Update 2022-03-24 08:43
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Jean-Sébastien
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<meta name="viewport" content="width=device-width, initial-scale=1">
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<title>Pre-Quantum Electrodynamics</title>
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<title>Pre-Quantum Electrodynamics</title>
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@ -1293,7 +1293,7 @@ Table of contents
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</summary>
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</summary>
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<ul>
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<ul>
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<li>
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<li>
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<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
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<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
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</li>
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@ -1637,7 +1637,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
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</div>
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</div>
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<div id="postamble" class="status">
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<div id="postamble" class="status">
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<p class="author">Author: Jean-Sébastien Caux</p>
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<p class="author">Author: Jean-Sébastien Caux</p>
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<p class="date">Created: 2022-03-22 Tue 10:52</p>
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<p class="date">Created: 2022-03-24 Thu 08:42</p>
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<p class="validation"></p>
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<!DOCTYPE html>
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<html lang="en">
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<head>
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<!-- 2022-03-24 Thu 08:42 -->
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<meta charset="utf-8">
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<meta name="viewport" content="width=device-width, initial-scale=1">
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<meta name="viewport" content="width=device-width, initial-scale=1">
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<title>Pre-Quantum Electrodynamics</title>
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<title>Pre-Quantum Electrodynamics</title>
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@ -1293,7 +1293,7 @@ Table of contents
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</summary>
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</summary>
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<ul>
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<ul>
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<li>
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<li>
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<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
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<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
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</li>
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</li>
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@ -1720,7 +1720,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
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</div>
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</div>
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<div id="postamble" class="status">
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<div id="postamble" class="status">
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<p class="author">Author: Jean-Sébastien Caux</p>
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<p class="author">Author: Jean-Sébastien Caux</p>
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<p class="date">Created: 2022-03-22 Tue 10:52</p>
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<p class="date">Created: 2022-03-24 Thu 08:42</p>
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<p class="validation"></p>
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<p class="validation"></p>
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</div>
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</div>
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<!DOCTYPE html>
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<!DOCTYPE html>
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<html lang="en">
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<html lang="en">
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<head>
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<head>
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<!-- 2022-03-22 Tue 10:52 -->
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<!-- 2022-03-24 Thu 08:42 -->
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<meta charset="utf-8">
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<meta charset="utf-8">
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<meta name="viewport" content="width=device-width, initial-scale=1">
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<meta name="viewport" content="width=device-width, initial-scale=1">
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<title>Pre-Quantum Electrodynamics</title>
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<title>Pre-Quantum Electrodynamics</title>
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@ -1293,7 +1293,7 @@ Table of contents
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</summary>
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</summary>
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<ul>
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<ul>
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<li>
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<li>
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<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
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<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
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</li>
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</li>
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@ -1637,7 +1637,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
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</div>
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</div>
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<div id="postamble" class="status">
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<div id="postamble" class="status">
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<p class="author">Author: Jean-Sébastien Caux</p>
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<p class="author">Author: Jean-Sébastien Caux</p>
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<p class="date">Created: 2022-03-22 Tue 10:52</p>
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<p class="date">Created: 2022-03-24 Thu 08:42</p>
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<p class="validation"></p>
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<p class="validation"></p>
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</div>
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</div>
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@ -1,7 +1,7 @@
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<!DOCTYPE html>
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<!DOCTYPE html>
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<html lang="en">
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<html lang="en">
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<head>
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<head>
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<!-- 2022-03-22 Tue 10:52 -->
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<!-- 2022-03-24 Thu 08:42 -->
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<meta charset="utf-8">
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<meta charset="utf-8">
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<meta name="viewport" content="width=device-width, initial-scale=1">
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<meta name="viewport" content="width=device-width, initial-scale=1">
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<title>Pre-Quantum Electrodynamics</title>
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<title>Pre-Quantum Electrodynamics</title>
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@ -1293,7 +1293,7 @@ Table of contents
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</summary>
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</summary>
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<ul>
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<ul>
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<li>
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<li>
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<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
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<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
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</li>
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</li>
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@ -1643,7 +1643,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
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</div>
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</div>
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<div id="postamble" class="status">
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<div id="postamble" class="status">
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<p class="author">Author: Jean-Sébastien Caux</p>
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<p class="author">Author: Jean-Sébastien Caux</p>
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<p class="date">Created: 2022-03-22 Tue 10:52</p>
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<p class="date">Created: 2022-03-24 Thu 08:42</p>
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<p class="validation"></p>
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<p class="validation"></p>
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</div>
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</div>
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<!DOCTYPE html>
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<html lang="en">
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<html lang="en">
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<head>
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<head>
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<!-- 2022-03-22 Tue 10:52 -->
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<!-- 2022-03-24 Thu 08:42 -->
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<meta charset="utf-8">
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<meta charset="utf-8">
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||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
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<meta name="viewport" content="width=device-width, initial-scale=1">
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<title>Pre-Quantum Electrodynamics</title>
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<title>Pre-Quantum Electrodynamics</title>
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@ -1293,7 +1293,7 @@ Table of contents
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</summary>
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</summary>
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<ul>
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<ul>
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<li>
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<li>
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<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
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<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
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</li>
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</li>
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@ -1639,7 +1639,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
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</div>
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</div>
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<div id="postamble" class="status">
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<div id="postamble" class="status">
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<p class="author">Author: Jean-Sébastien Caux</p>
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<p class="author">Author: Jean-Sébastien Caux</p>
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<p class="date">Created: 2022-03-22 Tue 10:52</p>
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<p class="date">Created: 2022-03-24 Thu 08:42</p>
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<p class="validation"></p>
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<p class="validation"></p>
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</div>
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</div>
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<!DOCTYPE html>
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<!DOCTYPE html>
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<html lang="en">
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<html lang="en">
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<head>
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<head>
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<!-- 2022-03-22 Tue 10:52 -->
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<!-- 2022-03-24 Thu 08:42 -->
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<meta charset="utf-8">
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<meta charset="utf-8">
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<meta name="viewport" content="width=device-width, initial-scale=1">
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<meta name="viewport" content="width=device-width, initial-scale=1">
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<title>Pre-Quantum Electrodynamics</title>
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<title>Pre-Quantum Electrodynamics</title>
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@ -1293,7 +1293,7 @@ Table of contents
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</summary>
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</summary>
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<ul>
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<ul>
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<li>
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<li>
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<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
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<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
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</li>
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</li>
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@ -1659,14 +1659,14 @@ Range of parameters: \(r \in [0, \infty[\), \(\varphi \in [0, 2\pi[\) and \(z \
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<div id="outline-container-c_m_cs_cyl_grad" class="outline-6">
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<div id="outline-container-c_m_cs_cyl_grad" class="outline-6">
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<h6 id="c_m_cs_cyl_grad"><a href="#c_m_cs_cyl_grad">Gradient</a></h6>
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<h6 id="c_m_cs_cyl_grad"><a href="#c_m_cs_cyl_grad">Gradient</a></h6>
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<div class="outline-text-6" id="text-c_m_cs_cyl_grad">
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<div class="outline-text-6" id="text-c_m_cs_cyl_grad">
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<div class="eqlabel" id="org699f087">
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<div class="eqlabel" id="org718e42d">
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<p>
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<p>
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<a id="cylgrad"></a><a href="./c_m_cs_cyl.html#cylgrad"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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<a id="cylgrad"></a><a href="./c_m_cs_cyl.html#cylgrad"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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<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"/>
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<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"/>
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<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"/>
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<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"/>
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</p>
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<div class="alteqlabels" id="org2197539">
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<div class="alteqlabels" id="org9ec66cd">
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<ul class="org-ul">
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<ul class="org-ul">
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<li>Gr4(1.79)</li>
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<li>Gr4(1.79)</li>
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</ul>
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</ul>
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<div id="outline-container-c_m_cs_cyl_div" class="outline-6">
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<div id="outline-container-c_m_cs_cyl_div" class="outline-6">
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<h6 id="c_m_cs_cyl_div"><a href="#c_m_cs_cyl_div">Divergence</a></h6>
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<h6 id="c_m_cs_cyl_div"><a href="#c_m_cs_cyl_div">Divergence</a></h6>
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<div class="outline-text-6" id="text-c_m_cs_cyl_div">
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<div class="outline-text-6" id="text-c_m_cs_cyl_div">
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<div class="eqlabel" id="org02508ba">
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<div class="eqlabel" id="orgd5ab218">
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<p>
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<p>
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<a id="cyl_div"></a><a href="./c_m_cs_cyl.html#cyl_div"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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<a id="cyl_div"></a><a href="./c_m_cs_cyl.html#cyl_div"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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<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"/>
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<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"/>
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<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"/>
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<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"/>
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</svg></a>
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</svg></a>
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</p>
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</p>
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<div class="alteqlabels" id="org7c0369d">
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<div class="alteqlabels" id="orgd93619e">
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<ul class="org-ul">
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<ul class="org-ul">
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<li>Gr4(2.21)</li>
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<li>Gr4(2.21)</li>
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</ul>
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</ul>
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@ -1715,14 +1715,14 @@ Range of parameters: \(r \in [0, \infty[\), \(\varphi \in [0, 2\pi[\) and \(z \
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<div id="outline-container-c_m_cs_cyl_curl" class="outline-6">
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<div id="outline-container-c_m_cs_cyl_curl" class="outline-6">
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<h6 id="c_m_cs_cyl_curl"><a href="#c_m_cs_cyl_curl">Curl</a></h6>
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<h6 id="c_m_cs_cyl_curl"><a href="#c_m_cs_cyl_curl">Curl</a></h6>
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<div class="outline-text-6" id="text-c_m_cs_cyl_curl">
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<div class="outline-text-6" id="text-c_m_cs_cyl_curl">
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<div class="eqlabel" id="orgc355dd0">
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<div class="eqlabel" id="orgabcc2d8">
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<p>
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<p>
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<a id="cyl_curl"></a><a href="./c_m_cs_cyl.html#cyl_curl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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<a id="cyl_curl"></a><a href="./c_m_cs_cyl.html#cyl_curl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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||||||
<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"/>
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<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"/>
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||||||
<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"/>
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<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"/>
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</svg></a>
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</svg></a>
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||||||
</p>
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</p>
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<div class="alteqlabels" id="org8037114">
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<div class="alteqlabels" id="orga07a427">
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<ul class="org-ul">
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<ul class="org-ul">
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<li>Gr4(2.21)</li>
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<li>Gr4(2.21)</li>
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</ul>
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</ul>
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@ -1771,7 +1771,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
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||||||
</div>
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</div>
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||||||
<div id="postamble" class="status">
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<div id="postamble" class="status">
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||||||
<p class="author">Author: Jean-Sébastien Caux</p>
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<p class="author">Author: Jean-Sébastien Caux</p>
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||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
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<p class="date">Created: 2022-03-24 Thu 08:42</p>
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||||||
<p class="validation"></p>
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<p class="validation"></p>
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||||||
</div>
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</div>
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<!DOCTYPE html>
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<!DOCTYPE html>
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<html lang="en">
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<html lang="en">
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||||||
<head>
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<head>
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||||||
<!-- 2022-03-22 Tue 10:52 -->
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<!-- 2022-03-24 Thu 08:42 -->
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||||||
<meta charset="utf-8">
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<meta charset="utf-8">
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||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
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<meta name="viewport" content="width=device-width, initial-scale=1">
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||||||
<title>Pre-Quantum Electrodynamics</title>
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<title>Pre-Quantum Electrodynamics</title>
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||||||
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@ -1293,7 +1293,7 @@ Table of contents
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||||||
</summary>
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</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1632,7 +1632,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1623,14 +1623,14 @@ which \(r\) is the distance from the chosen origin,
|
||||||
The usual Cartesian coordinates relate to spherical coordinates
|
The usual Cartesian coordinates relate to spherical coordinates
|
||||||
according to
|
according to
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org309b2e9">
|
<div class="eqlabel" id="org763df52">
|
||||||
<p>
|
<p>
|
||||||
<a id="sph_xyz"></a><a href="./c_m_cs_sph.html#sph_xyz"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="sph_xyz"></a><a href="./c_m_cs_sph.html#sph_xyz"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org7a6a40a">
|
<div class="alteqlabels" id="orgb59869b">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1655,14 +1655,14 @@ A generic vector can be expressed as
|
||||||
where the explicit relation between spherical and
|
where the explicit relation between spherical and
|
||||||
Cartesian unit vectors is
|
Cartesian unit vectors is
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org43b8824">
|
<div class="eqlabel" id="org923fbbc">
|
||||||
<p>
|
<p>
|
||||||
<a id="sph_uv"></a><a href="./c_m_cs_sph.html#sph_uv"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="sph_uv"></a><a href="./c_m_cs_sph.html#sph_uv"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org054cde6">
|
<div class="alteqlabels" id="org2051229">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1685,14 +1685,14 @@ and \(\hat{\boldsymbol \varphi} (\theta, \varphi)\).
|
||||||
<p>
|
<p>
|
||||||
An infinitesimal displacement \(d{\bf l}\) can be written as
|
An infinitesimal displacement \(d{\bf l}\) can be written as
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org0afd234">
|
<div class="eqlabel" id="orgb032a0d">
|
||||||
<p>
|
<p>
|
||||||
<a id="sph_dl"></a><a href="./c_m_cs_sph.html#sph_dl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="sph_dl"></a><a href="./c_m_cs_sph.html#sph_dl"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orgce4cca6">
|
<div class="alteqlabels" id="orgaeea797">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1708,14 +1708,14 @@ d{\bf l} = dr ~\hat{\boldsymbol r} + r d\theta ~\hat{\boldsymbol \theta} + r\sin
|
||||||
<p>
|
<p>
|
||||||
Infinitesimal volume element:
|
Infinitesimal volume element:
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org260d3f6">
|
<div class="eqlabel" id="orgf42297c">
|
||||||
<p>
|
<p>
|
||||||
<a id="sph_dtau"></a><a href="./c_m_cs_sph.html#sph_dtau"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="sph_dtau"></a><a href="./c_m_cs_sph.html#sph_dtau"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org5ac82f0">
|
<div class="alteqlabels" id="orgb0160b3">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1736,14 +1736,14 @@ Infinitesimal surface element: depends on situation.
