
\(d ~\hat{z}\), and a charge \(-q\) at \(-d ~\hat{z}\).
a system of two point charges \(\pm q\) separated by distance \(d\).
For definiteness, we put a charge \(q\) at coordinate
\(\frac{d}{2} ~\hat{z}\), and a charge \(-q\) at \(-\frac{d}{2} ~\hat{z}\).
</p>
<p>
By superposition, we have that
</p>
<div class="eqlabel" id="org50ef5fe">
<div class="eqlabel" id="org2ce446c">
<p>
<a id="p_dip_z"></a><a href="./ems_ca_mi.html#p_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="orga1a93a0">
<div class="alteqlabels" id="orgb1af7bf">
<ul class="org-ul">
<li>FLS II (6.8)</li>
<li>Gr (3.9)</li>
</ul>
@@ -1629,16 +1636,16 @@ By superposition, we have that
</div>
\begin{align}
\phi(x,y,z) = \frac{1}{4\pi \varepsilon_0} \left[ \frac{q}{[x^2 + y^2 + (z-d)^2]^{1/2}} - \frac{q}{[x^2 + y^2 + (z+d)^2]^{1/2}} \right]
\phi(x,y,z) = \frac{1}{4\pi \varepsilon_0} \left[ \frac{q}{[x^2 + y^2 + (z-d/2)^2]^{1/2}} - \frac{q}{[x^2 + y^2 + (z+d/2)^2]^{1/2}} \right]
\tag{p_dip_z}\label{p_dip_z}
\end{align}
<p>
Now it's obvious that \(\phi = 0\) when \(z = 0\). Therefore, in the region \(z &gt; 0\), this problem
is completely equivalent to a second problem: a point charge \(q\) at \(d ~\hat{z}\),
is completely equivalent to a second problem: a point charge \(q\) at \(\frac{d}{2} ~\hat{z}\),
and a grounded conductor on the whole plane \(z = 0\).
Yet another equivalent
problem in the region \(z &lt; 0\) is that of a charge \(-q\) at \(-d ~\hat{z}\) with a grounded
problem in the region \(z &lt; 0\) is that of a charge \(-q\) at \(-\frac{d}{2} ~\hat{z}\) with a grounded
conductor on the plane \(z = 0\).
</p>
@@ -1677,7 +1684,7 @@ 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>