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<!DOCTYPE html>
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<title>Pre-Quantum Electrodynamics</title>
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<title>Pre-Quantum Electrodynamics</title>
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</summary>
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<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
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<li>
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<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
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<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
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<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
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<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
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<hr><div id="postamble" class="status">
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<hr><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: 2022-02-08 Tue 06:55</p>
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<p class="date">Created: 2022-02-08 Tue 17:21</p>
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<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></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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<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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@ -272,6 +272,10 @@ 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="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
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</li>
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<li>
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<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
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<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
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<li>
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<li>
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<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
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<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
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@ -1712,7 +1716,7 @@ Wiley, 1986 [2nd edition]
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<hr><div id="postamble" class="status">
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<hr><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: 2022-02-08 Tue 06:55</p>
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<p class="date">Created: 2022-02-08 Tue 17:21</p>
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<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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</div>
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</div>
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build/c.html
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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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<!-- 2022-02-08 Tue 06:55 -->
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<!-- 2022-02-08 Tue 17:21 -->
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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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</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="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
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</li>
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<li>
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<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
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<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
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<li>
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<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
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<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
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@ -1629,7 +1633,7 @@ Table of contents
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<hr><div id="postamble" class="status">
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<hr><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: 2022-02-08 Tue 06:55</p>
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<p class="date">Created: 2022-02-08 Tue 17:21</p>
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<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></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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<!-- 2022-02-08 Tue 06:55 -->
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<!-- 2022-02-08 Tue 17:21 -->
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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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@ -272,6 +272,10 @@ 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="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
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</li>
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<li>
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<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
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<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
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@ -736,7 +740,7 @@ Table of contents
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</li>
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<li>
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<li>
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<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
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<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
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@ -1635,7 +1639,7 @@ Table of contents
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<hr><div id="postamble" class="status">
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<hr><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: 2022-02-08 Tue 06:55</p>
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<p class="date">Created: 2022-02-08 Tue 17:21</p>
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<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></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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<!-- 2022-02-08 Tue 06:55 -->
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<!-- 2022-02-08 Tue 17:21 -->
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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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</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="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
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</li>
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<li>
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<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
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<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
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<li>
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<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
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<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
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@ -1631,7 +1635,7 @@ Table of contents
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<hr><div id="postamble" class="status">
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<hr><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: 2022-02-08 Tue 06:55</p>
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<p class="date">Created: 2022-02-08 Tue 17:21</p>
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<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></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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<!-- 2022-02-08 Tue 06:55 -->
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<!-- 2022-02-08 Tue 17:21 -->
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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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@ -272,6 +272,10 @@ 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="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
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</li>
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<li>
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<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
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<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
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</li>
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<li>
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<li>
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<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
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<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
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@ -1622,47 +1626,39 @@ Table of contents
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\((r, \phi, z)\). Relation to Cartesian coordinates:
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\((r, \phi, z)\). Relation to Cartesian coordinates:
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</p>
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<p>
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\begin{equation}
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\[
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x = r \cos \phi, y = r \sin \phi, z = z
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x = r \cos \phi, y = r \sin \phi, z = z
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\label{Gr(1.74)}
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\label{Gr(1.74)}
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\]
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\end{equation}
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</p>
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The unit vectors are
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The unit vectors are
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\begin{equation}
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\[
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\hat{\bf r} = \cos \phi ~\hat{\bf x} + \sin \phi~\hat{\bf y},
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\hat{\bf r} = \cos \phi ~\hat{\bf x} + \sin \phi~\hat{\bf y},
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\hat{\boldsymbol \phi} = -\sin \theta ~\hat{\bf x} + \cos \phi~\hat{\bf y},
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\hat{\boldsymbol \phi} = -\sin \theta ~\hat{\bf x} + \cos \phi~\hat{\bf y},
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\hat{\bf z} = \hat{\bf z}.
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\hat{\bf z} = \hat{\bf z}.
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\label{Gr(1.75)}
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\label{Gr(1.75)}
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\]
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\end{equation}
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</p>
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Infinitesimal displacement:
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Infinitesimal displacement:
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\begin{equation}
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\[
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d{\bf l} = dr ~\hat{\bf r} + r d\phi~\hat{\boldsymbol \phi} + dz ~\hat{\bf z}.
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d{\bf l} = dr ~\hat{\bf r} + r d\phi~\hat{\boldsymbol \phi} + dz ~\hat{\bf z}.
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\label{Gr(1.77)}
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\label{Gr(1.77)}
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\]
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\end{equation}
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Volume element:
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Volume element:
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\begin{equation}
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\[
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d\tau = r dr d\phi dz
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d\tau = r dr d\phi dz
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\label{Gr(1.78)}
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\label{Gr(1.78)}
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\end{equation}
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Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in ]-\infty, \infty[\).
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Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in ]-\infty, \infty[\).
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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>
|
||||||
<div class="outline-text-6" id="text-c_m_cs_cyl_grad">
|
<div class="outline-text-6" id="text-c_m_cs_cyl_grad">
|
||||||
<div class="eqlabel" id="org1f82008">
|
<div class="eqlabel" id="orgc4b6bac">
|
||||||
<p>
|
<p>
|
||||||
<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">
|
<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">
|
||||||
<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="org0d07fad">
|
<div class="alteqlabels" id="orgdcdbcb4">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr4(1.79)</li>
|
<li>Gr4(1.79)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1688,32 +1684,26 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<p>
|
\begin{equation}
|
||||||
\[
|
{\boldsymbol \nabla} T = \frac{\partial T}{\partial r}~\hat{\bf r}
|
||||||
{\boldsymbol ∇} T = \frac{\partial T}{\partial r}~\hat{\bf r}
|
+ \frac{1}{r} \frac{\partial T}{\partial \phi}~\hat{\boldsymbol \phi}
|
||||||
</p>
|
+ \frac{\partial T}{\partial z} ~\hat{\bf z}
|
||||||
<ul class="org-ul">
|
|
||||||
<li>\frac{1}{r} \frac{\partial T}{\partial \phi}~\hat{\boldsymbol \phi}</li>
|
|
||||||
<li>\frac{\partial T}{\partial z} ~\hat{\bf z}</li>
|
|
||||||
</ul>
|
|
||||||
<p>
|
|
||||||
\tag{cylgrad}\label{cylgrad}
|
\tag{cylgrad}\label{cylgrad}
|
||||||
\]
|
\end{equation}
|
||||||
</p>
|
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-c_m_cs_cyl_div" class="outline-6">
|
<div id="outline-container-c_m_cs_cyl_div" class="outline-6">
|
||||||
<h6 id="c_m_cs_cyl_div"><a href="#c_m_cs_cyl_div">Divergence</a></h6>
|
<h6 id="c_m_cs_cyl_div"><a href="#c_m_cs_cyl_div">Divergence</a></h6>
|
||||||
<div class="outline-text-6" id="text-c_m_cs_cyl_div">
|
<div class="outline-text-6" id="text-c_m_cs_cyl_div">
|
||||||
<div class="eqlabel" id="org9646f8e">
|
<div class="eqlabel" id="orgf9d0262">
|
||||||
<p>
|
<p>
|
||||||
<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">
|
<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">
|
||||||
<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="orgef4d1a0">
|
<div class="alteqlabels" id="orgd456be1">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr4(2.21)</li>
|
<li>Gr4(2.21)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1722,32 +1712,26 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<p>
|
\begin{equation}
|
||||||
\[
|
{\boldsymbol \nabla} \cdot {\bf v} = \frac{1}{r} \frac{\partial}{\partial r} (r v_r)
|
||||||
{\boldsymbol ∇} ⋅ {\bf v} = \frac{1}{r} \frac{\partial}{\partial r} (r v_r)
|
+ \frac{1}{r} \frac{\partial v_{\phi}}{\partial \phi} + \frac{\partial v_z}{\partial z}.
