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Update 2022-02-08 17:21

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Jean-Sébastien
2022-02-08 17:21:33 +01:00
parent 077433c40a
commit 3454aba504
207 changed files with 1882 additions and 1097 deletions
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build/ems_es_ep_d.html
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-08 Tue 06:55 -->
<!-- 2022-02-08 Tue 17:21 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -272,6 +272,10 @@ Table of contents
</summary>
<ul>
<li>
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
</li>
<li>
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
</li>
@@ -736,7 +740,7 @@ Table of contents
</li>
<li>
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
</li>
<li>
@@ -1621,14 +1625,14 @@ Table of contents
<p>
Since this work is independent of the path chosen, we can define a function called the <b>electrostatic potential</b>
</p>
<div class="eqlabel" id="org7b9d6db">
<div class="eqlabel" id="orgf88a2fa">
<p>
<a id="es_pot"></a><a href="./ems_es_ep_d.html#es_pot"><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="org5460d6f">
<div class="alteqlabels" id="org0c763a9">
<ul class="org-ul">
<li>Gr (2.21)</li>
</ul>
@@ -1644,7 +1648,7 @@ V({\bf r}) \equiv -\int_{\cal O}^{\bf r} {\bf E} \cdot d{\bf l}
where \({\cal O}\) is some chosen reference point. The potential difference between two points is
well-defined without the need to specify the reference point,
</p>
<div class="main div" id="orgc8b6cdd">
<div class="main div" id="org769e30b">
<p>
\[
V({\bf b}) - V({\bf a}) = - \int_{\bf a}^{\bf b} {\bf E} \cdot d{\bf l}
@@ -1666,7 +1670,7 @@ V({\bf r}) = \frac{1}{4\pi \varepsilon_0} \frac{q}{r}
The electrostatic potential moreover inherits the superposition principle from the electric field,
so for a distribution of point charges \(q_i\) at positions \({\bf r}_i\), we have
</p>
<div class="core div" id="orgbee11d7">
<div class="core div" id="org9bf457d">
<p>
\[
V({\bf r}) = \frac{1}{4\pi\varepsilon_0} \sum_{i} \frac{q_i}{|{\bf r} - {\bf r}_i|}
@@ -1678,7 +1682,7 @@ so for a distribution of point charges \(q_i\) at positions \({\bf r}_i\), we ha
<p>
For a continuous charge density in a volume \({\cal V}\), we have
</p>
<div class="main div" id="org5bf43f8">
<div class="main div" id="orgd1a1103">
<p>
\[
V({\bf r}) = \frac{1}{4\pi \varepsilon_0} \int_{\cal V} d\tau' \frac{\rho({\bf r}')}{|{\bf r} - {\bf r}'|},
@@ -1690,7 +1694,7 @@ For a continuous charge density in a volume \({\cal V}\), we have
<p>
whereas for a surface or line charge distribution, respectively,
</p>
<div class="main div" id="org37f47b6">
<div class="main div" id="org5189f33">
<p>
\[
V({\bf r}) = \frac{1}{4\pi \varepsilon_0} \int_{\cal S} da' \frac{\sigma({\bf r}')}{|{\bf r} - {\bf r}'|},
@@ -1708,7 +1712,7 @@ whereas for a surface or line charge distribution, respectively,
<hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div>