|
||||||
<div id="outline-container-c_m_cs_sph_grad" class="outline-6">
|
<div id="outline-container-c_m_cs_sph_grad" class="outline-6">
|
||||||
<h6 id="c_m_cs_sph_grad"><a href="#c_m_cs_sph_grad">Gradient</a></h6>
|
<h6 id="c_m_cs_sph_grad"><a href="#c_m_cs_sph_grad">Gradient</a></h6>
|
||||||
<div class="outline-text-6" id="text-c_m_cs_sph_grad">
|
<div class="outline-text-6" id="text-c_m_cs_sph_grad">
|
||||||
<div class="eqlabel" id="org0a3cd9b">
|
<div class="eqlabel" id="orgbf5f354">
|
||||||
<p>
|
<p>
|
||||||
<a id="sph_grad"></a><a href="./c_m_cs_sph.html#sph_grad"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="sph_grad"></a><a href="./c_m_cs_sph.html#sph_grad"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orgdf69aa8">
|
<div class="alteqlabels" id="orgbda0409">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1760,14 +1760,14 @@ Infinitesimal surface element: depends on situation.
|
||||||
<div id="outline-container-c_m_cs_sph_div" class="outline-6">
|
<div id="outline-container-c_m_cs_sph_div" class="outline-6">
|
||||||
<h6 id="c_m_cs_sph_div"><a href="#c_m_cs_sph_div">Divergence</a></h6>
|
<h6 id="c_m_cs_sph_div"><a href="#c_m_cs_sph_div">Divergence</a></h6>
|
||||||
<div class="outline-text-6" id="text-c_m_cs_sph_div">
|
<div class="outline-text-6" id="text-c_m_cs_sph_div">
|
||||||
<div class="eqlabel" id="orgc4833f8">
|
<div class="eqlabel" id="orge3c6cf7">
|
||||||
<p>
|
<p>
|
||||||
<a id="sph_div"></a><a href="./c_m_cs_sph.html#sph_div"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="sph_div"></a><a href="./c_m_cs_sph.html#sph_div"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org12f3039">
|
<div class="alteqlabels" id="orged88fee">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1784,14 +1784,14 @@ Infinitesimal surface element: depends on situation.
|
||||||
<div id="outline-container-c_m_cs_sph_curl" class="outline-6">
|
<div id="outline-container-c_m_cs_sph_curl" class="outline-6">
|
||||||
<h6 id="c_m_cs_sph_curl"><a href="#c_m_cs_sph_curl">Curl</a></h6>
|
<h6 id="c_m_cs_sph_curl"><a href="#c_m_cs_sph_curl">Curl</a></h6>
|
||||||
<div class="outline-text-6" id="text-c_m_cs_sph_curl">
|
<div class="outline-text-6" id="text-c_m_cs_sph_curl">
|
||||||
<div class="eqlabel" id="org6a4b6db">
|
<div class="eqlabel" id="org34ae3e4">
|
||||||
<p>
|
<p>
|
||||||
<a id="sph_curl"></a><a href="./c_m_cs_sph.html#sph_curl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="sph_curl"></a><a href="./c_m_cs_sph.html#sph_curl"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org47ac74d">
|
<div class="alteqlabels" id="org5f176f6">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1810,14 +1810,14 @@ Infinitesimal surface element: depends on situation.
|
||||||
<div id="outline-container-c_m_cs_sph_lap" class="outline-6">
|
<div id="outline-container-c_m_cs_sph_lap" class="outline-6">
|
||||||
<h6 id="c_m_cs_sph_lap"><a href="#c_m_cs_sph_lap">Laplacian</a></h6>
|
<h6 id="c_m_cs_sph_lap"><a href="#c_m_cs_sph_lap">Laplacian</a></h6>
|
||||||
<div class="outline-text-6" id="text-c_m_cs_sph_lap">
|
<div class="outline-text-6" id="text-c_m_cs_sph_lap">
|
||||||
<div class="eqlabel" id="orgb7a43f7">
|
<div class="eqlabel" id="orgb40c79b">
|
||||||
<p>
|
<p>
|
||||||
<a id="sph_Lap"></a><a href="./c_m_cs_sph.html#sph_Lap"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="sph_Lap"></a><a href="./c_m_cs_sph.html#sph_Lap"><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="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"/>
|
<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"/>
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@ -1851,7 +1851,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
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|
||||||
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@ -1,7 +1,7 @@
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<!DOCTYPE html>
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<html lang="en">
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<html lang="en">
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<head>
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<head>
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||||||
<!-- 2022-03-22 Tue 10:52 -->
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<meta charset="utf-8">
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<meta charset="utf-8">
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||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
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<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
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|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1642,7 +1642,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
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@ -1,7 +1,7 @@
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||||||
<!DOCTYPE html>
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<!DOCTYPE html>
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<html lang="en">
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<html lang="en">
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||||||
<head>
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<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
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<meta charset="utf-8">
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<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
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<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1644,7 +1644,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
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|
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|
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|
||||||
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@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1615,9 +1615,9 @@ Table of contents
|
||||||
<div class="outline-text-5" id="text-c_m_dc_d2">
|
<div class="outline-text-5" id="text-c_m_dc_d2">
|
||||||
</div>
|
</div>
|
||||||
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|
||||||
<div id="outline-container-org78664e4" class="outline-6">
|
<div id="outline-container-org873f1bb" class="outline-6">
|
||||||
<h6 id="org78664e4"><a href="#org78664e4">Divergence of gradient</a></h6>
|
<h6 id="org873f1bb"><a href="#org873f1bb">Divergence of gradient</a></h6>
|
||||||
<div class="outline-text-6" id="text-org78664e4">
|
<div class="outline-text-6" id="text-org873f1bb">
|
||||||
<p>
|
<p>
|
||||||
\({\boldsymbol \nabla} \cdot ({\boldsymbol \nabla} T) \equiv {\boldsymbol \nabla}^2 T\) is called the <b>Laplacian</b> of the scalar field \(T\).
|
\({\boldsymbol \nabla} \cdot ({\boldsymbol \nabla} T) \equiv {\boldsymbol \nabla}^2 T\) is called the <b>Laplacian</b> of the scalar field \(T\).
|
||||||
The Laplacian of a vector field \({\boldsymbol \nabla}^2 {\bf v}\) is also defined as the vector with components
|
The Laplacian of a vector field \({\boldsymbol \nabla}^2 {\bf v}\) is also defined as the vector with components
|
||||||
|
|
@ -1626,44 +1626,44 @@ given by the Laplacian of the corresponding vector elements.
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgecb53d1" class="outline-6">
|
<div id="outline-container-orged6374e" class="outline-6">
|
||||||
<h6 id="orgecb53d1"><a href="#orgecb53d1">Curl of a gradient</a></h6>
|
<h6 id="orged6374e"><a href="#orged6374e">Curl of a gradient</a></h6>
|
||||||
<div class="outline-text-6" id="text-orgecb53d1">
|
<div class="outline-text-6" id="text-orged6374e">
|
||||||
<p>
|
<p>
|
||||||
This always vanishes.
|
This always vanishes.
|
||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
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|
||||||
<div id="outline-container-orgdeab960" class="outline-6">
|
<div id="outline-container-orgcf8bc6c" class="outline-6">
|
||||||
<h6 id="orgdeab960"><a href="#orgdeab960">Gradient of the divergence</a></h6>
|
<h6 id="orgcf8bc6c"><a href="#orgcf8bc6c">Gradient of the divergence</a></h6>
|
||||||
<div class="outline-text-6" id="text-orgdeab960">
|
<div class="outline-text-6" id="text-orgcf8bc6c">
|
||||||
<p>
|
<p>
|
||||||
\({\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v})\) does not appear often in physics. No special name.
|
\({\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v})\) does not appear often in physics. No special name.
|
||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org11519c8" class="outline-6">
|
<div id="outline-container-orgc1dc4c7" class="outline-6">
|
||||||
<h6 id="org11519c8"><a href="#org11519c8">Divergence of a curl</a></h6>
|
<h6 id="orgc1dc4c7"><a href="#orgc1dc4c7">Divergence of a curl</a></h6>
|
||||||
<div class="outline-text-6" id="text-org11519c8">
|
<div class="outline-text-6" id="text-orgc1dc4c7">
|
||||||
<p>
|
<p>
|
||||||
This always vanishes.
|
This always vanishes.
|
||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org8bb99ae" class="outline-6">
|
<div id="outline-container-org766740d" class="outline-6">
|
||||||
<h6 id="org8bb99ae"><a href="#org8bb99ae">Curl of curl</a></h6>
|
<h6 id="org766740d"><a href="#org766740d">Curl of curl</a></h6>
|
||||||
<div class="outline-text-6" id="text-org8bb99ae">
|
<div class="outline-text-6" id="text-org766740d">
|
||||||
<div class="eqlabel" id="org38dd889">
|
<div class="eqlabel" id="orga94a832">
|
||||||
<p>
|
<p>
|
||||||
<a id="curlcurl"></a><a href="./c_m_dc_d2.html#curlcurl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="curlcurl"></a><a href="./c_m_dc_d2.html#curlcurl"><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="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"/>
|
<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>
|
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|
||||||
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|
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|
||||||
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|
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|
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|
||||||
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|
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|
||||||
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|
||||||
|
|
@ -1694,7 +1694,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1643,7 +1643,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1640,7 +1640,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1664,7 +1664,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1622,14 +1622,14 @@ explicited as follows:
|
||||||
<p>
|
<p>
|
||||||
<b>Gradient of a product</b>:
|
<b>Gradient of a product</b>:
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org89b1475">
|
<div class="eqlabel" id="orge6e6a80">
|
||||||
<p>
|
<p>
|
||||||
<a id="grad_prod"></a><a href="./c_m_dc_pr.html#grad_prod"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="grad_prod"></a><a href="./c_m_dc_pr.html#grad_prod"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orgc71740f">
|
<div class="alteqlabels" id="orgf9842ae">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (3)</li>
|
<li>Gr (3)</li>
|
||||||
<li>W (1-111)</li>
|
<li>W (1-111)</li>
|
||||||
|
|
@ -1649,14 +1649,14 @@ explicited as follows:
|
||||||
<p>
|
<p>
|
||||||
<b>Gradient of a scalar product</b>:
|
<b>Gradient of a scalar product</b>:
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="orgdcd103a">
|
<div class="eqlabel" id="orgb8556f5">
|
||||||
<p>
|
<p>
|
||||||
<a id="grad_sprod"></a><a href="./c_m_dc_pr.html#grad_sprod"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="grad_sprod"></a><a href="./c_m_dc_pr.html#grad_sprod"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org5dbb766">
|
<div class="alteqlabels" id="org884e962">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (4)</li>
|
<li>Gr (4)</li>
|
||||||
<li>W (1-112)</li>
|
<li>W (1-112)</li>
|
||||||
|
|
@ -1676,14 +1676,14 @@ explicited as follows:
|
||||||
<p>
|
<p>
|
||||||
<b>Divergence of a product</b>:
|
<b>Divergence of a product</b>:
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org16aa48b">
|
<div class="eqlabel" id="org3da56b1">
|
||||||
<p>
|
<p>
|
||||||
<a id="div_prod"></a><a href="./c_m_dc_pr.html#div_prod"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="div_prod"></a><a href="./c_m_dc_pr.html#div_prod"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org03b99ec">
|
<div class="alteqlabels" id="orgeb30387">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (5)</li>
|
<li>Gr (5)</li>
|
||||||
<li>W (1-115)</li>
|
<li>W (1-115)</li>
|
||||||
|
|
@ -1703,14 +1703,14 @@ explicited as follows:
|
||||||
<p>
|
<p>
|
||||||
<b>Divergence of a cross product</b>:
|
<b>Divergence of a cross product</b>:
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="orga48567e">
|
<div class="eqlabel" id="orgbfaa39d">
|
||||||
<p>
|
<p>
|
||||||
<a id="div_xprod"></a><a href="./c_m_dc_pr.html#div_xprod"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="div_xprod"></a><a href="./c_m_dc_pr.html#div_xprod"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org0aece97">
|
<div class="alteqlabels" id="orgca8e0c0">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (6)</li>
|
<li>Gr (6)</li>
|
||||||
<li>W (1-116)</li>
|
<li>W (1-116)</li>
|
||||||
|
|
@ -1730,14 +1730,14 @@ explicited as follows:
|
||||||
<p>
|
<p>
|
||||||
<b>Curl of a product</b>:
|
<b>Curl of a product</b>:
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org3dec348">
|
<div class="eqlabel" id="org5b32772">
|
||||||
<p>
|
<p>
|
||||||
<a id="curl_prod"></a><a href="./c_m_dc_pr.html#curl_prod"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="curl_prod"></a><a href="./c_m_dc_pr.html#curl_prod"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orgd0f6f07">
|
<div class="alteqlabels" id="org22a6f09">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (7)</li>
|
<li>Gr (7)</li>
|
||||||
<li>W (1-118)</li>
|
<li>W (1-118)</li>
|
||||||
|
|
@ -1757,14 +1757,14 @@ explicited as follows:
|
||||||
<p>
|
<p>
|
||||||
<b>Curl of a cross product</b>:
|
<b>Curl of a cross product</b>:
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="orga9f7b57">
|
<div class="eqlabel" id="org81448bf">
|
||||||
<p>
|
<p>
|
||||||
<a id="curl_xprod"></a><a href="./c_m_dc_pr.html#curl_xprod"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="curl_xprod"></a><a href="./c_m_dc_pr.html#curl_xprod"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org69dc8a6">
|
<div class="alteqlabels" id="org5de3f60">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (8)</li>
|
<li>Gr (8)</li>
|
||||||
<li>W (1-119)</li>
|
<li>W (1-119)</li>
|
||||||
|
|
@ -1805,7 +1805,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1639,7 +1639,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1651,7 +1651,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1636,14 +1636,14 @@ Resolution of divergence of \(\hat{\bf r}/r^2\) paradox:
|
||||||
More generally,
|
More generally,
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="eqlabel" id="orga7ea793">
|
<div class="eqlabel" id="orgcf3b8a6">
|
||||||
<p>
|
<p>
|
||||||
<a id="divdel"></a><a href="./c_m_dd_3d.html#divdel"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="divdel"></a><a href="./c_m_dd_3d.html#divdel"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org2afb48e">
|
<div class="alteqlabels" id="orgd295657">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (1.100)</li>
|
<li>Gr (1.100)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1662,14 +1662,14 @@ More generally,
|
||||||
Since
|
Since
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="eqlabel" id="org0791e6b">
|
<div class="eqlabel" id="org8e3f2ff">
|
||||||
<p>
|
<p>
|
||||||
<a id="div1or"></a><a href="./c_m_dd_3d.html#div1or"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="div1or"></a><a href="./c_m_dd_3d.html#div1or"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org5b1c286">
|
<div class="alteqlabels" id="orgd9d8d13">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (1.101)</li>
|
<li>Gr (1.101)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1685,14 +1685,14 @@ Since
|
||||||
<p>
|
<p>
|
||||||
we have that
|
we have that
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org72632aa">
|
<div class="eqlabel" id="org4584082">
|
||||||
<p>
|
<p>
|
||||||
<a id="Lap1or"></a><a href="./c_m_dd_3d.html#Lap1or"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Lap1or"></a><a href="./c_m_dd_3d.html#Lap1or"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orgc9783d9">
|
<div class="alteqlabels" id="org4002cb1">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (1.102)</li>
|
<li>Gr (1.102)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1724,7 +1724,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1657,7 +1657,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1642,7 +1642,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1640,7 +1640,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1649,7 +1649,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1643,7 +1643,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1650,7 +1650,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1615,9 +1615,9 @@ Table of contents