|
||||||
</p>
|
|
||||||
<ul class="org-ul">
|
|
||||||
<li>\frac{1}{r} \frac{∂ v_{φ}}{∂ φ} + \frac{\partial v_z}{\partial z}.</li>
|
|
||||||
</ul>
|
|
||||||
<p>
|
|
||||||
\tag{cyl_div}
|
\tag{cyl_div}
|
||||||
\label{cyl_div}
|
\label{cyl_div}
|
||||||
\]
|
\end{equation}
|
||||||
</p>
|
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-c_m_cs_cyl_curl" class="outline-6">
|
<div id="outline-container-c_m_cs_cyl_curl" class="outline-6">
|
||||||
<h6 id="c_m_cs_cyl_curl"><a href="#c_m_cs_cyl_curl">Curl</a></h6>
|
<h6 id="c_m_cs_cyl_curl"><a href="#c_m_cs_cyl_curl">Curl</a></h6>
|
||||||
<div class="outline-text-6" id="text-c_m_cs_cyl_curl">
|
<div class="outline-text-6" id="text-c_m_cs_cyl_curl">
|
||||||
<div class="eqlabel" id="org174b722">
|
<div class="eqlabel" id="orgeb922d3">
|
||||||
<p>
|
<p>
|
||||||
<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">
|
<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">
|
||||||
<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="org9f83d45">
|
<div class="alteqlabels" id="org66ae846">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr4(2.21)</li>
|
<li>Gr4(2.21)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1756,36 +1740,24 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<p>
|
\begin{align}
|
||||||
\[
|
{\boldsymbol \nabla} \times {\bf v} = \left( \frac{1}{r} \frac{\partial v_z}{\partial \phi} - \frac{\partial v_{\phi}}{\partial z}\right) ~\hat{\bf r}
|
||||||
{\boldsymbol ∇} × {\bf v} = \left( \frac{1}{r} \frac{\partial v_z}{\partial \phi} - \frac{∂ v_{φ}}{∂ z}\right) ~\hat{\bf r}
|
+ \left( \frac{\partial v_r}{\partial z} - \frac{\partial v_z}{\partial r} \right) ~\hat{\boldsymbol \phi} \nonumber \\
|
||||||
</p>
|
+ \frac{1}{r} \left( \frac{\partial}{\partial r} (r v_{\phi}) - \frac{\partial v_r}{\partial \phi} \right) ~\hat{\bf z}
|
||||||
<ul class="org-ul">
|
|
||||||
<li>\left( \frac{\partial v_r}{\partial z} - \frac{\partial v_z}{\partial r} \right) ~\hat{\boldsymbol \phi}</li>
|
|
||||||
<li>\frac{1}{r} \left( \frac{\partial}{\partial r} (r v_{φ}) - \frac{\partial v_r}{\partial \phi} \right) ~\hat{\bf z}</li>
|
|
||||||
</ul>
|
|
||||||
<p>
|
|
||||||
\tag{cyl_curl}
|
\tag{cyl_curl}
|
||||||
\label{cyl_curl}
|
\label{cyl_curl}
|
||||||
\]
|
\end{align}
|
||||||
</p>
|
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-c_m_cs_cyl_lap" class="outline-6">
|
<div id="outline-container-c_m_cs_cyl_lap" class="outline-6">
|
||||||
<h6 id="c_m_cs_cyl_lap"><a href="#c_m_cs_cyl_lap">Laplacian</a></h6>
|
<h6 id="c_m_cs_cyl_lap"><a href="#c_m_cs_cyl_lap">Laplacian</a></h6>
|
||||||
<div class="outline-text-6" id="text-c_m_cs_cyl_lap">
|
<div class="outline-text-6" id="text-c_m_cs_cyl_lap">
|
||||||
<p>
|
\begin{equation}
|
||||||
\[
|
{\boldsymbol \nabla}^2 T = \frac{1}{r} \frac{\partial}{\partial r} \left( r \frac{\partial T}{\partial r} \right)
|
||||||
{\boldsymbol ∇}^2 T = \frac{1}{r} \frac{\partial}{\partial r} \left( r \frac{\partial T}{\partial r} \right)
|
+ \frac{1}{r^2} \frac{\partial^2 T}{\partial \phi^2} + \frac{\partial^2 T}{\partial z^2}
|
||||||
</p>
|
|
||||||
<ul class="org-ul">
|
|
||||||
<li>\frac{1}{r^2} \frac{\partial^2 T}{\partial \phi^2} + \frac{\partial^2 T}{\partial z^2}</li>
|
|
||||||
</ul>
|
|
||||||
<p>
|
|
||||||
\label{Gr(1.82)}
|
\label{Gr(1.82)}
|
||||||
\]
|
\end{equation}
|
||||||
</p>
|
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
@ -1795,7 +1767,7 @@ Range of parameters: \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1624,7 +1628,7 @@ Table of contents
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1688,70 +1692,46 @@ 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">
|
||||||
<p>
|
\begin{equation}
|
||||||
\[
|
{\boldsymbol \nabla} T = \frac{\partial T}{\partial r} \hat{\boldsymbol r} + \frac{1}{r} \frac{\partial T}{\partial \theta} \hat{\boldsymbol \theta}
|
||||||
{\boldsymbol ∇} T = \frac{\partial T}{\partial r} \hat{\boldsymbol r} + \frac{1}{r} \frac{\partial T}{\partial \theta} \hat{\boldsymbol \theta}
|
+ \frac{1}{r\sin \theta} \frac{\partial T}{\partial \phi} \hat{\boldsymbol \phi}.
|
||||||
</p>
|
|
||||||
<ul class="org-ul">
|
|
||||||
<li>\frac{1}{r\sin \theta} \frac{\partial T}{\partial \phi} \hat{\boldsymbol \phi}.</li>
|
|
||||||
</ul>
|
|
||||||
<p>
|
|
||||||
\label{Gr(1.70)}
|
\label{Gr(1.70)}
|
||||||
\]
|
\end{equation}
|
||||||
</p>
|
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<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">
|
||||||
<p>
|
\begin{equation}
|
||||||
\[
|
{\boldsymbol \nabla} \cdot {\bf v} = \frac{1}{r^2} \frac{\partial}{\partial r} (r^2 v_r) + \frac{1}{r\sin \theta} \frac{\partial}{\partial \theta} (\sin\theta v_{\theta})
|
||||||
{\boldsymbol ∇} ⋅ {\bf v} = \frac{1}{r^2} \frac{\partial}{\partial r} (r^2 v_r) + \frac{1}{r\sin \theta} \frac{\partial}{\partial \theta} (sinθ v_{θ})
|
+ \frac{1}{r \sin \theta} \frac{\partial v_{\phi}}{\partial \phi}
|
||||||
</p>
|
|
||||||
<ul class="org-ul">
|
|
||||||
<li>\frac{1}{r \sin \theta} \frac{∂ v_{φ}}{∂ φ}</li>
|
|
||||||
</ul>
|
|
||||||
<p>
|
|
||||||
\label{Gr(1.71)}
|
\label{Gr(1.71)}
|
||||||
\]
|
\end{equation}
|
||||||
</p>
|
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<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">
|
||||||
<p>
|
\begin{equation}
|
||||||
\[
|
{\boldsymbol \nabla} \times {\bf v} = \frac{1}{r\sin \theta} \left[ \frac{\partial}{\partial \theta} (\sin \theta v_{\phi}) - \frac{\partial v_{\theta}}{\partial \phi} \right] \hat{\bf r}
|
||||||
{\boldsymbol ∇} × {\bf v} = \frac{1}{r\sin \theta} \left[ \frac{\partial}{\partial \theta} (sin θ v_{φ}) - \frac{∂ v_{θ}}{∂ φ} \right] \hat{\bf r}
|
+ \frac{1}{r} \left[ \frac{1}{\sin \theta} \frac{\partial v_r}{\partial \phi} - \frac{\partial}{\partial r} (r v_{\phi}) \right] \hat{\boldsymbol \theta}
|
||||||
</p>
|
+ \frac{1}{r} \left[ \frac{\partial}{\partial r} (r v_{\theta}) - \frac{\partial v_r}{\partial \theta} \right] \hat{\boldsymbol \phi}
|
||||||
<ul class="org-ul">
|
|
||||||
<li>\frac{1}{r} \left[ \frac{1}{\sin \theta} \frac{\partial v_r}{\partial \phi} - \frac{\partial}{\partial r} (r v_{φ}) \right] \hat{\boldsymbol \theta}</li>
|
|
||||||
<li>\frac{1}{r} \left[ \frac{\partial}{\partial r} (r v_{θ}) - \frac{\partial v_r}{\partial \theta} \right] \hat{\boldsymbol \phi}</li>
|
|
||||||
</ul>
|
|
||||||
<p>
|
|
||||||
\label{Gr(1.72)}
|
\label{Gr(1.72)}
|
||||||
\]
|
\end{equation}
|
||||||
</p>
|
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<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">
|
||||||
<p>
|
\begin{equation}
|
||||||
\[
|
{\boldsymbol \nabla}^2 T = \frac{1}{r^2} \frac{\partial}{\partial r} \left(r^2 \frac{\partial T}{\partial r}\right)
|
||||||
{\boldsymbol ∇}^2 T = \frac{1}{r^2} \frac{\partial}{\partial r} \left(r^2 \frac{\partial T}{\partial r}\right)
|
+ \frac{1}{r^2 \sin \theta} \frac{\partial}{\partial \theta} \left( \sin \theta \frac{\partial T}{\partial \theta}\right)
|
||||||
</p>
|
+ \frac{1}{r^2 \sin^2 \theta} \frac{\partial^2 T}{\partial \phi^2}
|
||||||
<ul class="org-ul">
|
|
||||||
<li>\frac{1}{r^2 \sin \theta} \frac{\partial}{\partial \theta} \left( sin θ \frac{\partial T}{\partial \theta}\right)</li>
|
|
||||||
<li>\frac{1}{r^2 \sin^2 \theta} \frac{\partial^2 T}{\partial \phi^2}</li>
|
|
||||||
</ul>
|
|
||||||
<p>
|
|
||||||
\label{Gr(1.73)}
|
\label{Gr(1.73)}
|
||||||
\]
|
\end{equation}
|
||||||
</p>
|
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
@ -1761,7 +1741,7 @@ Infinitesimal surface element: depends on situation.
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1634,7 +1638,7 @@ Table of contents
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1636,7 +1640,7 @@ v_x & v_y & v_z \end{array} \right| \nonumber \\
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1620,9 +1624,9 @@ 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>
|
||||||
|
|
||||||
<div id="outline-container-orgc3b89bb" class="outline-6">
|
<div id="outline-container-org5fd48d1" class="outline-6">
|
||||||
<h6 id="orgc3b89bb"><a href="#orgc3b89bb">Divergence of gradient</a></h6>
|
<h6 id="org5fd48d1"><a href="#org5fd48d1">Divergence of gradient</a></h6>
|
||||||
<div class="outline-text-6" id="text-orgc3b89bb">
|
<div class="outline-text-6" id="text-org5fd48d1">
|
||||||
<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
|
||||||
|
|
@ -1631,36 +1635,36 @@ given by the Laplacian of the corresponding vector elements.
