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Update 2022-02-10 08:34

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Jean-Sébastien
2022-02-10 08:34:34 +01:00
parent f3c2446d19
commit f8446c1405
204 changed files with 803 additions and 790 deletions
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build/ems_es_ep_bc.html
+9 -8
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-09 Wed 22:40 -->
<!-- 2022-02-10 Thu 08:32 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1634,14 +1634,14 @@ applied to a small loop straddling the surface:
<p>
We can unify both boundary conditions into a single equation:
</p>
<div class="eqlabel" id="org17fbc45">
<div class="eqlabel" id="org2b69233">
<p>
<a id="Edisc"></a><a href="./ems_es_ep_bc.html#Edisc"><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="org7a21d0c">
<div class="alteqlabels" id="orgb48dc0f">
<ul class="org-ul">
<li>Gr (2.33)</li>
</ul>
@@ -1676,14 +1676,14 @@ The gradient however inherits the discontinuity of the electrostatic field, sinc
\]
or
</p>
<div class="eqlabel" id="orgc1e3983">
<div class="eqlabel" id="orgfe43f46">
<p>
<a id="dpdisc"></a><a href="./ems_es_ep_bc.html#dpdisc"><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="org84bec06">
<div class="alteqlabels" id="org2a29f71">
<ul class="org-ul">
<li>Gr (2.36)</li>
</ul>
@@ -1705,9 +1705,10 @@ is the <b>normal derivative</b> of the potential.
</p>
<p>
This is the kind of boundary condition that we need to fix a unique solution to Poisson's equation:
This is the kind of boundary condition that we need to fix a unique solution
to Poisson's equation <a href="./ems_es_ep_PL.html#Poi">🐟</a>:
our only problem is that <a href="./ems_es_ep_bc.html#dpdisc">dpdisc</a> gives the change of the normal derivative of \(V\), not
its value. However, if we assume (as in our first case corollary) that there are no charges living outside
its value. However, if we assume that there are no charges living outside
of our volume \({\cal V}\), we find that <a href="./ems_es_ep_bc.html#dpdisc">dpdisc</a> fully specifies the potential's normal derivative
if the surface charge is known.
</p>
@@ -1728,7 +1729,7 @@ 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 22:40</p>
<p class="date">Created: 2022-02-10 Thu 08:32</p>
<p class="validation"></p>
</div>