|
||||||
<div class="outline-text-5" id="text-c_m_ic_lsv">
|
<div class="outline-text-5" id="text-c_m_ic_lsv">
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orge29f03b" class="outline-6">
|
<div id="outline-container-org2ee5abe" class="outline-6">
|
||||||
<h6 id="orge29f03b"><a href="#orge29f03b">Line Integrals</a></h6>
|
<h6 id="org2ee5abe"><a href="#org2ee5abe">Line Integrals</a></h6>
|
||||||
<div class="outline-text-6" id="text-orge29f03b">
|
<div class="outline-text-6" id="text-org2ee5abe">
|
||||||
<p>
|
<p>
|
||||||
\[
|
\[
|
||||||
{\int_{\bf a}^{\bf b}}_{\cal P} {\bf v} \cdot d{\bf l}
|
{\int_{\bf a}^{\bf b}}_{\cal P} {\bf v} \cdot d{\bf l}
|
||||||
|
|
@ -1646,9 +1646,9 @@ Integral over a closed loop:
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org099f03d" class="outline-6">
|
<div id="outline-container-org5c34665" class="outline-6">
|
||||||
<h6 id="org099f03d"><a href="#org099f03d">Surface Integrals</a></h6>
|
<h6 id="org5c34665"><a href="#org5c34665">Surface Integrals</a></h6>
|
||||||
<div class="outline-text-6" id="text-org099f03d">
|
<div class="outline-text-6" id="text-org5c34665">
|
||||||
<p>
|
<p>
|
||||||
\[
|
\[
|
||||||
\int_{\cal S} {\bf v} \cdot d{\bf a}
|
\int_{\cal S} {\bf v} \cdot d{\bf a}
|
||||||
|
|
@ -1668,9 +1668,9 @@ Over a closed surface:
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgdad74b8" class="outline-6">
|
<div id="outline-container-org3f94a4e" class="outline-6">
|
||||||
<h6 id="orgdad74b8"><a href="#orgdad74b8">Volume Integrals</a></h6>
|
<h6 id="org3f94a4e"><a href="#org3f94a4e">Volume Integrals</a></h6>
|
||||||
<div class="outline-text-6" id="text-orgdad74b8">
|
<div class="outline-text-6" id="text-org3f94a4e">
|
||||||
<p>
|
<p>
|
||||||
\[
|
\[
|
||||||
\int_{\cal V} T d\tau
|
\int_{\cal V} T d\tau
|
||||||
|
|
@ -1711,7 +1711,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1613,14 +1613,14 @@ Table of contents
|
||||||
<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"/>
|
<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><span class="headline-id">c.m.ic.stokes</span></h5>
|
</svg></a><span class="headline-id">c.m.ic.stokes</span></h5>
|
||||||
<div class="outline-text-5" id="text-c_m_ic_stokes">
|
<div class="outline-text-5" id="text-c_m_ic_stokes">
|
||||||
<div class="eqlabel" id="org31b82d5">
|
<div class="eqlabel" id="org46c1290">
|
||||||
<p>
|
<p>
|
||||||
<a id="Stokes"></a><a href="./c_m_ic_stokes.html#Stokes"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Stokes"></a><a href="./c_m_ic_stokes.html#Stokes"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org6073175">
|
<div class="alteqlabels" id="org1c7e7a7">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (1.57)</li>
|
<li>Gr (1.57)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1665,7 +1665,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1639,7 +1639,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1652,7 +1652,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1652,7 +1652,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1655,7 +1655,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1641,7 +1641,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1670,7 +1670,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1665,7 +1665,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
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|
||||||
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|
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|
||||||
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|
||||||
|
|
|
||||||
|
|
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|
||||||
<!DOCTYPE html>
|
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|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
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|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1699,7 +1699,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
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|
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|
||||||
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|
||||||
|
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|
||||||
|
|
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|
||||||
<!DOCTYPE html>
|
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|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
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|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1665,7 +1665,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
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|
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|
||||||
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|
||||||
|
|
|
||||||
|
|
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|
||||||
<!DOCTYPE html>
|
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|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1712,7 +1712,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
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|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1638,7 +1638,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
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|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1657,7 +1657,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
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|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1684,7 +1684,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
10
build/d.html
10
build/d.html
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
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|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1614,8 +1614,8 @@ Table of contents
|
||||||
</svg></a><span class="headline-id">d</span></h2>
|
</svg></a><span class="headline-id">d</span></h2>
|
||||||
|
|
||||||
<div class="outline-text-2" id="text-d">
|
<div class="outline-text-2" id="text-d">
|
||||||
<details class="objectives" id="orgfd6e83a">
|
<details class="objectives" id="orgb872990">
|
||||||
<summary id="org337d4b3">
|
<summary id="org860974a">
|
||||||
Objectives
|
Objectives
|
||||||
</summary>
|
</summary>
|
||||||
|
|
||||||
|
|
@ -1679,7 +1679,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1659,7 +1659,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1654,7 +1654,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1657,7 +1657,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1654,7 +1654,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1676,7 +1676,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1659,7 +1659,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1656,7 +1656,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1659,7 +1659,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1657,7 +1657,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1662,7 +1662,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1663,7 +1663,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1614,8 +1614,8 @@ Table of contents
|
||||||
</svg></a><span class="headline-id">emd</span></h2>
|
</svg></a><span class="headline-id">emd</span></h2>
|
||||||
|
|
||||||
<div class="outline-text-2" id="text-emd">
|
<div class="outline-text-2" id="text-emd">
|
||||||
<details class="prereq" id="orgeb3e60e">
|
<details class="prereq" id="orgabe80a6">
|
||||||
<summary id="org898f63b">
|
<summary id="orgccf4253">
|
||||||
Prerequisites
|
Prerequisites
|
||||||
</summary>
|
</summary>
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
|
|
@ -1624,8 +1624,8 @@ Prerequisites
|
||||||
</ul>
|
</ul>
|
||||||
</details>
|
</details>
|
||||||
|
|
||||||
<details class="objectives" id="org11fe244">
|
<details class="objectives" id="orgf2d0735">
|
||||||
<summary id="org360a5fd">
|
<summary id="orge4261f8">
|
||||||
Objectives
|
Objectives
|
||||||
</summary>
|
</summary>
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
|
|
@ -1666,7 +1666,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1640,7 +1640,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1644,18 +1644,18 @@ Empirically: the changing magnetic field induces an electric current around
|
||||||
the circuit. This current is really driven by an electric field having a component
|
the circuit. This current is really driven by an electric field having a component
|
||||||
along the wire. The line integral of this field is called the
|
along the wire. The line integral of this field is called the
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="orgc1ab4b8">
|
<div class="core div" id="orgb0fd5b4">
|
||||||
<p>
|
<p>
|
||||||
<b>Electromotive force (or electromotance)</b>,
|
<b>Electromotive force (or electromotance)</b>,
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org1ce0462">
|
<div class="eqlabel" id="orgb0e7cde">
|
||||||
<p>
|
<p>
|
||||||
<a id="elmofo"></a><a href="./emd_Fl_Fl.html#elmofo"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="elmofo"></a><a href="./emd_Fl_Fl.html#elmofo"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orge2b1b8b">
|
<div class="alteqlabels" id="org516a196">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (7.9)</li>
|
<li>Gr (7.9)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1680,14 +1680,14 @@ The precise statement associated to Faraday's observations
|
||||||
is that the electromotive force is proportional
|
is that the electromotive force is proportional
|
||||||
to the rate of change of the magnetic flux,
|
to the rate of change of the magnetic flux,
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="orgb4b21bf">
|
<div class="eqlabel" id="orgab619b1">
|
||||||
<p>
|
<p>
|
||||||
<a id="Fl_flux"></a><a href="./emd_Fl_Fl.html#Fl_flux"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Fl_flux"></a><a href="./emd_Fl_Fl.html#Fl_flux"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org4e36847">
|
<div class="alteqlabels" id="org969857c">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (7.14)</li>
|
<li>Gr (7.14)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1702,18 +1702,18 @@ to the rate of change of the magnetic flux,
|
||||||
\]
|
\]
|
||||||
so we obtain
|
so we obtain
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org3b354eb">
|
<div class="core div" id="org5419feb">
|
||||||
<p>
|
<p>
|
||||||
<b>Faraday's law</b> (integral form <i>N.B.: for a stationary loop</i>)
|
<b>Faraday's law</b> (integral form <i>N.B.: for a stationary loop</i>)
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org3323690">
|
<div class="eqlabel" id="org4696e9f">
|
||||||
<p>
|
<p>
|
||||||
<a id="Fl_int"></a><a href="./emd_Fl_Fl.html#Fl_int"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Fl_int"></a><a href="./emd_Fl_Fl.html#Fl_int"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orgc991325">
|
<div class="alteqlabels" id="org439dfef">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (7.15)</li>
|
<li>Gr (7.15)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1737,15 +1737,15 @@ for any loop (on a wire or not). Using Stokes' theorem,
|
||||||
\]
|
\]
|
||||||
we obtain
|
we obtain
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org5eb686c">
|
<div class="core div" id="org49ffd42">
|
||||||
<div class="eqlabel" id="org7ca80cd">
|
<div class="eqlabel" id="org5ecebad">
|
||||||
<p>
|
<p>
|
||||||
<a id="Fl"></a><a href="./emd_Fl_Fl.html#Fl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Fl"></a><a href="./emd_Fl_Fl.html#Fl"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org859ac4a">
|
<div class="alteqlabels" id="org6a61522">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (7.16)</li>
|
<li>Gr (7.16)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1790,7 +1790,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1639,14 +1639,14 @@ W = \frac{1}{2} I \oint {\bf A} \cdot d{\bf l} = \frac{1}{2} \oint ({\bf A} \cdo
|
||||||
\]
|
\]
|
||||||
Generalization to volume currents:
|
Generalization to volume currents:
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org3409c0a">
|
<div class="eqlabel" id="orge9580af">
|
||||||
<p>
|
<p>
|
||||||
<a id="W_intAJ"></a><a href="./emd_Fl_e.html#W_intAJ"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="W_intAJ"></a><a href="./emd_Fl_e.html#W_intAJ"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org84f1d51">
|
<div class="alteqlabels" id="orgbe0c60a">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (7.31)</li>
|
<li>Gr (7.31)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1681,15 +1681,15 @@ W = \frac{1}{2\mu_0} \left[ \int_{\cal V} d\tau B^2 - \int_{\cal V} d\tau {\bold
|
||||||
\]
|
\]
|
||||||
We can integrate over all space: after neglecting boundary terms (assuming fields fall to zero at infinity), we are left with
|
We can integrate over all space: after neglecting boundary terms (assuming fields fall to zero at infinity), we are left with
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="orgced7757">
|
<div class="core div" id="org9173f2d">
|
||||||
<div class="eqlabel" id="orgd899514">
|
<div class="eqlabel" id="org717e156">
|
||||||
<p>
|
<p>
|
||||||
<a id="W_intBsq"></a><a href="./emd_Fl_e.html#W_intBsq"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="W_intBsq"></a><a href="./emd_Fl_e.html#W_intBsq"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orgf7c92a2">
|
<div class="alteqlabels" id="org0d5a0b3">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (7.34)</li>
|
<li>Gr (7.34)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1718,7 +1718,7 @@ W_{mag} &= \frac{1}{2} \int d\tau ~({\bf A} \cdot {\bf J}) &= \frac{1}{2
|
||||||
which are equations <a href="./ems_es_e.html#W_vcd">W_vcd</a>, <a href="./ems_es_e.html#W_intEsq">W_intEsq</a>, <a href="./emd_Fl_e.html#W_intAJ">W_intAJ</a> and <a href="./emd_Fl_e.html#W_intBsq">W_intBsq</a>.
|
which are equations <a href="./ems_es_e.html#W_vcd">W_vcd</a>, <a href="./ems_es_e.html#W_intEsq">W_intEsq</a>, <a href="./emd_Fl_e.html#W_intAJ">W_intAJ</a> and <a href="./emd_Fl_e.html#W_intBsq">W_intBsq</a>.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="example div" id="orge558476">
|
<div class="example div" id="org34d5a7d">
|
||||||
<p>
|
<p>
|
||||||
<b>Example: energy in coaxial cable</b>
|
<b>Example: energy in coaxial cable</b>
|
||||||
</p>
|
</p>
|
||||||
|
|
@ -1768,7 +1768,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1641,14 +1641,14 @@ so
|
||||||
\]
|
\]
|
||||||
and we can write the mutual inductance as the <b>Neumann formula</b>,
|
and we can write the mutual inductance as the <b>Neumann formula</b>,
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org3ec4c18">
|
<div class="eqlabel" id="org1f70ff2">
|
||||||
<p>
|
<p>
|
||||||
<a id="Newmann_M"></a><a href="./emd_Fl_i.html#Newmann_M"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Newmann_M"></a><a href="./emd_Fl_i.html#Newmann_M"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org7ff8d1e">
|
<div class="alteqlabels" id="org57de753">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (7.22)</li>
|
<li>Gr (7.22)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1665,14 +1665,14 @@ M_{21} = \frac{\mu_0}{4\pi} \oint_{{\cal P}_1} \oint_{{\cal P}_2} \frac{d{\bf l}
|
||||||
Two things:
|
Two things:
|
||||||
first, \(M_{21}\) is purely geometrical. Second,
|
first, \(M_{21}\) is purely geometrical. Second,
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="orge7f5edd">
|
<div class="eqlabel" id="org43668cc">
|
||||||
<p>
|
<p>
|
||||||
<a id="Msym"></a><a href="./emd_Fl_i.html#Msym"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Msym"></a><a href="./emd_Fl_i.html#Msym"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org54ddc77">
|
<div class="alteqlabels" id="org7b1e4fa">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (7.23)</li>
|
<li>Gr (7.23)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1687,7 +1687,7 @@ M_{12} = M_{21}
|
||||||
\]
|
\]
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="example div" id="org1bcebe3">
|
<div class="example div" id="orgecf7176">
|
||||||
<p>
|
<p>
|
||||||
<b>Example: solenoid in solenoid</b>
|
<b>Example: solenoid in solenoid</b>
|
||||||
</p>
|
</p>
|
||||||
|
|
@ -1735,14 +1735,14 @@ What if we vary current in loop 1? Flux in 2 will vary. Induces EMF in loop 2:
|
||||||
\]
|
\]
|
||||||
Changing current also induces EMF in the source loop itself:
|
Changing current also induces EMF in the source loop itself:
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="orgdaaac4e">
|
<div class="eqlabel" id="org2512f69">
|
||||||
<p>
|
<p>
|
||||||
<a id="PLI"></a><a href="./emd_Fl_i.html#PLI"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="PLI"></a><a href="./emd_Fl_i.html#PLI"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orgb8faf94">
|
<div class="alteqlabels" id="org080d683">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (7.25)</li>
|
<li>Gr (7.25)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1765,7 +1765,7 @@ Inductance: measured in <b>henries</b> (\(H\)). \(H = V s/A\).