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org5caf3f5" class="outline-6">
|
<div id="outline-container-org41a3448" class="outline-6">
|
||||||
<h6 id="org5caf3f5"><a href="#org5caf3f5">Curl of a gradient</a></h6>
|
<h6 id="org41a3448"><a href="#org41a3448">Curl of a gradient</a></h6>
|
||||||
<div class="outline-text-6" id="text-org5caf3f5">
|
<div class="outline-text-6" id="text-org41a3448">
|
||||||
<p>
|
<p>
|
||||||
This always vanishes.
|
This always vanishes.
|
||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org4f9116a" class="outline-6">
|
<div id="outline-container-org6c4b5a7" class="outline-6">
|
||||||
<h6 id="org4f9116a"><a href="#org4f9116a">Gradient of the divergence</a></h6>
|
<h6 id="org6c4b5a7"><a href="#org6c4b5a7">Gradient of the divergence</a></h6>
|
||||||
<div class="outline-text-6" id="text-org4f9116a">
|
<div class="outline-text-6" id="text-org6c4b5a7">
|
||||||
<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-org2c1c081" class="outline-6">
|
<div id="outline-container-org68b62ab" class="outline-6">
|
||||||
<h6 id="org2c1c081"><a href="#org2c1c081">Divergence of a curl</a></h6>
|
<h6 id="org68b62ab"><a href="#org68b62ab">Divergence of a curl</a></h6>
|
||||||
<div class="outline-text-6" id="text-org2c1c081">
|
<div class="outline-text-6" id="text-org68b62ab">
|
||||||
<p>
|
<p>
|
||||||
This always vanishes.
|
This always vanishes.
|
||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgc977e97" class="outline-6">
|
<div id="outline-container-org62690be" class="outline-6">
|
||||||
<h6 id="orgc977e97"><a href="#orgc977e97">Curl of curl</a></h6>
|
<h6 id="org62690be"><a href="#org62690be">Curl of curl</a></h6>
|
||||||
<div class="outline-text-6" id="text-orgc977e97">
|
<div class="outline-text-6" id="text-org62690be">
|
||||||
<p>
|
<p>
|
||||||
\[
|
\[
|
||||||
{\boldsymbol \nabla} \times ({\boldsymbol \nabla} \times {\bf v}) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v}) - {\boldsymbol \nabla}^2 {\bf v}
|
{\boldsymbol \nabla} \times ({\boldsymbol \nabla} \times {\bf v}) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v}) - {\boldsymbol \nabla}^2 {\bf v}
|
||||||
|
|
@ -1674,7 +1678,7 @@ This always vanishes.
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
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||||||
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|
||||||
<title>Pre-Quantum Electrodynamics</title>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
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|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1635,7 +1639,7 @@ The <b>del/grad/nabla operator</b> is defined as
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
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<html lang="en">
|
<html lang="en">
|
||||||
<head>
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|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<meta charset="utf-8">
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<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1632,7 +1636,7 @@ Table of contents
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1656,7 +1660,7 @@ is a vector called the <b>gradient</b> of \(T\).
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1629,7 +1633,7 @@ Six product rules (on inside front cover of Gr).
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1631,7 +1635,7 @@ Table of contents
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1643,7 +1647,7 @@ Consequences: for any smooth differentiable function \(f(x)\),
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1618,43 +1622,37 @@ 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.dd.3d</span></h5>
|
</svg></a><span class="headline-id">c.m.dd.3d</span></h5>
|
||||||
<div class="outline-text-5" id="text-c_m_dd_3d">
|
<div class="outline-text-5" id="text-c_m_dd_3d">
|
||||||
<p>
|
\begin{equation}
|
||||||
\[
|
|
||||||
\delta^{(3)} ({\bf r} - {\bf r}') = \delta (x - x') \delta (y - y') \delta (z - z')
|
\delta^{(3)} ({\bf r} - {\bf r}') = \delta (x - x') \delta (y - y') \delta (z - z')
|
||||||
\label{Gr(1.96)}
|
\label{Gr(1.96)}
|
||||||
\]
|
\end{equation}
|
||||||
</p>
|
|
||||||
|
|
||||||
<p>
|
\begin{equation}
|
||||||
\[
|
|
||||||
\int d\tau f({\bf r}) \delta^{(3)} ({\bf r} - {\bf a}) = f({\bf a})
|
\int d\tau f({\bf r}) \delta^{(3)} ({\bf r} - {\bf a}) = f({\bf a})
|
||||||
\label{Gr(1.97)}
|
\label{Gr(1.97)}
|
||||||
\]
|
\end{equation}
|
||||||
</p>
|
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
Resolution of divergence of \(\hat{\bf r}/r^2\) paradox:
|
Resolution of divergence of \(\hat{\bf r}/r^2\) paradox:
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<p>
|
\begin{equation}
|
||||||
\[
|
|
||||||
{\boldsymbol \nabla} \cdot \left(\frac{\hat{\bf r}}{r^2} \right)= 4\pi \delta^{(3)} ({\bf r}).
|
{\boldsymbol \nabla} \cdot \left(\frac{\hat{\bf r}}{r^2} \right)= 4\pi \delta^{(3)} ({\bf r}).
|
||||||
\label{Gr(1.99)}
|
\label{Gr(1.99)}
|
||||||
\]
|
\end{equation}
|
||||||
</p>
|
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
More generally,
|
More generally,
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="eqlabel" id="org99c1900">
|
<div class="eqlabel" id="org276d185">
|
||||||
<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="orge7a14d6">
|
<div class="alteqlabels" id="org676b181">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (1.100)</li>
|
<li>Gr (1.100)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1662,43 +1660,37 @@ More generally,
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
<p>
|
\begin{equation}
|
||||||
\[
|
|
||||||
\boxed{
|
\boxed{
|
||||||
{\boldsymbol \nabla} \cdot \left(\frac{{\bf r} - {\bf r}'}{|{\bf r} - {\bf r}'|^3} \right)= 4\pi \delta^{(3)} ({\bf r}).
|
{\boldsymbol \nabla} \cdot \left(\frac{{\bf r} - {\bf r}'}{|{\bf r} - {\bf r}'|^3} \right)= 4\pi \delta^{(3)} ({\bf r}).
|
||||||
}
|
}
|
||||||
\tag{divdel}\label{divdel}
|
\tag{divdel}\label{divdel}
|
||||||
\]
|
\end{equation}
|
||||||
</p>
|
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
Since
|
Since
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<p>
|
\begin{equation}
|
||||||
\[
|
|
||||||
{\boldsymbol \nabla}_1 \left(\frac{1}{r_{12}}\right) = -\frac{\hat{\bf r}_{12}}{r_{12}^2}
|
{\boldsymbol \nabla}_1 \left(\frac{1}{r_{12}}\right) = -\frac{\hat{\bf r}_{12}}{r_{12}^2}
|
||||||
\label{Gr(1.101)}
|
\label{Gr(1.101)}
|
||||||
\]
|
\end{equation}
|
||||||
</p>
|
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
we have that
|
we have that
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<p>
|
\begin{equation}
|
||||||
\[
|
|
||||||
{\boldsymbol \nabla}^2 \left( \frac{1}{|{\bf r} - {\bf r}'|} \right) = -4\pi \delta^{(3)} ({\bf r} - {\bf r}')
|
{\boldsymbol \nabla}^2 \left( \frac{1}{|{\bf r} - {\bf r}'|} \right) = -4\pi \delta^{(3)} ({\bf r} - {\bf r}')
|
||||||
\label{Gr(1.102)}
|
\label{Gr(1.102)}
|
||||||
\]
|
\end{equation}
|
||||||
</p>
|
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1622,12 +1626,10 @@ Table of contents
|
||||||
Try to calculate this directly:
|
Try to calculate this directly:
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<p>
|
\begin{equation}
|
||||||
\[
|
|
||||||
{\boldsymbol \nabla} \cdot \frac{\hat{\bf r}}{r^2} = \frac{1}{r^2} \frac{\partial}{\partial r} \left( r^2 \frac{1}{r^2}\right) =^{?} 0
|
{\boldsymbol \nabla} \cdot \frac{\hat{\bf r}}{r^2} = \frac{1}{r^2} \frac{\partial}{\partial r} \left( r^2 \frac{1}{r^2}\right) =^{?} 0
|
||||||
\label{Gr(1.84)}
|
\label{Gr(1.84)}
|
||||||
\]
|
\end{equation}
|
||||||
</p>
|
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
Now apply the divergence theorem.
|
Now apply the divergence theorem.
|
||||||
|
|
@ -1635,16 +1637,14 @@ Integrate over a sphere of radius \(R\) centered at the origin (Prob. 1.38b):
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
<p>
|
\begin{equation}
|
||||||
\[
|
|
||||||
\oint \frac{\hat{\bf r}}{r^2} \cdot d{\bf a} = \int \left(\frac{1}{R^2} \hat{\bf r} \right) \cdot \left( R^2 \sin \theta d\theta d\phi ~\hat{\bf r} \right)
|
\oint \frac{\hat{\bf r}}{r^2} \cdot d{\bf a} = \int \left(\frac{1}{R^2} \hat{\bf r} \right) \cdot \left( R^2 \sin \theta d\theta d\phi ~\hat{\bf r} \right)
|
||||||
= \int_0^{\pi} d\theta \sin \theta \int_0^{2\pi} d\phi = 4\pi
|
= \int_0^{\pi} d\theta \sin \theta \int_0^{2\pi} d\phi = 4\pi
|
||||||
\label{Gr(1.85)}
|
\label{Gr(1.85)}
|
||||||
\]
|
\end{equation}
|
||||||
</p>
|
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
Problem: in (1.84), we've divided by zero when \(r = 0\).
|
Problem: in Gr(1.84), we've divided by zero when \(r = 0\).
|
||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
@ -1653,7 +1653,7 @@ Problem: in (1.84), we've divided by zero when \(r = 0\).
