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Update 2022-02-09 22:41

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Jean-Sébastien
2022-02-09 22:41:42 +01:00
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commit f3c2446d19
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-09 Wed 07:31 -->
<!-- 2022-02-09 Wed 22:40 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -408,17 +408,13 @@ Table of contents
<li>
<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
</li>
<li>
<a href="./ems_es_ep_c.html#ems_es_ep_c">Comments on the Electrostatic Potential</a><span class="headline-id">ems.es.ep.c</span>
</li>
<li>
<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
</li>
<li>
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">The Poisson Equation and the Laplace Equation</a><span class="headline-id">ems.es.ep.PL</span>
<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
</li>
<li>
@@ -430,29 +426,8 @@ Table of contents
</details>
</li>
<li>
<details>
<summary>
<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
</summary>
<ul>
<li>
<a href="./ems_es_e_pcd.html#ems_es_e_pcd">The Energy of a Point Charge Distribution</a><span class="headline-id">ems.es.e.pcd</span>
</li>
<li>
<a href="./ems_es_e_ccd.html#ems_es_e_ccd">The Energy of a Continuous Charge Distribution</a><span class="headline-id">ems.es.e.ccd</span>
</li>
<li>
<a href="./ems_es_e_c.html#ems_es_e_c">Comments on Electrostatic Energy</a><span class="headline-id">ems.es.e.c</span>
</li>
</ul>
</details>
</li>
<li>
@@ -1646,7 +1621,7 @@ We thus obtain
\]
Recognizing the proper velocity, we thus get that charge density and current density can together form the
</p>
<div class="core div" id="orgb04fcdf">
<div class="core div" id="org89215da">
<p>
{\bf Current density 4-vector}
\[
@@ -1659,7 +1634,7 @@ Recognizing the proper velocity, we thus get that charge density and current den
<p>
The continuity equation (\ref{eq:continuity}) takes the simple form
</p>
<div class="core div" id="orgd67b414">
<div class="core div" id="org44f5152">
<p>
{\bf Continuity equation}
\[
@@ -1671,7 +1646,7 @@ The continuity equation (\ref{eq:continuity}) takes the simple form
<p>
while similarly the notation simplifies for
</p>
<div class="main div" id="org39ea8b8">
<div class="main div" id="orgf889ae0">
<p>
{\bf Maxwell's equations}
\[
@@ -1686,7 +1661,7 @@ while similarly the notation simplifies for
<p>
In terms of \(F^{\mu \nu}\) and the proper velocity \(\eta^\mu\), we also have the
</p>
<div class="main div" id="org5c9b443">
<div class="main div" id="orgb0de89f">
<p>
{\bf Minkowski force on a charge \(q\)}
\[
@@ -1736,7 +1711,7 @@ the Lorenz gauge (\ref{eq:InhomogeneousMaxwellLorenzGauge}) here expressed as
\]
Defining the
</p>
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<div class="main div" id="org0b75933">
<p>
{\bf d'Alembertian operator}
\[
@@ -1749,7 +1724,7 @@ Defining the
we obtain the final form of
</p>
<div class="core div" id="org47df391">
<div class="core div" id="org36f1813">
<p>
{\bf Maxwell's equations (Lorenz gauge, 4-vector notation)}
\[
@@ -1779,7 +1754,7 @@ 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 07:31</p>
<p class="date">Created: 2022-02-09 Wed 22:40</p>
<p class="validation"></p>
</div>