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
<div class="example div" id="org11544ba">
|
<div class="example div" id="orgce99b7c">
|
||||||
<p>
|
<p>
|
||||||
<b>Example: self-inductance of toroidal coil</b>
|
<b>Example: self-inductance of toroidal coil</b>
|
||||||
</p>
|
</p>
|
||||||
|
|
@ -1804,7 +1804,7 @@ Inductance (like capacitance) is intrinsically positive. Use Lenz law.
|
||||||
Think of <i>back EMF</i>.
|
Think of <i>back EMF</i>.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="example div" id="org52373ca">
|
<div class="example div" id="orgb4d543b">
|
||||||
<p>
|
<p>
|
||||||
<b>Example: circuit</b>
|
<b>Example: circuit</b>
|
||||||
</p>
|
</p>
|
||||||
|
|
@ -1853,7 +1853,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1637,7 +1637,7 @@ law in integral form:
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
<div class="example div" id="orgfcd2e61">
|
<div class="example div" id="org2badd21">
|
||||||
<p>
|
<p>
|
||||||
<b>Example: loop with time-dependent flux</b>
|
<b>Example: loop with time-dependent flux</b>
|
||||||
</p>
|
</p>
|
||||||
|
|
@ -1664,7 +1664,7 @@ Increasing \({\bf B}\): clockwise (viewed from above) \({\bf E}\) from Lenz.
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div class="example div" id="orgafdd47c">
|
<div class="example div" id="org6994570">
|
||||||
<p>
|
<p>
|
||||||
<b>Example: wheel with charged rim traversed by flux</b>
|
<b>Example: wheel with charged rim traversed by flux</b>
|
||||||
</p>
|
</p>
|
||||||
|
|
@ -1705,7 +1705,7 @@ called the <b>quasistatic</b> approximation, and works provided we deal with
|
||||||
<i>slow enough</i> phenomena.
|
<i>slow enough</i> phenomena.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="example div" id="org6631fcc">
|
<div class="example div" id="orgddce4f1">
|
||||||
<p>
|
<p>
|
||||||
<b>Example: field from wire with time-dependent current</b>
|
<b>Example: field from wire with time-dependent current</b>
|
||||||
</p>
|
</p>
|
||||||
|
|
@ -1764,7 +1764,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1640,7 +1640,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1616,18 +1616,18 @@ Table of contents
|
||||||
<p>
|
<p>
|
||||||
Full set of equations for the electromagnetic field:
|
Full set of equations for the electromagnetic field:
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org71429ce">
|
<div class="core div" id="org96eda60">
|
||||||
<p>
|
<p>
|
||||||
<b>Maxwell's equations</b> <i>(in vacuum)</i>
|
<b>Maxwell's equations</b> <i>(in vacuum)</i>
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org92aa36d">
|
<div class="eqlabel" id="org99bc512">
|
||||||
<p>
|
<p>
|
||||||
<a id="Max_vac"></a><a href="./emd_Me_Me.html#Max_vac"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Max_vac"></a><a href="./emd_Me_Me.html#Max_vac"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orgd8ea0a7">
|
<div class="alteqlabels" id="org0385504">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1644,7 +1644,7 @@ Full set of equations for the electromagnetic field:
|
||||||
<p>
|
<p>
|
||||||
Complement:
|
Complement:
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org93d1ad6">
|
<div class="core div" id="org8bd62bd">
|
||||||
<p>
|
<p>
|
||||||
Force law <a href="./ems_ms_lf_pc.html#LorFo">LorFo</a>
|
Force law <a href="./ems_ms_lf_pc.html#LorFo">LorFo</a>
|
||||||
\[
|
\[
|
||||||
|
|
@ -1667,15 +1667,15 @@ take divergence of \((iv)\) and use \((i)\).
|
||||||
<p>
|
<p>
|
||||||
Better way of writing: all fields on left, all sources on right,
|
Better way of writing: all fields on left, all sources on right,
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org82c9083">
|
<div class="core div" id="org3b3efc0">
|
||||||
<div class="eqlabel" id="org1583626">
|
<div class="eqlabel" id="orgaa87be2">
|
||||||
<p>
|
<p>
|
||||||
<a id="Max_vac_s"></a><a href="./emd_Me_Me.html#Max_vac_s"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Max_vac_s"></a><a href="./emd_Me_Me.html#Max_vac_s"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orgfc0a16c">
|
<div class="alteqlabels" id="org3e69b1d">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (7.42)</li>
|
<li>Gr (7.42)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1713,7 +1713,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1622,15 +1622,15 @@ The term which should be zero (but isn't) in <a href="./emd_Me_ebM.html#divcurlB
|
||||||
\]
|
\]
|
||||||
The extra term would thus be eliminated if we were to put
|
The extra term would thus be eliminated if we were to put
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="orgfb244bd">
|
<div class="core div" id="org65d0a3c">
|
||||||
<div class="eqlabel" id="org02e358a">
|
<div class="eqlabel" id="org2343c92">
|
||||||
<p>
|
<p>
|
||||||
<a id="AmpMax"></a><a href="./emd_Me_dc.html#AmpMax"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="AmpMax"></a><a href="./emd_Me_dc.html#AmpMax"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orgf266507">
|
<div class="alteqlabels" id="org09fe122">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (7.36)</li>
|
<li>Gr (7.36)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1659,18 +1659,18 @@ Real confirmation of Maxwell's theory: 1888, Hertz's experiments on propagation
|
||||||
<p>
|
<p>
|
||||||
Maxwell baptized this term the
|
Maxwell baptized this term the
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="orgb3e1688">
|
<div class="core div" id="org9a1c650">
|
||||||
<p>
|
<p>
|
||||||
<b>Displacement current</b>
|
<b>Displacement current</b>
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org5bc6ac9">
|
<div class="eqlabel" id="orgea96ca5">
|
||||||
<p>
|
<p>
|
||||||
<a id="Jd"></a><a href="./emd_Me_dc.html#Jd"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Jd"></a><a href="./emd_Me_dc.html#Jd"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org2273d93">
|
<div class="alteqlabels" id="org147727a">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (7.37)</li>
|
<li>Gr (7.37)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1724,7 +1724,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1630,14 +1630,14 @@ Fatal inconsistency: div of curl must always vanish. Check on \((iii)\):
|
||||||
\]
|
\]
|
||||||
But: try same with \((iv)\):
|
But: try same with \((iv)\):
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org1332a90">
|
<div class="eqlabel" id="org5adad0c">
|
||||||
<p>
|
<p>
|
||||||
<a id="divcurlB"></a><a href="./emd_Me_ebM.html#divcurlB"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="divcurlB"></a><a href="./emd_Me_ebM.html#divcurlB"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orgc919b58">
|
<div class="alteqlabels" id="orga04de46">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (7.35)</li>
|
<li>Gr (7.35)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1682,7 +1682,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1663,7 +1663,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1614,8 +1614,8 @@ Table of contents
|
||||||
</svg></a><span class="headline-id">emd.ce</span></h3>
|
</svg></a><span class="headline-id">emd.ce</span></h3>
|
||||||
|
|
||||||
<div class="outline-text-3" id="text-emd_ce">
|
<div class="outline-text-3" id="text-emd_ce">
|
||||||
<details class="prereq" id="org4aea2a7">
|
<details class="prereq" id="orgbcfd9aa">
|
||||||
<summary id="orgbb42f82">
|
<summary id="orgfd4a1b6">
|
||||||
Prerequisites
|
Prerequisites
|
||||||
</summary>
|
</summary>
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
|
|
@ -1623,8 +1623,8 @@ Prerequisites
|
||||||
</ul>
|
</ul>
|
||||||
</details>
|
</details>
|
||||||
|
|
||||||
<details class="objectives" id="orgacf1d30">
|
<details class="objectives" id="orgb58d097">
|
||||||
<summary id="org560d61d">
|
<summary id="org5cd5f85">
|
||||||
Objectives
|
Objectives
|
||||||
</summary>
|
</summary>
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
|
|
@ -1662,7 +1662,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1616,18 +1616,18 @@ Table of contents
|
||||||
<p>
|
<p>
|
||||||
The angular momentum of EM fields is directly given by
|
The angular momentum of EM fields is directly given by
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="org8982815">
|
<div class="main div" id="orgc2d5343">
|
||||||
<p>
|
<p>
|
||||||
<b>Angular momentum of EM fields</b>
|
<b>Angular momentum of EM fields</b>
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org8297ce4">
|
<div class="eqlabel" id="orgd4d0682">
|
||||||
<p>
|
<p>
|
||||||
<a id="lrxg"></a><a href="./emd_ce_amom.html#lrxg"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="lrxg"></a><a href="./emd_ce_amom.html#lrxg"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orgc1dccb2">
|
<div class="alteqlabels" id="orgf246c58">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1661,7 +1661,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1635,7 +1635,7 @@ This means that
|
||||||
\]
|
\]
|
||||||
Since this is true for any volume, we have (re)derived the
|
Since this is true for any volume, we have (re)derived the
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org1d21244">
|
<div class="core div" id="orgc746662">
|
||||||
<p>
|
<p>
|
||||||
<b>Continuity equation</b> <a href="./ems_ms_ce.html#conteq">conteq</a>
|
<b>Continuity equation</b> <a href="./ems_ms_ce.html#conteq">conteq</a>
|
||||||
\[
|
\[
|
||||||
|
|
@ -1675,7 +1675,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1628,18 +1628,18 @@ in which the first integral can be interpreted as the momentum stored in the EM
|
||||||
<p>
|
<p>
|
||||||
This is thus simply a conservation law for momentum, with
|
This is thus simply a conservation law for momentum, with
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="orgbd3d67d">
|
<div class="main div" id="org9032358">
|
||||||
<p>
|
<p>
|
||||||
<b>Momentum density in the EM fields</b>
|
<b>Momentum density in the EM fields</b>
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org2b66251">
|
<div class="eqlabel" id="org0649d73">
|
||||||
<p>
|
<p>
|
||||||
<a id="gExB"></a><a href="./emd_ce_mom.html#gExB"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="gExB"></a><a href="./emd_ce_mom.html#gExB"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org006aaa0">
|
<div class="alteqlabels" id="org7dc7b00">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1655,18 +1655,18 @@ This is thus simply a conservation law for momentum, with
|
||||||
<p>
|
<p>
|
||||||
In a region in which the mechanical momentum is not changing due to external influences, we then have the
|
In a region in which the mechanical momentum is not changing due to external influences, we then have the
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="orgd647d42">
|
<div class="main div" id="org72dfdb8">
|
||||||
<p>
|
<p>
|
||||||
<b>Continuity equation for EM momentum</b>
|
<b>Continuity equation for EM momentum</b>
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org84364f8">
|
<div class="eqlabel" id="org89a6b5f">
|
||||||
<p>
|
<p>
|
||||||
<a id="contg"></a><a href="./emd_ce_mom.html#contg"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="contg"></a><a href="./emd_ce_mom.html#contg"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org03c5d23">
|
<div class="alteqlabels" id="orgd3a1580">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1699,7 +1699,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1667,18 +1667,18 @@ and similarly for \({\boldsymbol B}\). We thus get
|
||||||
<p>
|
<p>
|
||||||
This expression can be greatly simplified by introducing the
|
This expression can be greatly simplified by introducing the
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="org63be843">
|
<div class="main div" id="orge483101">
|
||||||
<p>
|
<p>
|
||||||
<b>Maxwell stress tensor</b>
|
<b>Maxwell stress tensor</b>
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org7c75f9d">
|
<div class="eqlabel" id="org42e9f16">
|
||||||
<p>
|
<p>
|
||||||
<a id="MaxST"></a><a href="./emd_ce_mst.html#MaxST"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="MaxST"></a><a href="./emd_ce_mst.html#MaxST"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orgd84a618">
|
<div class="alteqlabels" id="orgf3e9098">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1699,18 +1699,18 @@ The element \(T_{ij}\) represents the force per unit area in the \(i\) direction
|
||||||
<p>
|
<p>
|
||||||
We then obtain the
|
We then obtain the
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="orgfeaab67">
|
<div class="main div" id="org3664d29">
|
||||||
<p>
|
<p>
|
||||||
<b>EM force per unit volume</b>
|
<b>EM force per unit volume</b>
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org9fc5057">
|
<div class="eqlabel" id="org6136353">
|
||||||
<p>
|
<p>
|
||||||
<a id="fT"></a><a href="./emd_ce_mst.html#fT"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="fT"></a><a href="./emd_ce_mst.html#fT"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orgecbfdae">
|
<div class="alteqlabels" id="org7273a9f">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1726,18 +1726,18 @@ We then obtain the
|
||||||
<p>
|
<p>
|
||||||
where \({\boldsymbol S}\) is the Poynting vector. Integrating, we obtain the
|
where \({\boldsymbol S}\) is the Poynting vector. Integrating, we obtain the
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="org86829bd">
|
<div class="main div" id="org2a4f340">
|
||||||
<p>
|
<p>
|
||||||
<b>Total force on charges in volume</b>
|
<b>Total force on charges in volume</b>
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org2370cf3">
|
<div class="eqlabel" id="org0298272">
|
||||||
<p>
|
<p>
|
||||||
<a id="totFo"></a><a href="./emd_ce_mst.html#totFo"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="totFo"></a><a href="./emd_ce_mst.html#totFo"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orgc55376c">
|
<div class="alteqlabels" id="org1024eff">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1770,7 +1770,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1636,14 +1636,14 @@ done by EM forces? From Lorentz force law:
|
||||||
Really, we're looking at a small volume element \(d\tau\) carrying charge \(\rho d\tau\), moving
|
Really, we're looking at a small volume element \(d\tau\) carrying charge \(\rho d\tau\), moving
|
||||||
at velocity \({\bf v}\) such that \({\bf J} = \rho {\bf v}\). Thus,
|
at velocity \({\bf v}\) such that \({\bf J} = \rho {\bf v}\). Thus,
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="orge2567ac">
|
<div class="eqlabel" id="org0c693e0">
|
||||||
<p>
|
<p>
|
||||||
<a id="dWdt_intEJ"></a><a href="./emd_ce_poy.html#dWdt_intEJ"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="dWdt_intEJ"></a><a href="./emd_ce_poy.html#dWdt_intEJ"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org4d05a80">
|
<div class="alteqlabels" id="orge34a4b7">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (8.6)</li>
|
<li>Gr (8.6)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1683,18 +1683,18 @@ so we get
|
||||||
Substituting this in <a href="./emd_ce_poy.html#dWdt_intEJ">dWdt_intEJ</a> and using the divergence theorem,
|
Substituting this in <a href="./emd_ce_poy.html#dWdt_intEJ">dWdt_intEJ</a> and using the divergence theorem,
|
||||||
we obtain
|
we obtain
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="org36db96e">
|
<div class="main div" id="orgb7d7869">
|
||||||
<p>
|
<p>
|
||||||
<b>Poynting's theorem</b>
|
<b>Poynting's theorem</b>
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org21ce6b8">
|
<div class="eqlabel" id="org1a4b16b">
|
||||||
<p>
|
<p>
|
||||||
<a id="👉Thm"></a><a href="./emd_ce_poy.html#👉Thm"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="👉Thm"></a><a href="./emd_ce_poy.html#👉Thm"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org09a112b">
|
<div class="alteqlabels" id="org4feadff">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (8.9)</li>
|
<li>Gr (8.9)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1720,18 +1720,18 @@ energy is carried by EM fields out of \({\cal V}\) across its boundary surface.