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1634,7 +1638,7 @@ Table of contents
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1632,7 +1636,7 @@ Table of contents
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1641,7 +1645,7 @@ Table of contents
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
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|
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|
||||||
|
|
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|
||||||
<!DOCTYPE html>
|
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|
||||||
<html lang="en">
|
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|
||||||
<head>
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|
||||||
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|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
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|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1635,7 +1639,7 @@ This is know either as <b>Gauss' theorem</b>, <b>Green's theorem</b> or the <b>d
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1642,7 +1646,7 @@ or in other words
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1620,9 +1624,9 @@ 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-org860e5de" class="outline-6">
|
<div id="outline-container-org609a3df" class="outline-6">
|
||||||
<h6 id="org860e5de"><a href="#org860e5de">Line Integrals</a></h6>
|
<h6 id="org609a3df"><a href="#org609a3df">Line Integrals</a></h6>
|
||||||
<div class="outline-text-6" id="text-org860e5de">
|
<div class="outline-text-6" id="text-org609a3df">
|
||||||
<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}
|
||||||
|
|
@ -1651,9 +1655,9 @@ Integral over a closed loop:
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orged48130" class="outline-6">
|
<div id="outline-container-org8f657b7" class="outline-6">
|
||||||
<h6 id="orged48130"><a href="#orged48130">Surface Integrals</a></h6>
|
<h6 id="org8f657b7"><a href="#org8f657b7">Surface Integrals</a></h6>
|
||||||
<div class="outline-text-6" id="text-orged48130">
|
<div class="outline-text-6" id="text-org8f657b7">
|
||||||
<p>
|
<p>
|
||||||
\[
|
\[
|
||||||
\int_{\cal S} {\bf v} \cdot d{\bf a}
|
\int_{\cal S} {\bf v} \cdot d{\bf a}
|
||||||
|
|
@ -1673,9 +1677,9 @@ Over a closed surface:
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org4728536" class="outline-6">
|
<div id="outline-container-org2ec267e" class="outline-6">
|
||||||
<h6 id="org4728536"><a href="#org4728536">Volume Integrals</a></h6>
|
<h6 id="org2ec267e"><a href="#org2ec267e">Volume Integrals</a></h6>
|
||||||
<div class="outline-text-6" id="text-org4728536">
|
<div class="outline-text-6" id="text-org2ec267e">
|
||||||
<p>
|
<p>
|
||||||
\[
|
\[
|
||||||
\int_{\cal V} T d\tau
|
\int_{\cal V} T d\tau
|
||||||
|
|
@ -1703,7 +1707,7 @@ d\tau = dx dy dz
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1618,14 +1622,14 @@ 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="orgda53253">
|
<div class="eqlabel" id="org4321094">
|
||||||
<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="org14a6dc8">
|
<div class="alteqlabels" id="org03c3b7b">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Gr (1.57)</li>
|
<li>Gr (1.57)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
@ -1657,7 +1661,7 @@ the boundary shrinks to a point.
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1631,7 +1635,7 @@ Table of contents
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<meta charset="utf-8">
|
<meta charset="utf-8">
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|
||||||
</summary>
|
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|
||||||
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|
||||||
<li>
|
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|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
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||||||
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||||||
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|
||||||
|
|
||||||
</li>
|
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|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
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|
||||||
<li>
|
<li>
|
||||||
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|
@ -1644,7 +1648,7 @@ Table of contents
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
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|
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<!DOCTYPE html>
|
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|
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|
||||||
<head>
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|
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||||||
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||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
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|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
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|
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|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1644,7 +1648,7 @@ Table of contents
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
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|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
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|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1647,7 +1651,7 @@ Table of contents
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1633,7 +1637,7 @@ Table of contents
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1662,7 +1666,7 @@ this relation making plain that
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1657,7 +1661,7 @@ Component notation (in \({\mathbb R}^3\) with cartesian coordinates):
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1691,7 +1695,7 @@ Separation vector: for two position vectors \({\bf r}_a, {\bf r}_b\),
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
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|
||||||
</summary>
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||||||
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||||||
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||||||
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<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
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||||||
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|
||||||
|
</li>
|
||||||
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<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
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||||||
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||||||
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|
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|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
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||||||
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@ -1657,7 +1661,7 @@ In a general coordinate system with metric \(g\),
|
||||||
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|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
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||||||
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<!DOCTYPE html>
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<head>
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||||||
<!-- 2022-02-08 Tue 06:55 -->
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|
||||||
<meta charset="utf-8">
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|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
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<ul>
|
||||||
<li>
|
<li>
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||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
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||||||
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||||||
|
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||||||
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|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
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||||||
</li>
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||||||
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@ -1704,7 +1708,7 @@ All higher vector products can be reduced to combinations of single vector produ
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||||||
|
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||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
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|
||||||
|
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||||||
|
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<!DOCTYPE html>
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<html lang="en">
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<head>
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|
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<!-- 2022-02-08 Tue 06:55 -->
|
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|
||||||
<meta charset="utf-8">
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|
||||||
<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>
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||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
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<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
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@ -736,7 +740,7 @@ Table of contents
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||||||
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||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
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|
||||||
|
|
@ -1630,7 +1634,7 @@ Table of contents
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1649,7 +1653,7 @@ where
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1623,12 +1627,10 @@ If the curl of a vector field \({\bf F}\) vanishes, then \({\bf F}\) can be writ
|
||||||
<b>scalar potential</b> \(V\):
|
<b>scalar potential</b> \(V\):
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<p>
|
\begin{equation}
|
||||||
\[
|
|
||||||
{\boldsymbol \nabla} \times {\bf F} = 0 \Longleftrightarrow {\bf F} = -{\boldsymbol \nabla} V
|
{\boldsymbol \nabla} \times {\bf F} = 0 \Longleftrightarrow {\bf F} = -{\boldsymbol \nabla} V
|
||||||
\label{Gr(1.103)}
|
\label{Gr(1.103)}
|
||||||
\]
|
\end{equation}
|
||||||
</p>
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-c_m_vf_pot_irrot" class="outline-6">
|
<div id="outline-container-c_m_vf_pot_irrot" class="outline-6">
|
||||||
|
|
@ -1678,7 +1680,7 @@ The following conditions are equivalent:
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
14
build/d.html
14
build/d.html
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1619,8 +1623,8 @@ 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="org8e87179">
|
<details class="objectives" id="orgdc678ad">
|
||||||
<summary id="org5aefd0c">
|
<summary id="org6e8a387">
|
||||||
Objectives
|
Objectives
|
||||||
</summary>
|
</summary>
|
||||||
|
|
||||||
|
|
@ -1671,7 +1675,7 @@ I have little doubt you'll pass the course.
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1651,7 +1655,7 @@ As a strict minimum, you should be able to:
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1646,7 +1650,7 @@ As a strict minimum, you should be able to:
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1649,7 +1653,7 @@ As a strict minimum, you should be able to:
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1646,7 +1650,7 @@ As a strict minimum, you should be able to:
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1668,7 +1672,7 @@ As a strict minimum, you should be able to:
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1651,7 +1655,7 @@ a point source charge \(q\) at \({\bf r}_s\) with an infinite grounded conductin
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1648,7 +1652,7 @@ As a strict minimum, you should be able to:
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1651,7 +1655,7 @@ As a strict minimum, you should be able to:
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1649,7 +1653,7 @@ As a strict minimum, you should be able to:
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1659,7 +1663,7 @@ Things you should be able to do (ideally: from scratch, on a blank sheet of pape
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1653,7 +1657,7 @@ As a strict minimum, you should be able to:
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1619,8 +1623,8 @@ 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="orgfca423d">
|
<details class="prereq" id="org91070ea">
|
||||||
<summary id="org226d692">
|
<summary id="orgec443fc">
|
||||||
Prerequisites
|
Prerequisites
|
||||||
</summary>
|
</summary>
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
|
|
@ -1629,8 +1633,8 @@ Prerequisites
|
||||||
</ul>
|
</ul>
|
||||||
</details>
|
</details>
|
||||||
|
|
||||||
<details class="objectives" id="org9195c9d">
|
<details class="objectives" id="org7a852ae">
|
||||||
<summary id="org58d183b">
|
<summary id="org301eba1">
|
||||||
Objectives
|
Objectives
|
||||||
</summary>
|
</summary>
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
|
|
@ -1658,7 +1662,7 @@ Objectives
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1632,7 +1636,7 @@ Table of contents
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1659,7 +1663,7 @@ 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="org9907fe5">
|
<div class="core div" id="orgcb2b8bd">
|
||||||
<p>
|
<p>
|
||||||
<b>Electromotive force (or electromotance)</b>,
|
<b>Electromotive force (or electromotance)</b>,
|
||||||
\[
|
\[
|
||||||
|
|
@ -1681,7 +1685,7 @@ to the rate of change of the magnetic flux,
|
||||||
\]
|
\]
|
||||||
so we obtain
|
so we obtain
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org511a243">
|
<div class="core div" id="org826bbb5">
|
||||||
<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>)
|
||||||
\[
|
\[
|
||||||
|
|
@ -1699,7 +1703,7 @@ for any loop (on a wire or not). Using Stokes' theorem,
|
||||||
\]
|
\]
|
||||||
we obtain
|
we obtain
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="orgb9e0e05">
|
<div class="core div" id="org4f576bd">
|
||||||
<p>
|
<p>
|
||||||
<b>Faraday's law</b> (differential form)
|
<b>Faraday's law</b> (differential form)
|
||||||
\[
|
\[
|
||||||
|
|
@ -1723,7 +1727,7 @@ to an opposing counter-reaction.
