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Jean-Sébastien
2022-02-21 10:35:02 +01:00
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<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-17 Thu 08:42 -->
<!-- 2022-02-21 Mon 10:33 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -602,11 +602,11 @@ Table of contents
</summary>
<ul>
<li>
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
</li>
<li>
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
</li>
@@ -614,21 +614,12 @@ Table of contents
</details>
</li>
<li>
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
<details>
<summary>
</li>
<li>
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
</summary>
<ul>
<li>
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
</li>
</ul>
</details>
</li>
<li>
@@ -640,11 +631,15 @@ Table of contents
</summary>
<ul>
<li>
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
</li>
<li>
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
</li>
<li>
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
</li>
@@ -661,6 +656,10 @@ Table of contents
</summary>
<ul>
<li>
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
</li>
<li>
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
</li>
@@ -698,10 +697,6 @@ Table of contents
</summary>
<ul>
<li>
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
</li>
<li>
<details>
<summary>
@@ -1435,7 +1430,7 @@ Table of contents
</li>
<li>
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
</li>
<li>
@@ -1621,7 +1616,7 @@ 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="org3a57dc2">
<div class="core div" id="org9b4ea6e">
<p>
{\bf Current density 4-vector}
\[
@@ -1634,7 +1629,7 @@ 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="org6faa174">
<div class="core div" id="org9936fb7">
<p>
{\bf Continuity equation}
\[
@@ -1646,7 +1641,7 @@ The continuity equation (\ref{eq:continuity}) takes the simple form
<p>
while similarly the notation simplifies for
</p>
<div class="main div" id="org73344ed">
<div class="main div" id="org7cd0769">
<p>
{\bf Maxwell's equations}
\[
@@ -1661,7 +1656,7 @@ 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="org5774b49">
<div class="main div" id="org0bf6c7c">
<p>
{\bf Minkowski force on a charge \(q\)}
\[
@@ -1711,7 +1706,7 @@ the Lorenz gauge (\ref{eq:InhomogeneousMaxwellLorenzGauge}) here expressed as
\]
Defining the
</p>
<div class="main div" id="org3df58ff">
<div class="main div" id="orgcf001aa">
<p>
{\bf d'Alembertian operator}
\[
@@ -1724,7 +1719,7 @@ Defining the
we obtain the final form of
</p>
<div class="core div" id="org4bf95d0">
<div class="core div" id="orgb586138">
<p>
{\bf Maxwell's equations (Lorenz gauge, 4-vector notation)}
\[
@@ -1756,7 +1751,7 @@ 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: 2022-02-17 Thu 08:42</p>
<p class="date">Created: 2022-02-21 Mon 10:33</p>
<p class="validation"></p>
</div>