|
||||||
<p>
|
<p>
|
||||||
Energy per unit time, per unit area carried by EM fields: given by the
|
Energy per unit time, per unit area carried by EM fields: given by the
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org0bf3f6c">
|
<div class="core div" id="orgdc56ce9">
|
||||||
<p>
|
<p>
|
||||||
<b>Poynting vector</b>
|
<b>Poynting vector</b>
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org327095e">
|
<div class="eqlabel" id="orga61d997">
|
||||||
<p>
|
<p>
|
||||||
<a id="PoyntingVec"></a><a href="./emd_ce_poy.html#PoyntingVec"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="PoyntingVec"></a><a href="./emd_ce_poy.html#PoyntingVec"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org7684a8e">
|
<div class="alteqlabels" id="orgb7a4cb9">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (8.10)</li>
|
<li>Gr (8.10)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1750,18 +1750,18 @@ Energy per unit time, per unit area carried by EM fields: given by the
|
||||||
<p>
|
<p>
|
||||||
We can thus express Poynting's theorem more compactly:
|
We can thus express Poynting's theorem more compactly:
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org4255191">
|
<div class="core div" id="orgd48d57f">
|
||||||
<p>
|
<p>
|
||||||
<b>Poynting's theorem</b> (integral form)
|
<b>Poynting's theorem</b> (integral form)
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="orgd0524d3">
|
<div class="eqlabel" id="org32c9daf">
|
||||||
<p>
|
<p>
|
||||||
<a id="PoyntingThm_int"></a><a href="./emd_ce_poy.html#PoyntingThm_int"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="PoyntingThm_int"></a><a href="./emd_ce_poy.html#PoyntingThm_int"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org8acaa16">
|
<div class="alteqlabels" id="org59d2761">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (8.11)</li>
|
<li>Gr (8.11)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1780,18 +1780,18 @@ We can thus express Poynting's theorem more compactly:
|
||||||
<p>
|
<p>
|
||||||
where we have defined the total
|
where we have defined the total
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org85e77e2">
|
<div class="core div" id="org5e10531">
|
||||||
<p>
|
<p>
|
||||||
<b>Energy in electromagnetic fields</b>
|
<b>Energy in electromagnetic fields</b>
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org7d4ae3d">
|
<div class="eqlabel" id="orgad6f50f">
|
||||||
<p>
|
<p>
|
||||||
<a id="Uem"></a><a href="./emd_ce_poy.html#Uem"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Uem"></a><a href="./emd_ce_poy.html#Uem"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org7a55647">
|
<div class="alteqlabels" id="orga3df7bc">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (8.5)</li>
|
<li>Gr (8.5)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1820,18 +1820,18 @@ Then,
|
||||||
\]
|
\]
|
||||||
so we get the
|
so we get the
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="orgbdb096d">
|
<div class="core div" id="orgb7a11e9">
|
||||||
<p>
|
<p>
|
||||||
<b>Poynting theorem</b> (differential form)
|
<b>Poynting theorem</b> (differential form)
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org9c56948">
|
<div class="eqlabel" id="orga2e5c79">
|
||||||
<p>
|
<p>
|
||||||
<a id="PoyntingThm"></a><a href="./emd_ce_poy.html#PoyntingThm"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="PoyntingThm"></a><a href="./emd_ce_poy.html#PoyntingThm"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orgdfe3994">
|
<div class="alteqlabels" id="org0cf780d">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (8.14)</li>
|
<li>Gr (8.14)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1854,7 +1854,7 @@ and has a similar for to the continuity equation
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
<div class="example div" id="org15b725b">
|
<div class="example div" id="org1083447">
|
||||||
<p>
|
<p>
|
||||||
<b>Example: Joule heating</b>
|
<b>Example: Joule heating</b>
|
||||||
</p>
|
</p>
|
||||||
|
|
@ -1911,7 +1911,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1614,8 +1614,8 @@ Table of contents
|
||||||
</svg></a><span class="headline-id">emd.emw</span></h3>
|
</svg></a><span class="headline-id">emd.emw</span></h3>
|
||||||
|
|
||||||
<div class="outline-text-3" id="text-emd_emw">
|
<div class="outline-text-3" id="text-emd_emw">
|
||||||
<details class="prereq" id="org17a8cef">
|
<details class="prereq" id="org92d8d0c">
|
||||||
<summary id="org45e360a">
|
<summary id="orgb97228e">
|
||||||
Prerequisites
|
Prerequisites
|
||||||
</summary>
|
</summary>
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
|
|
@ -1624,8 +1624,8 @@ Prerequisites
|
||||||
</ul>
|
</ul>
|
||||||
</details>
|
</details>
|
||||||
|
|
||||||
<details class="objectives" id="org91615eb">
|
<details class="objectives" id="org5c24096">
|
||||||
<summary id="orgec366bf">
|
<summary id="orge645495">
|
||||||
Objectives
|
Objectives
|
||||||
</summary>
|
</summary>
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
|
|
@ -1659,7 +1659,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1644,18 +1644,18 @@ so for a monochromatic EM plan wave,
|
||||||
\]
|
\]
|
||||||
or more succinctly:
|
or more succinctly:
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="orgdf4b8bc">
|
<div class="main div" id="orga5c9575">
|
||||||
<p>
|
<p>
|
||||||
<b>Poynting vector of a monochromatic EM wave</b>
|
<b>Poynting vector of a monochromatic EM wave</b>
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org3913519">
|
<div class="eqlabel" id="org72a5a32">
|
||||||
<p>
|
<p>
|
||||||
<a id="Poynting_mpw"></a><a href="./emd_emw_ep.html#Poynting_mpw"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Poynting_mpw"></a><a href="./emd_emw_ep.html#Poynting_mpw"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org8b59092">
|
<div class="alteqlabels" id="org7e5d7a7">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (9.57)</li>
|
<li>Gr (9.57)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1678,7 +1678,7 @@ This has a transparent physical interpretation: the energy density \(u\) flows w
|
||||||
<p>
|
<p>
|
||||||
Similary, we get the
|
Similary, we get the
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="org21912bb">
|
<div class="main div" id="orgd6eada9">
|
||||||
<p>
|
<p>
|
||||||
<b>Momentum density of a monochromatic EM wave</b>
|
<b>Momentum density of a monochromatic EM wave</b>
|
||||||
\[
|
\[
|
||||||
|
|
@ -1729,7 +1729,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1636,14 +1636,14 @@ From Faraday: \({\boldsymbol \nabla} \times {\bf E} = -\partial {\bf B}/\partia
|
||||||
\]
|
\]
|
||||||
so \({\bf E}\) and \({\bf B}\) are mutually perpendicular, and
|
so \({\bf E}\) and \({\bf B}\) are mutually perpendicular, and
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org619c73f">
|
<div class="eqlabel" id="org44bb1e2">
|
||||||
<p>
|
<p>
|
||||||
<a id="EBmpw"></a><a href="./emd_emw_mpw.html#EBmpw"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="EBmpw"></a><a href="./emd_emw_mpw.html#EBmpw"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orgaad096d">
|
<div class="alteqlabels" id="org0064233">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (9.47)</li>
|
<li>Gr (9.47)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1662,18 +1662,18 @@ B_0 = \frac{k}{\omega} E_0 = \frac{1}{c} E_0.
|
||||||
Generalizing to propagation in the direction of an arbitrary wavevector
|
Generalizing to propagation in the direction of an arbitrary wavevector
|
||||||
\({\boldsymbol k}\) and (transverse) polarization vector \(\hat{\boldsymbol n}\), we have the
|
\({\boldsymbol k}\) and (transverse) polarization vector \(\hat{\boldsymbol n}\), we have the
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org9c77e17">
|
<div class="core div" id="org83aeece">
|
||||||
<p>
|
<p>
|
||||||
<b>E and B fields for a monochromatic EM plane wave</b>
|
<b>E and B fields for a monochromatic EM plane wave</b>
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org54506e2">
|
<div class="eqlabel" id="org82e71ea">
|
||||||
<p>
|
<p>
|
||||||
<a id="mpw"></a><a href="./emd_emw_mpw.html#mpw"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="mpw"></a><a href="./emd_emw_mpw.html#mpw"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orgb384c79">
|
<div class="alteqlabels" id="orgb1b901e">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (9.49)</li>
|
<li>Gr (9.49)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1724,7 +1724,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1641,18 +1641,18 @@ These take the form of coupled first-order partial differential equations for \(
|
||||||
Since \({\boldsymbol \nabla} \cdot {\bf E} = 0\) and \({\boldsymbol \nabla} \cdot {\bf B} = 0\),
|
Since \({\boldsymbol \nabla} \cdot {\bf E} = 0\) and \({\boldsymbol \nabla} \cdot {\bf B} = 0\),
|
||||||
we get the
|
we get the
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org0b3ebdc">
|
<div class="core div" id="orge19d256">
|
||||||
<p>
|
<p>
|
||||||
<b>Wave equations for electric and magnetic fields in vacuum</b>
|
<b>Wave equations for electric and magnetic fields in vacuum</b>
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="orge465a34">
|
<div class="eqlabel" id="orgff19c15">
|
||||||
<p>
|
<p>
|
||||||
<a id="WaveEq"></a><a href="./emd_emw_we.html#WaveEq"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="WaveEq"></a><a href="./emd_emw_we.html#WaveEq"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org3ff5ea0">
|
<div class="alteqlabels" id="orga8c7165">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (9.41)</li>
|
<li>Gr (9.41)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1714,7 +1714,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1638,7 +1638,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1638,7 +1638,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1648,18 +1648,18 @@ dI = \frac{\partial \sigma_b}{\partial t} da_{\perp} = \frac{\partial P}{\partia
|
||||||
\]
|
\]
|
||||||
We therefore have the
|
We therefore have the
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org64396a0">
|
<div class="core div" id="orgc00904a">
|
||||||
<p>
|
<p>
|
||||||
<b>Polarization current density</b>
|
<b>Polarization current density</b>
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="orgf37fc4f">
|
<div class="eqlabel" id="org3742df8">
|
||||||
<p>
|
<p>
|
||||||
<a id="Jp"></a><a href="./emdm_Me_Mem.html#Jp"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Jp"></a><a href="./emdm_Me_Mem.html#Jp"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org12af1ad">
|
<div class="alteqlabels" id="org6073635">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (7.48)</li>
|
<li>Gr (7.48)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1683,7 +1683,7 @@ the polarization current is the result of linear motion of charge when
|
||||||
polarization changes). We can check consistency with the continuity equation
|
polarization changes). We can check consistency with the continuity equation
|
||||||
associated to the conservation of bound charges:
|
associated to the conservation of bound charges:
|
||||||
</p>
|
</p>
|
||||||
<aside id="org0322793">
|
<aside id="orgff2c75f">
|
||||||
<p>
|
<p>
|
||||||
Note the unfortunate labelling: it would have been nicer to have \(\rho_b\) be the charge associated to current \({\boldsymbol J}_b\) but this is not the common convention.
|
Note the unfortunate labelling: it would have been nicer to have \(\rho_b\) be the charge associated to current \({\boldsymbol J}_b\) but this is not the common convention.