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1678,7 +1682,7 @@ 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="org0a53c4e">
|
<div class="core div" id="org612a7d5">
|
||||||
<p>
|
<p>
|
||||||
\[
|
\[
|
||||||
W_{mag} = \frac{1}{2\mu_0} \int d\tau B^2
|
W_{mag} = \frac{1}{2\mu_0} \int d\tau B^2
|
||||||
|
|
@ -1699,7 +1703,7 @@ W_{mag} = \frac{1}{2} \int d\tau ({\bf A} \cdot {\bf J}) = \frac{1}{2\mu_0} \int
|
||||||
\hspace{2cm} \mbox{(7.31 and 7.34)}
|
\hspace{2cm} \mbox{(7.31 and 7.34)}
|
||||||
\end{align}
|
\end{align}
|
||||||
|
|
||||||
<div class="example div" id="orge7b1ecf">
|
<div class="example div" id="org8806452">
|
||||||
<p>
|
<p>
|
||||||
\paragraph{Example 7.13:} coaxial cable (inner cylinder radius \(a\), outer \(b\)) carries current \(I\).
|
\paragraph{Example 7.13:} coaxial cable (inner cylinder radius \(a\), outer \(b\)) carries current \(I\).
|
||||||
Find energy stored in section of length \(l\).
|
Find energy stored in section of length \(l\).
|
||||||
|
|
@ -1725,7 +1729,7 @@ Note: gives easy way to find inductance, since \(W = \frac{1}{2} L I^2\).
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1658,7 +1662,7 @@ M_{12} = M_{21}
|
||||||
\]
|
\]
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="example div" id="orgc2d0a32">
|
<div class="example div" id="org105c83a">
|
||||||
<p>
|
<p>
|
||||||
\paragraph{Example 7.10:}
|
\paragraph{Example 7.10:}
|
||||||
short solenoid (length \(l\), radius \(a\), \(n_1\) turns per unit length) lies concentrically inside
|
short solenoid (length \(l\), radius \(a\), \(n_1\) turns per unit length) lies concentrically inside
|
||||||
|
|
@ -1708,7 +1712,7 @@ Inductance: measured in {\bf henries} (\(H\)). \(H = V s/A\).
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
<div class="example div" id="org7f4b3fa">
|
<div class="example div" id="orgfde0fbc">
|
||||||
<p>
|
<p>
|
||||||
\paragraph{Example 7.11:} find self-inductance of toroidal coil with
|
\paragraph{Example 7.11:} find self-inductance of toroidal coil with
|
||||||
rectangular cross-section (inner radius \(a\), outer radius \(b\), height \(h\))
|
rectangular cross-section (inner radius \(a\), outer radius \(b\), height \(h\))
|
||||||
|
|
@ -1735,7 +1739,7 @@ Total flux: \(N\) times this, so self-inductance is
|
||||||
Inductance (like capacitance) is intrinsically positive. Use Lenz law. Think of {\bf back EMF}.
|
Inductance (like capacitance) is intrinsically positive. Use Lenz law. Think of {\bf back EMF}.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="example div" id="org37841ae">
|
<div class="example div" id="org88909b4">
|
||||||
<p>
|
<p>
|
||||||
\paragraph{Example 7.12:} circuit with inductance \(L\), resistor \(R\) and battery \({\cal E}_0\).
|
\paragraph{Example 7.12:} circuit with inductance \(L\), resistor \(R\) and battery \({\cal E}_0\).
|
||||||
What is the current ?
|
What is the current ?
|
||||||
|
|
@ -1761,7 +1765,7 @@ where \(\tau \equiv L/R\) is the {\bf time constant} of the circuit.
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1642,7 +1646,7 @@ law in integral form:
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
<div class="example div" id="orgfe52c32">
|
<div class="example div" id="org6f81c6a">
|
||||||
<p>
|
<p>
|
||||||
{\bf Example 7.7:}
|
{\bf Example 7.7:}
|
||||||
\({\bf B}(t)\) points up in circular region of radius \(R\). What is the induced \({\bf E}(t)\) ?
|
\({\bf B}(t)\) points up in circular region of radius \(R\). What is the induced \({\bf E}(t)\) ?
|
||||||
|
|
@ -1658,7 +1662,7 @@ Increasing \({\bf B}\): clockwise (viewed from above) \({\bf E}\) from Lenz.
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div class="example div" id="orgb289794">
|
<div class="example div" id="org5fbf230">
|
||||||
<p>
|
<p>
|
||||||
{\bf Example 7.8:} wheel or radius \(b\) with line charge \(\lambda\) on the rim.
|
{\bf Example 7.8:} wheel or radius \(b\) with line charge \(\lambda\) on the rim.
|
||||||
Uniform magnetic field \({\bf B}_0\) in central region up to \(a < b\),
|
Uniform magnetic field \({\bf B}_0\) in central region up to \(a < b\),
|
||||||
|
|
@ -1692,7 +1696,7 @@ called the {\bf quasistatic} approximation, and works provided we deal with
|
||||||
'slow enough' phenomena.
|
'slow enough' phenomena.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="example div" id="orgd4a9b9d">
|
<div class="example div" id="org4c83960">
|
||||||
<p>
|
<p>
|
||||||
{\bf Example 7.9:} infinitely long straight wire carries \(I(t)\). Find
|
{\bf Example 7.9:} infinitely long straight wire carries \(I(t)\). Find
|
||||||
induced \({\bf E}\) field as a function of distance \(s\) from wire.
|
induced \({\bf E}\) field as a function of distance \(s\) from wire.
|
||||||
|
|
@ -1727,7 +1731,7 @@ Reason: in this case, we've overstepped the quasistatic limit. We need
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1632,7 +1636,7 @@ Table of contents
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1621,7 +1625,7 @@ 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="org152d250">
|
<div class="core div" id="org61cd67c">
|
||||||
<p>
|
<p>
|
||||||
{\bf Maxwell's equations} {\it (in vacuum)}
|
{\bf Maxwell's equations} {\it (in vacuum)}
|
||||||
</p>
|
</p>
|
||||||
|
|
@ -1637,7 +1641,7 @@ Full set of equations for the electromagnetic field:
|
||||||
<p>
|
<p>
|
||||||
Complement:
|
Complement:
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org1c66368">
|
<div class="core div" id="org2b8e704">
|
||||||
<p>
|
<p>
|
||||||
{\bf Force law}
|
{\bf Force law}
|
||||||
\[
|
\[
|
||||||
|
|
@ -1661,7 +1665,7 @@ take divergence of \((iv)\).
|
||||||
<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="org1958d41">
|
<div class="core div" id="orgac16379">
|
||||||
\begin{align}
|
\begin{align}
|
||||||
(i) &{\boldsymbol \nabla} \cdot {\bf E} = \frac{\rho}{\varepsilon_0},
|
(i) &{\boldsymbol \nabla} \cdot {\bf E} = \frac{\rho}{\varepsilon_0},
|
||||||
&(iii) {\boldsymbol \nabla} \times {\bf E} + \frac{\partial {\bf B}}{\partial t} = 0, \\
|
&(iii) {\boldsymbol \nabla} \times {\bf E} + \frac{\partial {\bf B}}{\partial t} = 0, \\
|
||||||
|
|
@ -1678,7 +1682,7 @@ Better way of writing: all fields on left, all sources on right,
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1628,7 +1632,7 @@ the continuity equation as
|
||||||
\]
|
\]
|
||||||
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="orgff64dd3">
|
<div class="core div" id="orgc09ac90">
|
||||||
<p>
|
<p>
|
||||||
\[
|
\[
|
||||||
{\boldsymbol \nabla} \times {\bf B} = \mu_0 {\bf J} + \mu_0 \varepsilon_0 \frac{\partial {\bf E}}{\partial t}
|
{\boldsymbol \nabla} \times {\bf B} = \mu_0 {\bf J} + \mu_0 \varepsilon_0 \frac{\partial {\bf E}}{\partial t}
|
||||||
|
|
@ -1652,7 +1656,7 @@ 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="org4206404">
|
<div class="core div" id="orgd2c9b8e">
|
||||||
<p>
|
<p>
|
||||||
{\bf Displacement current}
|
{\bf Displacement current}
|
||||||
\[
|
\[
|
||||||
|
|
@ -1687,7 +1691,7 @@ Flat surface: OK, \(E = 0\) and \(I_{\mbox{enc}} = I\). Balloon surface: \(I
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1657,7 +1661,7 @@ So for non-steady currents, the 'current enclosed by a loop' is ill-defined.
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1655,7 +1659,7 @@ Maxwell's equations {\bf beg} for magnetic charges. But we've never found any!