|
||||||
</p>
|
</p>
|
||||||
|
|
@ -1705,15 +1705,15 @@ Changing magnetization does not lead to analogous accumulation of charge and cur
|
||||||
In view of this: total charge density can be separated into 2 parts,
|
In view of this: total charge density can be separated into 2 parts,
|
||||||
<b>free</b> and <b>bound</b>:
|
<b>free</b> and <b>bound</b>:
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="org56027a6">
|
<div class="main div" id="org7866a36">
|
||||||
<div class="eqlabel" id="org6fd2aed">
|
<div class="eqlabel" id="orge94a27e">
|
||||||
<p>
|
<p>
|
||||||
<a id="rhofb"></a><a href="./emdm_Me_Mem.html#rhofb"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="rhofb"></a><a href="./emdm_Me_Mem.html#rhofb"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org9e03f13">
|
<div class="alteqlabels" id="orgbb91da6">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (7.49)</li>
|
<li>Gr (7.49)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1733,15 +1733,15 @@ In view of this: total charge density can be separated into 2 parts,
|
||||||
and current can be separated into three parts, <b>free</b>, <b>bound</b> and
|
and current can be separated into three parts, <b>free</b>, <b>bound</b> and
|
||||||
<b>polarization</b>:
|
<b>polarization</b>:
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="org96443a3">
|
<div class="main div" id="org765eeee">
|
||||||
<div class="eqlabel" id="orga6b8e4a">
|
<div class="eqlabel" id="org49803b2">
|
||||||
<p>
|
<p>
|
||||||
<a id="Jfbp"></a><a href="./emdm_Me_Mem.html#Jfbp"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Jfbp"></a><a href="./emdm_Me_Mem.html#Jfbp"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orgddcfaf9">
|
<div class="alteqlabels" id="orgc87ffc7">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (7.50)</li>
|
<li>Gr (7.50)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1767,7 +1767,7 @@ Gauss's law: can be rewritten
|
||||||
\]
|
\]
|
||||||
where (as in static case)
|
where (as in static case)
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="orgdbd92f1">
|
<div class="core div" id="org91a1e38">
|
||||||
<p>
|
<p>
|
||||||
\[
|
\[
|
||||||
{\bf D} \equiv \varepsilon_0 {\bf E} + {\bf P}
|
{\bf D} \equiv \varepsilon_0 {\bf E} + {\bf P}
|
||||||
|
|
@ -1788,7 +1788,7 @@ or
|
||||||
\]
|
\]
|
||||||
where as before
|
where as before
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org7839f4c">
|
<div class="core div" id="org0c2e84f">
|
||||||
<p>
|
<p>
|
||||||
\[
|
\[
|
||||||
{\bf H} \equiv \frac{1}{\mu_0} {\bf B} - {\bf M}
|
{\bf H} \equiv \frac{1}{\mu_0} {\bf B} - {\bf M}
|
||||||
|
|
@ -1806,18 +1806,18 @@ bound parts, since they don't involve \(\rho\) or \({\bf J}\).
|
||||||
<p>
|
<p>
|
||||||
In terms of free charges and currents, we thus get
|
In terms of free charges and currents, we thus get
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org6597738">
|
<div class="core div" id="orgeeb0b35">
|
||||||
<p>
|
<p>
|
||||||
<b>Maxwell's equations</b> <i>(in matter)</i>
|
<b>Maxwell's equations</b> <i>(in matter)</i>
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="orgffcbbe9">
|
<div class="eqlabel" id="orgb9e6675">
|
||||||
<p>
|
<p>
|
||||||
<a id="Max_mat"></a><a href="./emdm_Me_Mem.html#Max_mat"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Max_mat"></a><a href="./emdm_Me_Mem.html#Max_mat"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org5c6c62d">
|
<div class="alteqlabels" id="org6367cef">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (7.55)</li>
|
<li>Gr (7.55)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1847,15 +1847,15 @@ This must all be complemented by the <b>constitutive relations</b> giving \({\bf
|
||||||
in terms of \({\bf E}\) and \({\bf B}\).
|
in terms of \({\bf E}\) and \({\bf B}\).
|
||||||
For the restricted case of linear media:
|
For the restricted case of linear media:
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="org2d4f8dd">
|
<div class="main div" id="orgd78e0b5">
|
||||||
<div class="eqlabel" id="org03c06a4">
|
<div class="eqlabel" id="org86e1a29">
|
||||||
<p>
|
<p>
|
||||||
<a id="consrel"></a><a href="./emdm_Me_Mem.html#consrel"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="consrel"></a><a href="./emdm_Me_Mem.html#consrel"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org45b4fff">
|
<div class="alteqlabels" id="org7ea2c8c">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (7.56,7.57)</li>
|
<li>Gr (7.56,7.57)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1898,7 +1898,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1616,18 +1616,18 @@ Table of contents
|
||||||
<p>
|
<p>
|
||||||
Discontinuities between different media, deduced from
|
Discontinuities between different media, deduced from
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="orgb7aedd2">
|
<div class="core div" id="org876a60b">
|
||||||
<p>
|
<p>
|
||||||
<b>Maxwell's equations</b> <i>(in matter)</i>, <i>integral form</i>
|
<b>Maxwell's equations</b> <i>(in matter)</i>, <i>integral form</i>
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org6c267cc">
|
<div class="eqlabel" id="orga776629">
|
||||||
<p>
|
<p>
|
||||||
<a id="Max_mat_int"></a><a href="./emdm_Me_bc.html#Max_mat_int"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Max_mat_int"></a><a href="./emdm_Me_bc.html#Max_mat_int"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org8952960">
|
<div class="alteqlabels" id="org6c05186">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1645,15 +1645,15 @@ Discontinuities between different media, deduced from
|
||||||
Applying \((i)\) to wafer-thin Gaussian pillbox straddling boundary between 2 materials:
|
Applying \((i)\) to wafer-thin Gaussian pillbox straddling boundary between 2 materials:
|
||||||
\({\bf D}_1 \cdot {\bf a} - {\bf D}_2 \cdot {\bf a} = \sigma_f a\) so
|
\({\bf D}_1 \cdot {\bf a} - {\bf D}_2 \cdot {\bf a} = \sigma_f a\) so
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="orgf92353e">
|
<div class="main div" id="org8d20540">
|
||||||
<div class="eqlabel" id="orgb9a9a3d">
|
<div class="eqlabel" id="org7926d65">
|
||||||
<p>
|
<p>
|
||||||
<a id="Ddisc"></a><a href="./emdm_Me_bc.html#Ddisc"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Ddisc"></a><a href="./emdm_Me_bc.html#Ddisc"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orga6c409d">
|
<div class="alteqlabels" id="orge1fcf9c">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (7.60)</li>
|
<li>Gr (7.60)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1672,9 +1672,9 @@ D^{\perp}_1 - D^{\perp}_2 = \sigma_f
|
||||||
<p>
|
<p>
|
||||||
Same reasoning applied to \((ii)\) gives <a href="./ems_ms_vp_mbc.html#Bdisc">Bdisc</a>
|
Same reasoning applied to \((ii)\) gives <a href="./ems_ms_vp_mbc.html#Bdisc">Bdisc</a>
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="orga22be6d">
|
<div class="main div" id="orgfa3145b">
|
||||||
<div class="eqlabel" id="orge0d8321">
|
<div class="eqlabel" id="orgddc00f3">
|
||||||
<div class="alteqlabels" id="orgb94a831">
|
<div class="alteqlabels" id="org80b4003">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1690,7 +1690,7 @@ B^{\perp}_1 - B^{\perp}_2 = 0
|
||||||
For \((iii)\): Amperian loop straddling surface: \({\bf E}_1 \cdot {\bf l} - {\bf E}_2 \cdot {\bf l} =
|
For \((iii)\): Amperian loop straddling surface: \({\bf E}_1 \cdot {\bf l} - {\bf E}_2 \cdot {\bf l} =
|
||||||
-\frac{d}{dt} \int_{\cal S} {\bf B} \cdot d{\bf a}\). Limit of small loop: flux vanishes, therefore
|
-\frac{d}{dt} \int_{\cal S} {\bf B} \cdot d{\bf a}\). Limit of small loop: flux vanishes, therefore
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="org55a1d42">
|
<div class="main div" id="org2dd2bbb">
|
||||||
<p>
|
<p>
|
||||||
\[
|
\[
|
||||||
{\bf E}_1^{\parallel} - {\bf E}_2^{\parallel} = 0
|
{\bf E}_1^{\parallel} - {\bf E}_2^{\parallel} = 0
|
||||||
|
|
@ -1704,7 +1704,7 @@ No volume current can contribute, but a surface current can. Can write
|
||||||
\(I_{f_{enc}} = {\bf K}_f \cdot (\hat{\bf n} \times {\bf l}) = ({\bf K}_f \times \hat{\bf n}) \cdot {\bf l}\)
|
\(I_{f_{enc}} = {\bf K}_f \cdot (\hat{\bf n} \times {\bf l}) = ({\bf K}_f \times \hat{\bf n}) \cdot {\bf l}\)
|
||||||
and thus (as we got before in <a href="./emsm_msm_H_A.html#Hdisc">Hdisc</a>)
|
and thus (as we got before in <a href="./emsm_msm_H_A.html#Hdisc">Hdisc</a>)
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="org4a2ee70">
|
<div class="main div" id="orgd223e2f">
|
||||||
<p>
|
<p>
|
||||||
\[
|
\[
|
||||||
{\bf H}_1^{\parallel} - {\bf H}_2^{\parallel} = {\bf K}_f \times \hat{\bf n}
|
{\bf H}_1^{\parallel} - {\bf H}_2^{\parallel} = {\bf K}_f \times \hat{\bf n}
|
||||||
|
|
@ -1720,15 +1720,15 @@ These are the general boundary conditions for electrodynamics.
|
||||||
<p>
|
<p>
|
||||||
In case of linear media: can be expressed in terms of \({\bf E}\) and \({\bf B}\) alone:
|
In case of linear media: can be expressed in terms of \({\bf E}\) and \({\bf B}\) alone:
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="org9e90e47">
|
<div class="main div" id="orgaafde6e">
|
||||||
<div class="eqlabel" id="org8bbc727">
|
<div class="eqlabel" id="orge514e83">
|
||||||
<p>
|
<p>
|
||||||
<a id="disc_lm"></a><a href="./emdm_Me_bc.html#disc_lm"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="disc_lm"></a><a href="./emdm_Me_bc.html#disc_lm"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orga51b616">
|
<div class="alteqlabels" id="org786e6ec">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (7.64)</li>
|
<li>Gr (7.64)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1748,14 +1748,14 @@ In case of linear media: can be expressed in terms of \({\bf E}\) and \({\bf B}
|
||||||
<p>
|
<p>
|
||||||
If there is no free charge and no free current at boundary:
|
If there is no free charge and no free current at boundary:
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="orgf07dc3e">
|
<div class="eqlabel" id="orga74521d">
|
||||||
<p>
|
<p>
|
||||||
<a id="disc_nfc"></a><a href="./emdm_Me_bc.html#disc_nfc"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="disc_nfc"></a><a href="./emdm_Me_bc.html#disc_nfc"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orgdd74046">
|
<div class="alteqlabels" id="orgac68624">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (7.64)</li>
|
<li>Gr (7.64)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1792,7 +1792,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1614,8 +1614,8 @@ Table of contents
|
||||||
</svg></a><span class="headline-id">emdm.emwm</span></h3>
|
</svg></a><span class="headline-id">emdm.emwm</span></h3>
|
||||||
|
|
||||||
<div class="outline-text-3" id="text-emdm_emwm">
|
<div class="outline-text-3" id="text-emdm_emwm">
|
||||||
<details class="prereq" id="org5c9f997">
|
<details class="prereq" id="org499ec58">
|
||||||
<summary id="orgcac0ec5">
|
<summary id="org504cdbb">
|
||||||
Prerequisites
|
Prerequisites
|
||||||
</summary>
|
</summary>
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
|
|
@ -1625,8 +1625,8 @@ Prerequisites
|
||||||
</ul>
|
</ul>
|
||||||
</details>
|
</details>
|
||||||
|
|
||||||
<details class="objectives" id="orgde042c7">
|
<details class="objectives" id="org76e4576">
|
||||||
<summary id="org6ca3c40">
|
<summary id="org77d80f7">
|
||||||
Objectives
|
Objectives
|
||||||
</summary>
|
</summary>
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
|
|
@ -1666,7 +1666,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1637,7 +1637,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1733,7 +1733,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1632,15 +1632,15 @@ For linear medium:
|
||||||
\]
|
\]
|
||||||
If the medium is homogeneous (no spatial dependence of \(\varepsilon\) or \(\mu\)),
|
If the medium is homogeneous (no spatial dependence of \(\varepsilon\) or \(\mu\)),
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="org3abedbf">
|
<div class="main div" id="orgead2b1c">
|
||||||
<div class="eqlabel" id="org6c3c992">
|
<div class="eqlabel" id="org9916855">
|
||||||
<p>
|
<p>
|
||||||
<a id="Max_lh"></a><a href="./emdm_emwm_plm.html#Max_lh"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Max_lh"></a><a href="./emdm_emwm_plm.html#Max_lh"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org4747e62">
|
<div class="alteqlabels" id="org5111273">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (9.65)</li>
|
<li>Gr (9.65)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1669,18 +1669,18 @@ v = \frac{1}{\sqrt{\mu \varepsilon}} = \frac{c}{n}
|
||||||
\]
|
\]
|
||||||
where the index of refraction of the material is defined as
|
where the index of refraction of the material is defined as
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="org92a77a7">
|
<div class="main div" id="org5237a1a">
|
||||||
<p>
|
<p>
|
||||||
<b>Index of refraction</b>
|
<b>Index of refraction</b>
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="orgb3ac891">
|
<div class="eqlabel" id="org6cb7362">
|
||||||
<p>
|
<p>
|
||||||
<a id="n"></a><a href="./emdm_emwm_plm.html#n"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="n"></a><a href="./emdm_emwm_plm.html#n"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orge10b1d5">
|
<div class="alteqlabels" id="orgc12f464">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (9.69)</li>
|
<li>Gr (9.69)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1743,7 +1743,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1649,7 +1649,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1671,14 +1671,14 @@ E_{0_I} - E_{0_R} = \beta E_{0_T}, \hspace{1cm}
|
||||||
Solving these coupled equations, we can write
|
Solving these coupled equations, we can write
|
||||||
outgoing amplitudes in terms of incident ones:
|
outgoing amplitudes in terms of incident ones:
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org0451818">
|
<div class="eqlabel" id="orgf6ae25d">
|
||||||
<p>
|
<p>
|
||||||
<a id="ERT"></a><a href="./emdm_emwm_refl_ni.html#ERT"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="ERT"></a><a href="./emdm_emwm_refl_ni.html#ERT"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orgca80cb9">
|
<div class="alteqlabels" id="org17eb76a">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (9.82)</li>
|
<li>Gr (9.82)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1744,7 +1744,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1635,14 +1635,14 @@ Transmitted wave:
|
||||||
\]
|
\]
|
||||||
All waves have the same frequency \(\omega\). Since \(\omega = k v\), the three wavevectors are related by
|
All waves have the same frequency \(\omega\). Since \(\omega = k v\), the three wavevectors are related by
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="orgd898837">
|
<div class="eqlabel" id="org512368e">
|
||||||
<p>
|
<p>
|
||||||
<a id="RTobliquek"></a><a href="./emdm_emwm_refl_oi.html#RTobliquek"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="RTobliquek"></a><a href="./emdm_emwm_refl_oi.html#RTobliquek"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orgabe9175">
|
<div class="alteqlabels" id="org1361b67">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1665,7 +1665,7 @@ These forms for incident, reflected and transmitted wave can be substituted in t
|
||||||
<p>
|
<p>
|
||||||
From now on we will orient the axes so that \({\boldsymbol k}_I\) lies in the \(xz\) plane. This means that \({\boldsymbol k}_R\) and \({\boldsymbol k}_T\) also lie in that plane. This is the
|
From now on we will orient the axes so that \({\boldsymbol k}_I\) lies in the \(xz\) plane. This means that \({\boldsymbol k}_R\) and \({\boldsymbol k}_T\) also lie in that plane. This is the
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org4e7e42a">
|
<div class="core div" id="org86dbe79">
|
||||||
<p>
|
<p>
|
||||||
<b>First law of reflection:</b>
|
<b>First law of reflection:</b>
|
||||||
the incident, reflected and transmitted wave vectors form a plane (called the plane of incidence) which also includes the normal to the surface.
|
the incident, reflected and transmitted wave vectors form a plane (called the plane of incidence) which also includes the normal to the surface.
|
||||||
|
|
@ -1680,7 +1680,7 @@ Specializing <a href="./emdm_emwm_refl_oi.html#RTobliquek">RTobliquek</a> to our
|
||||||
with the incidence (\(\theta_I\)) and reflection (\(\theta_R\)) angles
|
with the incidence (\(\theta_I\)) and reflection (\(\theta_R\)) angles
|
||||||
and the angle of refraction (\(\theta_T\)) obey the following laws:
|
and the angle of refraction (\(\theta_T\)) obey the following laws:
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org99d6843">
|
<div class="core div" id="orge55fc76">
|
||||||
<p>
|
<p>
|
||||||
<b>Law of reflection</b>
|
<b>Law of reflection</b>
|
||||||
\[
|
\[
|
||||||
|
|
@ -1697,14 +1697,14 @@ and the angle of refraction (\(\theta_T\)) obey the following laws:
|
||||||
<p>
|
<p>
|
||||||
This takes care of the spatially-dependent exponential factors in the boundary conditions. The coefficients must further obey
|
This takes care of the spatially-dependent exponential factors in the boundary conditions. The coefficients must further obey
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="orgdc0e7b2">
|
<div class="eqlabel" id="orga2e8f02">
|
||||||
<p>
|
<p>
|
||||||
<a id="EBRT"></a><a href="./emdm_emwm_refl_oi.html#EBRT"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="EBRT"></a><a href="./emdm_emwm_refl_oi.html#EBRT"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org6d39cd4">
|
<div class="alteqlabels" id="org12decff">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1750,18 +1750,18 @@ while the third equation becomes
|
||||||
\]
|
\]
|
||||||
Writing everything in terms of the incident amplitude, we get
|
Writing everything in terms of the incident amplitude, we get
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="org1929cd0">
|
<div class="main div" id="org29006a2">
|
||||||
<p>
|
<p>
|
||||||
<b>Fresnel's equations for reflection and transmission amplitudes (parallel case)</b>
|
<b>Fresnel's equations for reflection and transmission amplitudes (parallel case)</b>
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org0b8be69">
|
<div class="eqlabel" id="orgd431e6b">
|
||||||
<p>
|
<p>
|
||||||
<a id="Fresnel"></a><a href="./emdm_emwm_refl_oi.html#Fresnel"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Fresnel"></a><a href="./emdm_emwm_refl_oi.html#Fresnel"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org617a8e4">
|
<div class="alteqlabels" id="orgd3db507">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1785,15 +1785,15 @@ Amplitudes for transmitted and reflected wave: depend on angle of incidence:
|
||||||
Behaviour: for \(\theta_I = 0\) we recover <a href="./emdm_emwm_refl_ni.html#ERT">ERT</a>.
|
Behaviour: for \(\theta_I = 0\) we recover <a href="./emdm_emwm_refl_ni.html#ERT">ERT</a>.
|
||||||
For grazing waves \(\theta_I \rightarrow \pi/2\) we have that \(\alpha \rightarrow \infty\) and the wave is totally reflected. The most interesting angle is the one at which \(\alpha = \beta\) and the reflected wave has zero amplitude. This is known as
|
For grazing waves \(\theta_I \rightarrow \pi/2\) we have that \(\alpha \rightarrow \infty\) and the wave is totally reflected. The most interesting angle is the one at which \(\alpha = \beta\) and the reflected wave has zero amplitude. This is known as
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="org087c316">
|
<div class="main div" id="orgff8c46e">
|
||||||
<div class="eqlabel" id="orgb61a423">
|
<div class="eqlabel" id="org7aac922">
|
||||||
<p>
|
<p>
|
||||||
<a id="Brewster"></a><a href="./emdm_emwm_refl_oi.html#Brewster"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Brewster"></a><a href="./emdm_emwm_refl_oi.html#Brewster"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org4e4ad5e">
|
<div class="alteqlabels" id="orgb13b73c">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1846,7 +1846,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1633,7 +1633,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1639,7 +1639,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1659,7 +1659,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1683,7 +1683,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1693,7 +1693,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1614,8 +1614,8 @@ Table of contents
|
||||||
</svg></a><span class="headline-id">emf</span></h2>
|
</svg></a><span class="headline-id">emf</span></h2>
|
||||||
|
|
||||||
<div class="outline-text-2" id="text-emf">
|
<div class="outline-text-2" id="text-emf">
|
||||||
<details class="prereq" id="org85fb173">
|
<details class="prereq" id="orgb4e149b">
|
||||||
<summary id="orgdb11421">
|
<summary id="org0aed1f7">
|
||||||
Prerequisites
|
Prerequisites
|
||||||
</summary>
|
</summary>
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
|
|
@ -1623,8 +1623,8 @@ Prerequisites
|
||||||
</ul>
|
</ul>
|
||||||
</details>
|
</details>
|
||||||
|
|
||||||
<details class="objectives" id="orga59b9df">
|
<details class="objectives" id="org55d6b09">
|
||||||
<summary id="orgf26745f">
|
<summary id="org287324e">
|
||||||
Objectives
|
Objectives
|
||||||
</summary>
|
</summary>
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
|
|
@ -1660,7 +1660,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1657,7 +1657,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1656,7 +1656,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1616,14 +1616,14 @@ Table of contents
|
||||||
<p>
|
<p>
|
||||||
A more aesthetic choice is the <b>Lorenz gauge</b>:
|
A more aesthetic choice is the <b>Lorenz gauge</b>:
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="orgb29b121">
|
<div class="eqlabel" id="org3de3f9b">
|
||||||
<p>
|
<p>
|
||||||
<a id="LorenzG"></a><a href="./emf_g_Lg.html#LorenzG"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="LorenzG"></a><a href="./emf_g_Lg.html#LorenzG"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org2006eb5">
|
<div class="alteqlabels" id="orgc9fe8ca">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1635,14 +1635,14 @@ A more aesthetic choice is the <b>Lorenz gauge</b>:
|
||||||
\]
|
\]
|
||||||
which is chosen to put the second term in the left-hand side of <a href="./emf_svp.html#LapA">LapA</a> to zero. What remains is then
|
which is chosen to put the second term in the left-hand side of <a href="./emf_svp.html#LapA">LapA</a> to zero. What remains is then
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="orgcba4a5d">
|
<div class="eqlabel" id="org5b3094e">
|
||||||
<p>
|
<p>
|
||||||
<a id="ALorenzG"></a><a href="./emf_g_Lg.html#ALorenzG"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="ALorenzG"></a><a href="./emf_g_Lg.html#ALorenzG"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org2d4cecb">
|
<div class="alteqlabels" id="org687131e">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1654,14 +1654,14 @@ which is chosen to put the second term in the left-hand side of <a href="./emf_s
|
||||||
\]
|
\]
|
||||||
while the equation for \(\phi\) becomes
|
while the equation for \(\phi\) becomes
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org7c6aebc">
|
<div class="eqlabel" id="org29d69e0">
|
||||||
<p>
|
<p>
|
||||||
<a id="phiLorenzG"></a><a href="./emf_g_Lg.html#phiLorenzG"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="phiLorenzG"></a><a href="./emf_g_Lg.html#phiLorenzG"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org8b3cda4">
|
<div class="alteqlabels" id="org4856773">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1673,18 +1673,18 @@ while the equation for \(\phi\) becomes
|
||||||
\]
|
\]
|
||||||
These can be written compactly upon introducing a new operator: the
|
These can be written compactly upon introducing a new operator: the
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="orgd056ba8">
|
<div class="core div" id="orga269826">
|
||||||
<p>
|
<p>
|
||||||
<b>d'Alembertian operator</b>
|
<b>d'Alembertian operator</b>
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="orgfd937d0">
|
<div class="eqlabel" id="org39fa795">
|
||||||
<p>
|
<p>
|
||||||
<a id="dAl"></a><a href="./emf_g_Lg.html#dAl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="dAl"></a><a href="./emf_g_Lg.html#dAl"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org57101d6">
|
<div class="alteqlabels" id="orgf4aa848">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1700,18 +1700,18 @@ These can be written compactly upon introducing a new operator: the
|
||||||
<p>
|
<p>
|
||||||
so we get the
|
so we get the
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org037b830">
|
<div class="core div" id="org65e01f8">
|
||||||
<p>
|
<p>
|
||||||
<b>Inhomogeneous Maxwell equations</b> <i>(Lorenz gauge)</i>
|
<b>Inhomogeneous Maxwell equations</b> <i>(Lorenz gauge)</i>
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org9dce32f">
|
<div class="eqlabel" id="orgc262f70">
|
||||||
<p>
|
<p>
|
||||||
<a id="MaxLor"></a><a href="./emf_g_Lg.html#MaxLor"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="MaxLor"></a><a href="./emf_g_Lg.html#MaxLor"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org22f6c85">
|
<div class="alteqlabels" id="orgc540066">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1764,7 +1764,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1631,7 +1631,7 @@ Useful strategy: represent fields in terms of potentials.
|
||||||
Easiest: as we already saw (<a href="./ems_ms_vp_A.html#BcurlA">BcurlA</a>), we can write the magnetic
|
Easiest: as we already saw (<a href="./ems_ms_vp_A.html#BcurlA">BcurlA</a>), we can write the magnetic
|
||||||
field as a pure curl (since its divergence always vanishes):
|
field as a pure curl (since its divergence always vanishes):
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org0868f0a">
|
<div class="core div" id="org913ae4e">
|
||||||
<p>
|
<p>
|
||||||
\[
|
\[
|
||||||
{\boldsymbol B} = {\boldsymbol \nabla} \times {\boldsymbol A}
|
{\boldsymbol B} = {\boldsymbol \nabla} \times {\boldsymbol A}
|
||||||
|
|
@ -1648,15 +1648,15 @@ Putting this into Faraday's law <a href="./emd_Fl_Fl.html#Fl">Fl</a> gives
|
||||||
so this can be written as the gradient of a scalar.
|
so this can be written as the gradient of a scalar.