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1619,8 +1623,8 @@ 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="orge209dc2">
|
<details class="prereq" id="orgcfe0487">
|
||||||
<summary id="org650a07d">
|
<summary id="orge8a2c1d">
|
||||||
Prerequisites
|
Prerequisites
|
||||||
</summary>
|
</summary>
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
|
|
@ -1628,8 +1632,8 @@ Prerequisites
|
||||||
</ul>
|
</ul>
|
||||||
</details>
|
</details>
|
||||||
|
|
||||||
<details class="objectives" id="org4962fbd">
|
<details class="objectives" id="org87970ae">
|
||||||
<summary id="org509fe5e">
|
<summary id="org29e69c3">
|
||||||
Objectives
|
Objectives
|
||||||
</summary>
|
</summary>
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
|
|
@ -1654,7 +1658,7 @@ Objectives
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1621,7 +1625,7 @@ 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="org3de73d0">
|
<div class="main div" id="org15be82e">
|
||||||
<p>
|
<p>
|
||||||
{\bf Angular momentum of EM fields}
|
{\bf Angular momentum of EM fields}
|
||||||
\[
|
\[
|
||||||
|
|
@ -1638,7 +1642,7 @@ The angular momentum of EM fields is directly given by
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!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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|
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<!-- 2022-02-08 Tue 06:55 -->
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<!-- 2022-02-08 Tue 17:21 -->
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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>
|
<title>Pre-Quantum Electrodynamics</title>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1640,7 +1644,7 @@ 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="org20202cd">
|
<div class="core div" id="orgf7fdcf4">
|
||||||
<p>
|
<p>
|
||||||
{\bf Continuity equation}
|
{\bf Continuity equation}
|
||||||
\[
|
\[
|
||||||
|
|
@ -1668,7 +1672,7 @@ imposes a functional constraint on these sources: not {\it any} \(\rho\) and
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1633,7 +1637,7 @@ 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="org2bb42ec">
|
<div class="main div" id="orgeb408ef">
|
||||||
<p>
|
<p>
|
||||||
{\bf Momentum density in the EM fields}
|
{\bf Momentum density in the EM fields}
|
||||||
\[
|
\[
|
||||||
|
|
@ -1645,7 +1649,7 @@ 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="orgaafc4b4">
|
<div class="main div" id="org94bfc0c">
|
||||||
<p>
|
<p>
|
||||||
{\bf Continuity equation for EM momentum}
|
{\bf Continuity equation for EM momentum}
|
||||||
\[
|
\[
|
||||||
|
|
@ -1661,7 +1665,7 @@ In a region in which the mechanical momentum is not changing due to external inf
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1675,7 +1679,7 @@ 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="org9016172">
|
<div class="main div" id="org516af43">
|
||||||
<p>
|
<p>
|
||||||
{\bf Maxwell stress tensor}
|
{\bf Maxwell stress tensor}
|
||||||
\[
|
\[
|
||||||
|
|
@ -1698,7 +1702,7 @@ The element \(T_{ij}\) represents the force per unit area in the $i$th direction
|
||||||
<p>
|
<p>
|
||||||
We then obtain
|
We then obtain
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="org39d7962">
|
<div class="main div" id="org38f0a89">
|
||||||
<p>
|
<p>
|
||||||
{\bf EM force per unit volume}
|
{\bf EM force per unit volume}
|
||||||
\[
|
\[
|
||||||
|
|
@ -1710,7 +1714,7 @@ We then obtain
|
||||||
<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="org384fd10">
|
<div class="main div" id="orgf9a42ff">
|
||||||
<p>
|
<p>
|
||||||
{\bf Total force on charges in volume}
|
{\bf Total force on charges in volume}
|
||||||
\[
|
\[
|
||||||
|
|
@ -1726,7 +1730,7 @@ where \({\boldsymbol S}\) is the Poynting vector. Integrating, we obtain the
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1687,7 +1691,7 @@ so we get
|
||||||
Substituting this in \ref{Gr(8.6)} and using the divergence theorem,
|
Substituting this in \ref{Gr(8.6)} and using the divergence theorem,
|
||||||
we obtain
|
we obtain
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="org4fee5c1">
|
<div class="main div" id="org33b0d12">
|
||||||
<p>
|
<p>
|
||||||
{\bf Poynting's theorem}
|
{\bf Poynting's theorem}
|
||||||
\[
|
\[
|
||||||
|
|
@ -1712,7 +1716,7 @@ 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:
|
Energy per unit time, per unit area carried by EM fields:
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org31c447f">
|
<div class="core div" id="orgb00d4be">
|
||||||
<p>
|
<p>
|
||||||
{\bf Poynting vector}
|
{\bf Poynting vector}
|
||||||
\[
|
\[
|
||||||
|
|
@ -1725,7 +1729,7 @@ Energy per unit time, per unit area carried by EM fields:
|
||||||
<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="org0a1de2b">
|
<div class="core div" id="org618d06c">
|
||||||
<p>
|
<p>
|
||||||
{\bf Poynting's theorem}
|
{\bf Poynting's theorem}
|
||||||
\[
|
\[
|
||||||
|
|
@ -1738,7 +1742,7 @@ 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="org18b8949">
|
<div class="core div" id="orgb4f2685">
|
||||||
<p>
|
<p>
|
||||||
{\bf Energy in electromagnetic fields}
|
{\bf Energy in electromagnetic fields}
|
||||||
\[
|
\[
|
||||||
|
|
@ -1761,7 +1765,7 @@ Then,
|
||||||
\]
|
\]
|
||||||
so we get the
|
so we get the
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org3f5d20d">
|
<div class="core div" id="org1eaf77c">
|
||||||
<p>
|
<p>
|
||||||
{\bf Poynting theorem (differential form)}
|
{\bf Poynting theorem (differential form)}
|
||||||
\[
|
\[
|
||||||
|
|
@ -1778,7 +1782,7 @@ and has a similar for to the continuity equation
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
<div class="example div" id="org9d76705">
|
<div class="example div" id="org545c704">
|
||||||
<p>
|
<p>
|
||||||
\paragraph{Example 8.1} Current in a wire: Joule heating. Energy per unit time delivered to wire: from Poynting.
|
\paragraph{Example 8.1} Current in a wire: Joule heating. Energy per unit time delivered to wire: from Poynting.
|
||||||
Assuming that the field is uniform, the electric field parallel to the wire is
|
Assuming that the field is uniform, the electric field parallel to the wire is
|
||||||
|
|
@ -1810,7 +1814,7 @@ and the value is as expected.
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1619,8 +1623,8 @@ 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="orgdd3d3f8">
|
<details class="prereq" id="org5bcd123">
|
||||||
<summary id="orgd8f94af">
|
<summary id="org41526cb">
|
||||||
Prerequisites
|
Prerequisites
|
||||||
</summary>
|
</summary>
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
|
|
@ -1629,8 +1633,8 @@ Prerequisites
|
||||||
</ul>
|
</ul>
|
||||||
</details>
|
</details>
|
||||||
|
|
||||||
<details class="objectives" id="org8ebd2c8">
|
<details class="objectives" id="org81e7bec">
|
||||||
<summary id="org56a0c80">
|
<summary id="org62ac99a">
|
||||||
Objectives
|
Objectives
|
||||||
</summary>
|
</summary>
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
|
|
@ -1658,7 +1662,7 @@ Objectives
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1649,7 +1653,7 @@ so for a monochromatic EM plan wave,
|
||||||
\]
|
\]
|
||||||
or more succinctly:
|
or more succinctly:
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="org5ab2d39">
|
<div class="main div" id="orgeb0be24">
|
||||||
<p>
|
<p>
|
||||||
{\bf Poynting vector of a monochromatic EM wave}
|
{\bf Poynting vector of a monochromatic EM wave}
|
||||||
\[
|
\[
|
||||||
|
|
@ -1665,7 +1669,7 @@ 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="org703b070">
|
<div class="main div" id="org372457d">
|
||||||
<p>
|
<p>
|
||||||
{\bf Momentum density of a monochromatic EM wave}
|
{\bf Momentum density of a monochromatic EM wave}
|
||||||
\[
|
\[
|
||||||
|
|
@ -1703,7 +1707,7 @@ The {\it radiation pressure} is the momentum transfer per unit area per unit of
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1650,7 +1654,7 @@ 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="orgf8f14a8">
|
<div class="core div" id="org22a7fdd">
|
||||||
<p>
|
<p>
|
||||||
{\bf E and B fields for a monochromatic EM plane wave}
|
{\bf E and B fields for a monochromatic EM plane wave}
|
||||||
\[
|
\[
|
||||||
|
|
@ -1681,7 +1685,7 @@ or if you prefer explicit real parts (adding a possible phase shift \(\delta\)):
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1647,7 +1651,7 @@ 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="org6e2c86d">
|
<div class="core div" id="org1160663">
|
||||||
<p>
|
<p>
|
||||||
{\bf Wave equations for electric and magnetic fields in vacuum}
|
{\bf Wave equations for electric and magnetic fields in vacuum}
|
||||||
\[
|
\[
|
||||||
|
|
@ -1690,7 +1694,7 @@ the actual electric and magnetic fields are given by the real part.
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1630,7 +1634,7 @@ Table of contents
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1630,7 +1634,7 @@ Table of contents
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1654,7 +1658,7 @@ 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="orgb555ebf">
|
<div class="core div" id="orgff46cb4">
|
||||||
<p>
|
<p>
|
||||||
{\bf Polarization current density}
|
{\bf Polarization current density}
|
||||||
\[
|
\[
|
||||||
|
|
@ -1672,7 +1676,7 @@ 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="org86c5ff2">
|
<aside id="orgbce7d73">
|
||||||
<p>
|
<p>
|
||||||
Note the unfortunate labelling: it would have been nicer to have \(\rho_b\) be the charge associated to current
|
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 convention used here.
|
\({\boldsymbol J}_b\) but this is not the convention used here.
|
||||||
|
|
@ -1695,7 +1699,7 @@ 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,
|
||||||
{\it free} and {\it bound}:
|
{\it free} and {\it bound}:
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="orgf8c82b2">
|
<div class="main div" id="org4df7865">
|
||||||
<p>
|
<p>
|
||||||
\[
|
\[
|
||||||
\rho = \rho_f + \rho_b = \rho_f - {\boldsymbol \nabla} \cdot {\bf P}
|
\rho = \rho_f + \rho_b = \rho_f - {\boldsymbol \nabla} \cdot {\bf P}
|
||||||
|
|
@ -1708,7 +1712,7 @@ In view of this: total charge density can be separated into 2 parts,
|
||||||
and current can be separated into three parts, {\it free}, {\it bound} and
|
and current can be separated into three parts, {\it free}, {\it bound} and
|
||||||
{\it polarization}:
|
{\it polarization}:
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="org4054380">
|
<div class="main div" id="orgcc32502">
|
||||||
<p>
|
<p>
|
||||||
\[
|
\[
|
||||||
{\bf J} = {\bf J}_f + {\bf J}_b + {\bf J}_p = {\bf J}_f + {\boldsymbol ∇} × {\bf M}
|
{\bf J} = {\bf J}_f + {\bf J}_b + {\bf J}_p = {\bf J}_f + {\boldsymbol ∇} × {\bf M}
|
||||||
|
|
@ -1732,7 +1736,7 @@ Gauss's law: can be rewritten
|
||||||
\]
|
\]
|
||||||
where (as in static case)
|
where (as in static case)
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="orgf78b92c">
|
<div class="core div" id="org7600f00">
|
||||||
<p>
|
<p>
|
||||||
\[
|
\[
|
||||||
{\bf D} \equiv \varepsilon_0 {\bf E} + {\bf P}
|
{\bf D} \equiv \varepsilon_0 {\bf E} + {\bf P}
|
||||||
|
|
@ -1758,7 +1762,7 @@ or
|
||||||
\]
|
\]
|
||||||
where as before
|
where as before
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org513c514">
|
<div class="core div" id="orgb942ad8">
|
||||||
<p>
|
<p>
|
||||||
\[
|
\[
|
||||||
{\bf H} \equiv \frac{1}{\mu_0} {\bf B} - {\bf M}
|
{\bf H} \equiv \frac{1}{\mu_0} {\bf B} - {\bf M}
|
||||||
|
|
@ -1776,7 +1780,7 @@ 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="org686ea33">
|
<div class="core div" id="orgd9d30d5">
|
||||||
<p>
|
<p>
|
||||||
{\bf Maxwell's equations {\it (in matter)}}
|
{\bf Maxwell's equations {\it (in matter)}}
|
||||||
</p>
|
</p>
|
||||||
|
|
@ -1802,7 +1806,7 @@ Must be complemented by the {\bf constitutive relations} giving \({\bf D}\) and
|
||||||
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="org6accc1d">
|
<div class="main div" id="orge1df28e">
|
||||||
<p>
|
<p>
|
||||||
\[
|
\[
|
||||||
{\bf P} = \varepsilon_0 \chi_e {\bf E}, \hspace{1cm}
|
{\bf P} = \varepsilon_0 \chi_e {\bf E}, \hspace{1cm}
|
||||||
|
|
@ -1826,7 +1830,7 @@ where \(\varepsilon \equiv \varepsilon_0(1 + \chi_e)\) and \(\mu \equiv \mu_0 (1
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1621,7 +1625,7 @@ Table of contents
|
||||||
<p>
|
<p>
|
||||||
Discontinuities between different media, deduced from
|
Discontinuities between different media, deduced from
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org18c9c85">
|
<div class="core div" id="orgbbf71a6">
|
||||||
<p>
|
<p>
|
||||||
{\bf Maxwell's equations {\it (in matter)}, integral form}
|
{\bf Maxwell's equations {\it (in matter)}, integral form}
|
||||||
</p>
|
</p>
|
||||||
|
|
@ -1699,7 +1703,7 @@ These are basis of theory of reflection and refraction.
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1633,7 +1637,7 @@ Table of contents
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1629,7 +1633,7 @@ Table of contents
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1725,7 +1729,7 @@ so the final form of the fields is
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1656,7 +1660,7 @@ 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="orgc00345d">
|
<div class="main div" id="orgeaea7cb">
|
||||||
<p>
|
<p>
|
||||||
{\bf Index of refraction}
|
{\bf Index of refraction}
|
||||||
\[
|
\[
|
||||||
|
|
@ -1700,7 +1704,7 @@ I = \frac{1}{2} \varepsilon v E_0^2
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1644,7 +1648,7 @@ Detailed study: starts from boundary conditions \ref{Gr(7.64)},
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1624,7 +1628,7 @@ Table of contents
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1625,7 +1629,7 @@ Table of contents
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1716,7 +1720,7 @@ R + T = 1.
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1656,7 +1660,7 @@ 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="orgefbfc7d">
|
<div class="core div" id="orga1858e0">
|
||||||
<p>
|
<p>
|
||||||
{\bf First law of reflection:}
|
{\bf First law of reflection:}
|
||||||
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.
|
||||||
|
|
@ -1671,7 +1675,7 @@ Specializing (\ref{eq:RTObliquek}) to our notations, we have
|
||||||
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="org13fc947">
|
<div class="core div" id="orgc1aaaad">
|
||||||
<p>
|
<p>
|
||||||
{\bf Law of reflection}
|
{\bf Law of reflection}
|
||||||
\[
|
\[
|
||||||
|
|
@ -1729,7 +1733,7 @@ while the third equation becomes
|
||||||
\]
|
\]
|
||||||
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="orgd7a540b">
|
<div class="main div" id="org4da7748">
|
||||||
<p>
|
<p>
|
||||||
{\bf Fresnel's equations for reflection and transmission amplitudes (parallel case)}
|
{\bf Fresnel's equations for reflection and transmission amplitudes (parallel case)}
|
||||||
\[
|
\[
|
||||||
|
|
@ -1749,7 +1753,7 @@ Amplitudes for transmitted and reflected wave: depend on angle of incidence:
|
||||||
Behaviour: for \(\theta_I = 0\) we recover (\ref{Gr(9.82)}).
|
Behaviour: for \(\theta_I = 0\) we recover (\ref{Gr(9.82)}).
|
||||||
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="orgdb6468b">
|
<div class="main div" id="orge2d9787">
|
||||||
<p>
|
<p>
|
||||||
{\bf Brewster's angle {\it (at which the reflected wave amplitude vanishes)}}
|
{\bf Brewster's angle {\it (at which the reflected wave amplitude vanishes)}}
|
||||||
\[
|
\[
|
||||||
|
|
@ -1786,7 +1790,7 @@ Of course, we get \(R + T = 1\) as expected.
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
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|
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|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
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|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
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|
||||||
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|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1625,7 +1629,7 @@ Table of contents
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
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|
||||||
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<html lang="en">
|
||||||
<head>
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|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
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|
||||||
<meta charset="utf-8">
|
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|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
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|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1631,7 +1635,7 @@ Table of contents
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
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|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1651,7 +1655,7 @@ where \(A\) is a constant amplitude. Substituting and taking the real part,
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1675,7 +1679,7 @@ with an identical equation for \(B_z\). If \(E_z = 0\) the waves are called {\bf
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1684,7 +1688,7 @@ which is {\it greater} than \(c\). The energy of the wave however propagates at
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1619,8 +1623,8 @@ 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="org0b4147b">
|
<details class="prereq" id="org86ffe7e">
|
||||||
<summary id="orgaa9a8c2">
|
<summary id="org72ae362">
|
||||||
Prerequisites
|
Prerequisites
|
||||||
</summary>
|
</summary>
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
|
|
@ -1628,8 +1632,8 @@ Prerequisites
|
||||||
</ul>
|
</ul>
|
||||||
</details>
|
</details>
|
||||||
|
|
||||||
<details class="objectives" id="orgd0127b4">
|
<details class="objectives" id="org9d4a979">
|
||||||
<summary id="orgf210d58">
|
<summary id="org984c0c5">
|
||||||
Objectives
|
Objectives
|
||||||
</summary>
|
</summary>
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
|
|
@ -1652,7 +1656,7 @@ Objectives
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1649,7 +1653,7 @@ implementing a <b>gauge transformation</b>.