|
||||||
Making the choice \(-{\boldsymbol \nabla} \phi\) for this, we get
|
Making the choice \(-{\boldsymbol \nabla} \phi\) for this, we get
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org5ea4990">
|
<div class="core div" id="orgcc3047e">
|
||||||
<div class="eqlabel" id="orgccc2c0e">
|
<div class="eqlabel" id="org50da26e">
|
||||||
<p>
|
<p>
|
||||||
<a id="E_phiA"></a><a href="./emf_svp.html#E_phiA"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="E_phiA"></a><a href="./emf_svp.html#E_phiA"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orgc2e0dbe">
|
<div class="alteqlabels" id="org3a04a5a">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1673,15 +1673,15 @@ Making the choice \(-{\boldsymbol \nabla} \phi\) for this, we get
|
||||||
<p>
|
<p>
|
||||||
Using this potential representation for \({\boldsymbol E}\) and \({\boldsymbol B}\) automatically fulfills the two homogeneous Maxwell equations. For the inhomogeneous equations, substituting <a href="./emf_svp.html#E_phiA">E_phiA</a> into Gauss's law gives
|
Using this potential representation for \({\boldsymbol E}\) and \({\boldsymbol B}\) automatically fulfills the two homogeneous Maxwell equations. For the inhomogeneous equations, substituting <a href="./emf_svp.html#E_phiA">E_phiA</a> into Gauss's law gives
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="org7ca77db">
|
<div class="main div" id="orge407b00">
|
||||||
<div class="eqlabel" id="org49309f0">
|
<div class="eqlabel" id="orgad33676">
|
||||||
<p>
|
<p>
|
||||||
<a id="Lapphi"></a><a href="./emf_svp.html#Lapphi"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Lapphi"></a><a href="./emf_svp.html#Lapphi"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org1b03eff">
|
<div class="alteqlabels" id="org4f2824a">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1701,15 +1701,15 @@ whereas Ampère-Maxwell becomes
|
||||||
\]
|
\]
|
||||||
which becomes after simple rearrangement and use of the <a href="./c_m_dc_d2.html#curlcurl">curlcurl</a> identity \({\boldsymbol \nabla} \times \left({\boldsymbol \nabla} \times {\boldsymbol A}\right) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\boldsymbol A}) - {\boldsymbol \nabla}^2 {\boldsymbol A}\),
|
which becomes after simple rearrangement and use of the <a href="./c_m_dc_d2.html#curlcurl">curlcurl</a> identity \({\boldsymbol \nabla} \times \left({\boldsymbol \nabla} \times {\boldsymbol A}\right) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\boldsymbol A}) - {\boldsymbol \nabla}^2 {\boldsymbol A}\),
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="org930bf11">
|
<div class="main div" id="orga4d93c1">
|
||||||
<div class="eqlabel" id="org7818374">
|
<div class="eqlabel" id="orgbbedeec">
|
||||||
<p>
|
<p>
|
||||||
<a id="LapA"></a><a href="./emf_svp.html#LapA"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="LapA"></a><a href="./emf_svp.html#LapA"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org9e9918d">
|
<div class="alteqlabels" id="orgb9a7aee">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1744,7 +1744,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1640,7 +1640,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1618,8 +1618,8 @@ Table of contents
|
||||||
<li>Gr 3</li>
|
<li>Gr 3</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
||||||
<details class="prereq" id="orgd0e4e8d">
|
<details class="prereq" id="org587aea3">
|
||||||
<summary id="org949c0df">
|
<summary id="orgf03fd4d">
|
||||||
Prerequisites
|
Prerequisites
|
||||||
</summary>
|
</summary>
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
|
|
@ -1627,8 +1627,8 @@ Prerequisites
|
||||||
</ul>
|
</ul>
|
||||||
</details>
|
</details>
|
||||||
|
|
||||||
<details class="objectives" id="orgfb8d074">
|
<details class="objectives" id="orgedf1d47">
|
||||||
<summary id="org39be3a5">
|
<summary id="orgbfc64ab">
|
||||||
Objectives
|
Objectives
|
||||||
</summary>
|
</summary>
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
|
|
@ -1666,7 +1666,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1624,7 +1624,7 @@ A generic configuration of static charges coupled via the Coulomb interaction
|
||||||
defines an electrostatic problem, whose solution is in principle obtained
|
defines an electrostatic problem, whose solution is in principle obtained
|
||||||
from calculating either the field according to <a href="./ems_es_ef_ccd.html#E_vcd">E_vcd</a>
|
from calculating either the field according to <a href="./ems_es_ef_ccd.html#E_vcd">E_vcd</a>
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="org8236a16">
|
<div class="main div" id="orgce1c4bf">
|
||||||
<p>
|
<p>
|
||||||
|
|
||||||
</p>
|
</p>
|
||||||
|
|
@ -1638,7 +1638,7 @@ from calculating either the field according to <a href="./ems_es_ef_ccd.html#E_v
|
||||||
or (often simpler) by calculating the electrostatic potential, using either the
|
or (often simpler) by calculating the electrostatic potential, using either the
|
||||||
explicit construction <a href="./ems_es_ep_d.html#p_vcd">p_vcd</a>
|
explicit construction <a href="./ems_es_ep_d.html#p_vcd">p_vcd</a>
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="orgd333b49">
|
<div class="main div" id="orge8cb758">
|
||||||
<p>
|
<p>
|
||||||
|
|
||||||
</p>
|
</p>
|
||||||
|
|
@ -1658,7 +1658,7 @@ condition <a href="./ems_es_ef_cE.html#curlE0">curlE0</a> can be expressed as th
|
||||||
<a href="./ems_es_ep_PL.html#Poi">🐟</a>
|
<a href="./ems_es_ep_PL.html#Poi">🐟</a>
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="core div" id="orge399a4f">
|
<div class="core div" id="org65cda5b">
|
||||||
<p>
|
<p>
|
||||||
|
|
||||||
</p>
|
</p>
|
||||||
|
|
@ -1674,7 +1674,7 @@ condition <a href="./ems_es_ef_cE.html#curlE0">curlE0</a> can be expressed as th
|
||||||
<p>
|
<p>
|
||||||
In the specific case where the charge density vanishes, we fall back onto the simpler Laplace equation <a href="./ems_es_ep_PL.html#Lap">Lap</a>
|
In the specific case where the charge density vanishes, we fall back onto the simpler Laplace equation <a href="./ems_es_ep_PL.html#Lap">Lap</a>
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="orgea54c28">
|
<div class="core div" id="org9318a15">
|
||||||
<p>
|
<p>
|
||||||
|
|
||||||
</p>
|
</p>
|
||||||
|
|
@ -1712,7 +1712,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1630,14 +1630,14 @@ In one dimension, the potential is a single-variable
|
||||||
function \(\phi (x)\) and the Laplace equation reads
|
function \(\phi (x)\) and the Laplace equation reads
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="eqlabel" id="orgd14f5e0">
|
<div class="eqlabel" id="orgd38ad90">
|
||||||
<p>
|
<p>
|
||||||
<a id="Lap_1d"></a><a href="./ems_ca_fe_L.html#Lap_1d"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Lap_1d"></a><a href="./ems_ca_fe_L.html#Lap_1d"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orgdd168eb">
|
<div class="alteqlabels" id="org23686dc">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1652,14 +1652,14 @@ function \(\phi (x)\) and the Laplace equation reads
|
||||||
<p>
|
<p>
|
||||||
The solution to this is
|
The solution to this is
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org9e3195b">
|
<div class="eqlabel" id="org78665cb">
|
||||||
<p>
|
<p>
|
||||||
<a id="Lap_1d_sol"></a><a href="./ems_ca_fe_L.html#Lap_1d_sol"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Lap_1d_sol"></a><a href="./ems_ca_fe_L.html#Lap_1d_sol"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org7a39d73">
|
<div class="alteqlabels" id="orge0dbdb5">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (3.6)</li>
|
<li>Gr (3.6)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1718,14 +1718,14 @@ In two dimensions, the potential becomes a function
|
||||||
of two variables (here: \(x\) and \(y\)), so Laplace's
|
of two variables (here: \(x\) and \(y\)), so Laplace's
|
||||||
equation now reads
|
equation now reads
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org01996f8">
|
<div class="eqlabel" id="orgd4e7f28">
|
||||||
<p>
|
<p>
|
||||||
<a id="Lap_2d"></a><a href="./ems_ca_fe_L.html#Lap_2d"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Lap_2d"></a><a href="./ems_ca_fe_L.html#Lap_2d"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org518eefc">
|
<div class="alteqlabels" id="orga64f9ad">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1778,14 +1778,14 @@ a point equals its value averaged over a sphere
|
||||||
\(S_R({\bf r})\) of any radius \(R\) centered on this point
|
\(S_R({\bf r})\) of any radius \(R\) centered on this point
|
||||||
(and of course not containing any charges),
|
(and of course not containing any charges),
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org1ec3447">
|
<div class="eqlabel" id="org598b2e6">
|
||||||
<p>
|
<p>
|
||||||
<a id="p_ball_avg"></a><a href="./ems_ca_fe_L.html#p_ball_avg"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="p_ball_avg"></a><a href="./ems_ca_fe_L.html#p_ball_avg"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org832c6a2">
|
<div class="alteqlabels" id="orgdb48832">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1797,8 +1797,8 @@ a point equals its value averaged over a sphere
|
||||||
\]
|
\]
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<details id="org653c3ca">
|
<details id="orgd997cbe">
|
||||||
<summary id="org9063816">
|
<summary id="org6b22e3f">
|
||||||
<strong>Physicist's proof</strong>
|
<strong>Physicist's proof</strong>
|
||||||
</summary>
|
</summary>
|
||||||
<p>
|
<p>
|
||||||
|
|
@ -1860,8 +1860,8 @@ proving the theorem.
|
||||||
</p>
|
</p>
|
||||||
</details>
|
</details>
|
||||||
|
|
||||||
<details id="org086b4a6">
|
<details id="org2ff5eec">
|
||||||
<summary id="orgd2d3c6e">
|
<summary id="orgc0446a1">
|
||||||
<strong>Formal proof</strong>
|
<strong>Formal proof</strong>
|
||||||
</summary>
|
</summary>
|
||||||
|
|
||||||
|
|
@ -1911,14 +1911,14 @@ we get the following general
|
||||||
<p>
|
<p>
|
||||||
<b>Theorem</b>:
|
<b>Theorem</b>:
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org6d0244a">
|
<div class="eqlabel" id="orge37257a">
|
||||||
<p>
|
<p>
|
||||||
<a id="dfdR_intLap"></a><a href="./ems_ca_fe_L.html#dfdR_intLap"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="dfdR_intLap"></a><a href="./ems_ca_fe_L.html#dfdR_intLap"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org227c883">
|
<div class="alteqlabels" id="orgb3a7f07">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1971,19 +1971,19 @@ are necessarily positive, we thus require \(f_x > 0\), \(f_y > 0\) and \(f
|
||||||
of the \(f_x + f_y + f_z = 0\) condition above.
|
of the \(f_x + f_y + f_z = 0\) condition above.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="eqlabel" id="orga00aa93">
|
<div class="eqlabel" id="org39eb572">
|
||||||
<p>
|
<p>
|
||||||
<a id="Earnshaw"></a><a href="./ems_ca_fe_L.html#Earnshaw"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Earnshaw"></a><a href="./ems_ca_fe_L.html#Earnshaw"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="orge0f050e">
|
<div class="alteqlabels" id="org2cc4d11">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
<div class="info div" id="org81fcf04">
|
<div class="info div" id="orgcd59178">
|
||||||
<p>
|
<p>
|
||||||
<b>Earnshaw's theorem (physical version)</b> <br>
|
<b>Earnshaw's theorem (physical version)</b> <br>
|
||||||
</p>
|
</p>
|
||||||
|
|
@ -2102,7 +2102,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1613,11 +1613,11 @@ Table of contents
|
||||||
<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"/>
|
<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><span class="headline-id">ems.ca.fe.g</span></h5>
|
</svg></a><span class="headline-id">ems.ca.fe.g</span></h5>
|
||||||
<div class="outline-text-5" id="text-ems_ca_fe_g">
|
<div class="outline-text-5" id="text-ems_ca_fe_g">
|
||||||
<div class="info div" id="orgef35f51">
|
<div class="info div" id="org60c1b11">
|
||||||
<p>
|
<p>
|
||||||
<b>George Green</b>
|
<b>George Green</b>
|
||||||
</p>
|
</p>
|
||||||
<aside id="org432d494">
|
<aside id="org0b1da41">
|
||||||
<p>
|
<p>
|
||||||
See a <a href="https://en.wikipedia.org/wiki/George%5C_Green%5C_(mathematician)">short bio on wikipedia</a>
|
See a <a href="https://en.wikipedia.org/wiki/George%5C_Green%5C_(mathematician)">short bio on wikipedia</a>
|
||||||
</p>
|
</p>
|
||||||
|
|
@ -1650,14 +1650,14 @@ and
|
||||||
\]
|
\]
|
||||||
Substituting this in the divergence theorem gives <b>Green's first identity</b>
|
Substituting this in the divergence theorem gives <b>Green's first identity</b>
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="orgfd30f5d">
|
<div class="eqlabel" id="org3d01833">
|
||||||
<p>
|
<p>
|
||||||
<a id="Green1"></a><a href="./ems_ca_fe_g.html#Green1"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Green1"></a><a href="./ems_ca_fe_g.html#Green1"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org3125160">
|
<div class="alteqlabels" id="orga726fcd">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>J (1.34)</li>
|
<li>J (1.34)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1675,14 +1675,14 @@ As an aside for now, for completeness, if we do the same thing again but with \(
|
||||||
interchanged, and subtract the result, we obtain another useful result known as
|
interchanged, and subtract the result, we obtain another useful result known as
|
||||||
<b>Green's second identity</b> or <b>Green's theorem</b>
|
<b>Green's second identity</b> or <b>Green's theorem</b>
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="org028fffd">
|
<div class="eqlabel" id="org964d072">
|
||||||
<p>
|
<p>
|
||||||
<a id="Green2"></a><a href="./ems_ca_fe_g.html#Green2"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Green2"></a><a href="./ems_ca_fe_g.html#Green2"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org9ea869b">
|
<div class="alteqlabels" id="orge29c408">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>J (1.35)</li>
|
<li>J (1.35)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1718,7 +1718,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1635,14 +1635,14 @@ This yields
|
||||||
The first term on the left-hand side vanishes since \(\Phi\) satisfies Laplace.
|
The first term on the left-hand side vanishes since \(\Phi\) satisfies Laplace.
|
||||||
The right-hand side can be made to vanish if \(\Phi\) obeys either
|
The right-hand side can be made to vanish if \(\Phi\) obeys either
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="orgfa460b1">
|
<div class="eqlabel" id="org0acb722">
|
||||||
<p>
|
<p>
|
||||||
<a id="Dirichlet"></a><a href="./ems_ca_fe_uP.html#Dirichlet"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Dirichlet"></a><a href="./ems_ca_fe_uP.html#Dirichlet"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org14f7efc">
|
<div class="alteqlabels" id="org03f8c83">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1654,14 +1654,14 @@ The right-hand side can be made to vanish if \(\Phi\) obeys either
|
||||||
<p>
|
<p>
|
||||||
or
|
or
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="orgcd08c73">
|
<div class="eqlabel" id="org3d1a359">
|
||||||
<p>
|
<p>
|
||||||
<a id="Neumann"></a><a href="./ems_ca_fe_uP.html#Neumann"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="Neumann"></a><a href="./ems_ca_fe_uP.html#Neumann"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org6976f14">
|
<div class="alteqlabels" id="orga2c0bab">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
@ -1689,19 +1689,19 @@ additive constant.
|
||||||
<p>
|
<p>
|
||||||
We can thus finally state the
|
We can thus finally state the
|
||||||
</p>
|
</p>
|
||||||
<div class="eqlabel" id="orgd45117f">
|
<div class="eqlabel" id="orgf4dd440">
|
||||||
<p>
|
<p>
|
||||||
<a id="uniq_thm"></a><a href="./ems_ca_fe_uP.html#uniq_thm"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
<a id="uniq_thm"></a><a href="./ems_ca_fe_uP.html#uniq_thm"><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="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"/>
|
<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>
|
</svg></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="alteqlabels" id="org2d283cb">
|
<div class="alteqlabels" id="org786cfb7">
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
<div class="core div" id="orgf2a5ea9">
|
<div class="core div" id="org9b96393">
|
||||||
<p>
|
<p>
|
||||||
<b>Uniqueness Theorem</b>
|
<b>Uniqueness Theorem</b>
|
||||||
</p>
|
</p>
|
||||||
|
|
@ -1740,7 +1740,7 @@ Reading other books, you might be misled into thinking that there are numerous c
|
||||||
and corollaries and that things are
|
and corollaries and that things are
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="info div" id="orgd298dad">
|
<div class="info div" id="org333667e">
|
||||||
<p>
|
<p>
|
||||||
<b>Comment/warning</b>: <b>uniqueness theorem on uniqueness theorems</b> <br>
|
<b>Comment/warning</b>: <b>uniqueness theorem on uniqueness theorems</b> <br>
|
||||||
Do not be misled: there is a <i>unique</i> uniqueness theorem for the
|
Do not be misled: there is a <i>unique</i> uniqueness theorem for the
|
||||||
|
|
@ -1767,7 +1767,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-03-22 Tue 10:52 -->
|
<!-- 2022-03-24 Thu 08:42 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -1293,7 +1293,7 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
|
<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
||||||
|
|
@ -1645,7 +1645,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||||
<p class="date">Created: 2022-03-22 Tue 10:52</p>
|
<p class="date">Created: 2022-03-24 Thu 08:42</p>
|
||||||
<p class="validation"></p>
|
<p class="validation"></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
Some files were not shown because too many files have changed in this diff Show More
Loading…
Reference in New Issue