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1648,7 +1652,7 @@ Although Gauss's law looks nice in the Coulomb gauge, Amp{\`e}re-Maxwell does no
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1634,7 +1638,7 @@ while the equation for \(V\) 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="orgd5ba96e">
|
<div class="core div" id="orgd4a4d0b">
|
||||||
<p>
|
<p>
|
||||||
{\bf d'Alembertian operator}
|
{\bf d'Alembertian operator}
|
||||||
\[
|
\[
|
||||||
|
|
@ -1647,7 +1651,7 @@ 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="org15005e7">
|
<div class="core div" id="orgbeb1250">
|
||||||
<p>
|
<p>
|
||||||
{\bf Inhomogeneous Maxwell equations (Lorenz gauge)}
|
{\bf Inhomogeneous Maxwell equations (Lorenz gauge)}
|
||||||
\[
|
\[
|
||||||
|
|
@ -1684,7 +1688,7 @@ we have by direct inspection
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1635,7 +1639,7 @@ Useful strategy: represent fields in terms of potentials.
|
||||||
<p>
|
<p>
|
||||||
Easiest:
|
Easiest:
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="org389d31f">
|
<div class="core div" id="org45e0ed0">
|
||||||
<p>
|
<p>
|
||||||
\[
|
\[
|
||||||
{\boldsymbol B} = {\boldsymbol \nabla} \times {\boldsymbol A}
|
{\boldsymbol B} = {\boldsymbol \nabla} \times {\boldsymbol A}
|
||||||
|
|
@ -1651,7 +1655,7 @@ Putting this into Faraday's law gives
|
||||||
\]
|
\]
|
||||||
so this can be written as the gradient of a scalar (by choice: \(-{\boldsymbol \nabla} V\)) so we get
|
so this can be written as the gradient of a scalar (by choice: \(-{\boldsymbol \nabla} V\)) so we get
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="orgbbcf54f">
|
<div class="core div" id="orgb9810af">
|
||||||
<p>
|
<p>
|
||||||
\[
|
\[
|
||||||
{\boldsymbol E} = -{\boldsymbol \nabla} V - \frac{\partial {\boldsymbol A}}{\partial t}
|
{\boldsymbol E} = -{\boldsymbol \nabla} V - \frac{\partial {\boldsymbol A}}{\partial t}
|
||||||
|
|
@ -1664,7 +1668,7 @@ so this can be written as the gradient of a scalar (by choice: \(-{\boldsymbol \
|
||||||
<p>
|
<p>
|
||||||
Using this potential representation for \({\boldsymbol E}\) and \({\boldsymbol B}\) automatically fulfills the two homogeneous Maxwell equations. For the inhomogeneous equations, substituting (\ref{eq:E_from_Potentials}) 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 (\ref{eq:E_from_Potentials}) into Gauss's law gives
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="org2d36baf">
|
<div class="main div" id="org1c236f0">
|
||||||
<p>
|
<p>
|
||||||
\[
|
\[
|
||||||
{\boldsymbol \nabla}^2 V + \frac{\partial}{\partial t} {\boldsymbol \nabla} \cdot {\boldsymbol A} = -\frac{\rho}{\varepsilon_0}
|
{\boldsymbol \nabla}^2 V + \frac{\partial}{\partial t} {\boldsymbol \nabla} \cdot {\boldsymbol A} = -\frac{\rho}{\varepsilon_0}
|
||||||
|
|
@ -1680,7 +1684,7 @@ whereas Amp{\`ere}-Maxwell becomes
|
||||||
\]
|
\]
|
||||||
which becomes after simple rearrangement and use of the 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 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="orga7cdd8b">
|
<div class="main div" id="orgf3f4dcd">
|
||||||
<p>
|
<p>
|
||||||
\[
|
\[
|
||||||
\left( {\boldsymbol ∇}^2 {\boldsymbol A} - μ_0 ε_0 \frac{∂^2 {\boldsymbol A}}{∂ t^2} \right)
|
\left( {\boldsymbol ∇}^2 {\boldsymbol A} - μ_0 ε_0 \frac{∂^2 {\boldsymbol A}}{∂ t^2} \right)
|
||||||
|
|
@ -1703,7 +1707,7 @@ which becomes after simple rearrangement and use of the identity \({\boldsymbol
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1632,7 +1636,7 @@ Table of contents
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1619,8 +1623,8 @@ Table of contents
|
||||||
</svg></a><span class="headline-id">ems.ca</span></h3>
|
</svg></a><span class="headline-id">ems.ca</span></h3>
|
||||||
|
|
||||||
<div class="outline-text-3" id="text-ems_ca">
|
<div class="outline-text-3" id="text-ems_ca">
|
||||||
<details class="prereq" id="org9f1c7db">
|
<details class="prereq" id="orgbb80f83">
|
||||||
<summary id="orgbf053b0">
|
<summary id="org379b6a1">
|
||||||
Prerequisites
|
Prerequisites
|
||||||
</summary>
|
</summary>
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
|
|
@ -1628,8 +1632,8 @@ Prerequisites
|
||||||
</ul>
|
</ul>
|
||||||
</details>
|
</details>
|
||||||
|
|
||||||
<details class="objectives" id="org06b35e7">
|
<details class="objectives" id="orgd1100e2">
|
||||||
<summary id="org6416a57">
|
<summary id="org27953b9">
|
||||||
Objectives
|
Objectives
|
||||||
</summary>
|
</summary>
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
|
|
@ -1654,7 +1658,7 @@ Objectives
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1624,7 +1628,7 @@ 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="orgb912407">
|
<div class="main div" id="org14f8ad7">
|
||||||
\begin{equation*}
|
\begin{equation*}
|
||||||
{\bf E} ({\bf r}) = \frac{1}{4\pi\varepsilon_0} \int_{\mathbb{R}^3} d\tau' \rho({\bf r}') \frac{{\bf r} - {\bf r}'}{|{\bf r} - {\bf r}'|^3}
|
{\bf E} ({\bf r}) = \frac{1}{4\pi\varepsilon_0} \int_{\mathbb{R}^3} d\tau' \rho({\bf r}') \frac{{\bf r} - {\bf r}'}{|{\bf r} - {\bf r}'|^3}
|
||||||
\end{equation*}
|
\end{equation*}
|
||||||
|
|
@ -1634,7 +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 (\ref{eq:V_from_rho})
|
explicit construction (\ref{eq:V_from_rho})
|
||||||
</p>
|
</p>
|
||||||
<div class="main div" id="orgc09a05f">
|
<div class="main div" id="org83b53d5">
|
||||||
<p>
|
<p>
|
||||||
\[
|
\[
|
||||||
V({\bf r}) = \frac{1}{4\pi \varepsilon_0} \int_{\mathbb{R}^3} d\tau' \frac{\rho({\bf r}')}{|{\bf r} - {\bf r}'|}.
|
V({\bf r}) = \frac{1}{4\pi \varepsilon_0} \int_{\mathbb{R}^3} d\tau' \frac{\rho({\bf r}')}{|{\bf r} - {\bf r}'|}.
|
||||||
|
|
@ -1650,7 +1654,7 @@ condition (\ref{Gr(2.20)}) can be expressed as the single
|
||||||
'local' (differential) condition (Poisson's equation) (\ref{eq:Poisson})
|
'local' (differential) condition (Poisson's equation) (\ref{eq:Poisson})
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="core div" id="orgbe52068">
|
<div class="core div" id="org52d8655">
|
||||||
<p>
|
<p>
|
||||||
\[
|
\[
|
||||||
{\boldsymbol \nabla}^2 V = -\frac{\rho}{\varepsilon_0}.
|
{\boldsymbol \nabla}^2 V = -\frac{\rho}{\varepsilon_0}.
|
||||||
|
|
@ -1664,7 +1668,7 @@ condition (\ref{Gr(2.20)}) can be expressed as the single
|
||||||
In the specific case where the charge density vanishes, we fall back onto the simpler
|
In the specific case where the charge density vanishes, we fall back onto the simpler
|
||||||
Laplace equation
|
Laplace equation
|
||||||
</p>
|
</p>
|
||||||
<div class="core div" id="orgb4303af">
|
<div class="core div" id="orgceb6a79">
|
||||||
<p>
|
<p>
|
||||||
\[
|
\[
|
||||||
{\boldsymbol \nabla}^2 V = 0
|
{\boldsymbol \nabla}^2 V = 0
|
||||||
|
|
@ -1686,7 +1690,7 @@ Laplace equation
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1698,7 +1702,7 @@ 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="info div" id="orga2b5411">
|
<div class="info div" id="org12caa26">
|
||||||
<p>
|
<p>
|
||||||
<b>Earnshaw's theorem</b> <br>
|
<b>Earnshaw's theorem</b> <br>
|
||||||
Since solutions to Laplace's equation have no local minimum,
|
Since solutions to Laplace's equation have no local minimum,
|
||||||
|
|
@ -1788,7 +1792,7 @@ This all feels a bit amateurish and not very systematic. Can we be more precise
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -1,7 +1,7 @@
|
||||||
<!DOCTYPE html>
|
<!DOCTYPE html>
|
||||||
<html lang="en">
|
<html lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2022-02-08 Tue 06:55 -->
|
<!-- 2022-02-08 Tue 17:21 -->
|
||||||
<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>
|
||||||
|
|
@ -272,6 +272,10 @@ Table of contents
|
||||||
</summary>
|
</summary>
|
||||||
<ul>
|
<ul>
|
||||||
<li>
|
<li>
|
||||||
|
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
|
||||||
|
|
||||||
|
</li>
|
||||||
|
<li>
|
||||||
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
|
|
@ -736,7 +740,7 @@ Table of contents
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
|
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
|
||||||
|
|
||||||
</li>
|
</li>
|
||||||
<li>
|
<li>
|
||||||
|
|
@ -1618,11 +1622,11 @@ 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="orgbc8a544">
|
<div class="info div" id="org8d7045e">
|
||||||
<p>
|
<p>
|
||||||
<b>George Green</b>
|
<b>George Green</b>
|
||||||
</p>
|
</p>
|
||||||
<aside id="org5513bf5">
|
<aside id="org53725f0">
|
||||||
<p>
|
<p>
|
||||||
See a \href{short biography of George Green on Wikipedia}{https://en.wikipedia.org/wiki/George\_Green\_(mathematician)}.
|
See a \href{short biography of George Green on Wikipedia}{https://en.wikipedia.org/wiki/George\_Green\_(mathematician)}.
|
||||||
</p>
|
</p>
|
||||||
|
|
@ -1676,7 +1680,7 @@ interchanged, and subtract the result, we obtain another useful result known as
|
||||||
|
|
||||||
<hr><div id="postamble" class="status">
|
<hr><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: 2022-02-08 Tue 06:55</p>
|
<p class="date">Created: 2022-02-08 Tue 17:21</p>
|
||||||
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
|
||||||
Some files were not shown because too many files have changed in this diff Show More
Loading…
Reference in New Issue