Update 2022-02-21 10:35
This commit is contained in:
Jean-Sébastien
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ec8a4ca406
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build/a.html
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build/a.html
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<!DOCTYPE html>
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<html lang="en">
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<head>
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<!-- 2022-02-17 Thu 08:42 -->
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<!-- 2022-02-21 Mon 10:33 -->
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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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<title>Pre-Quantum Electrodynamics</title>
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@ -602,11 +602,11 @@ Table of contents
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</summary>
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<ul>
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<li>
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<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
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<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
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</li>
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||||
<li>
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||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
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<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
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</li>
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@ -614,21 +614,12 @@ Table of contents
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</details>
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</li>
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<li>
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<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
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<details>
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<summary>
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</li>
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||||
<li>
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<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
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</summary>
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<ul>
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<li>
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<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
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</li>
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</ul>
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</details>
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</li>
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<li>
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@ -640,11 +631,15 @@ Table of contents
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</summary>
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<ul>
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<li>
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<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
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<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
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</li>
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<li>
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<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
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<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
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</li>
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<li>
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<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
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</li>
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@ -661,6 +656,10 @@ Table of contents
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</summary>
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<ul>
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||||
<li>
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<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
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</li>
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||||
<li>
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<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
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</li>
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@ -698,10 +697,6 @@ Table of contents
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</summary>
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<ul>
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<li>
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<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
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</li>
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||||
<li>
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||||
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||||
<details>
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||||
<summary>
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@ -1435,7 +1430,7 @@ Table of contents
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</li>
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<li>
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<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
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<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
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</li>
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<li>
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@ -1621,7 +1616,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
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</div>
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<div id="postamble" class="status">
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<p class="author">Author: Jean-Sébastien Caux</p>
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<p class="date">Created: 2022-02-17 Thu 08:42</p>
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<p class="date">Created: 2022-02-21 Mon 10:33</p>
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<p class="validation"></p>
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</div>
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@ -1,7 +1,7 @@
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<!DOCTYPE html>
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<html lang="en">
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||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
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||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
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||||
|
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@ -602,11 +602,11 @@ Table of contents
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</summary>
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||||
<ul>
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||||
<li>
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||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
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<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
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</li>
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<li>
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<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
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<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
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</li>
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@ -614,21 +614,12 @@ Table of contents
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</details>
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</li>
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<li>
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<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
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<details>
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<summary>
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</li>
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<li>
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<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
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</summary>
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<ul>
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<li>
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<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
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</li>
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</ul>
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</details>
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||||
</li>
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<li>
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@ -640,11 +631,15 @@ Table of contents
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</summary>
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<ul>
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<li>
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<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
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<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
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</li>
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<li>
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<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
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<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
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</li>
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<li>
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<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
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</li>
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@ -661,6 +656,10 @@ Table of contents
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</summary>
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<ul>
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<li>
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<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
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</li>
|
||||
<li>
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<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
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</li>
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@ -698,10 +697,6 @@ Table of contents
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|||
</summary>
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<ul>
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||||
<li>
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<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
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</li>
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<li>
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||||
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<details>
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||||
<summary>
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@ -1435,7 +1430,7 @@ Table of contents
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|||
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</li>
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<li>
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<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
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<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
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</li>
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<li>
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@ -1704,7 +1699,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
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|||
</div>
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||||
<div id="postamble" class="status">
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||||
<p class="author">Author: Jean-Sébastien Caux</p>
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||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
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||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
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||||
<p class="validation"></p>
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||||
</div>
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||||
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41
build/c.html
41
build/c.html
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@ -1,7 +1,7 @@
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<!DOCTYPE html>
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||||
<html lang="en">
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||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
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||||
|
|
@ -602,11 +602,11 @@ Table of contents
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|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
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||||
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</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
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</li>
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@ -614,21 +614,12 @@ Table of contents
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</details>
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</li>
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<li>
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<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
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<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
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<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
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</summary>
|
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<ul>
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<li>
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<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
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</li>
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</ul>
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</details>
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||||
</li>
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<li>
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@ -640,11 +631,15 @@ Table of contents
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</summary>
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<ul>
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<li>
|
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<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
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<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
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|
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</li>
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<li>
|
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<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
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<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
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</li>
|
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<li>
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<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
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</li>
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@ -661,6 +656,10 @@ Table of contents
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</summary>
|
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<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
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|
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</li>
|
||||
<li>
|
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<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
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|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
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@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
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<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
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||||
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||||
</li>
|
||||
<li>
|
||||
|
|
@ -1621,7 +1616,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
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|||
</div>
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||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
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<p class="date">Created: 2022-02-17 Thu 08:42</p>
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||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
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|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
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|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
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</li>
|
||||
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||||
|
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@ -614,21 +614,12 @@ Table of contents
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|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
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|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
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</summary>
|
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<ul>
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<li>
|
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<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
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|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
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||||
|
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@ -640,11 +631,15 @@ Table of contents
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|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
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<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
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|
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</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1627,7 +1622,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1623,7 +1618,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1643,14 +1638,14 @@ Range of parameters: \(r \in [0, \infty[\), \(\varphi \in [0, 2\pi[\) and \(z \
|
|||
<div id="outline-container-c_m_cs_cyl_grad" class="outline-6">
|
||||
<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="eqlabel" id="org7b9a99f">
|
||||
<div class="eqlabel" id="org238184d">
|
||||
<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">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org2c751cd">
|
||||
<div class="alteqlabels" id="org0747d47">
|
||||
<ul class="org-ul">
|
||||
<li>Gr4(1.79)</li>
|
||||
</ul>
|
||||
|
|
@ -1671,14 +1666,14 @@ Range of parameters: \(r \in [0, \infty[\), \(\varphi \in [0, 2\pi[\) and \(z \
|
|||
<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>
|
||||
<div class="outline-text-6" id="text-c_m_cs_cyl_div">
|
||||
<div class="eqlabel" id="orga3e29d1">
|
||||
<div class="eqlabel" id="orgcf8ddd8">
|
||||
<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">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org3d0b2fa">
|
||||
<div class="alteqlabels" id="org0a61378">
|
||||
<ul class="org-ul">
|
||||
<li>Gr4(2.21)</li>
|
||||
</ul>
|
||||
|
|
@ -1699,14 +1694,14 @@ Range of parameters: \(r \in [0, \infty[\), \(\varphi \in [0, 2\pi[\) and \(z \
|
|||
<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>
|
||||
<div class="outline-text-6" id="text-c_m_cs_cyl_curl">
|
||||
<div class="eqlabel" id="org204f3ee">
|
||||
<div class="eqlabel" id="orgb593e8e">
|
||||
<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">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org42e15eb">
|
||||
<div class="alteqlabels" id="org3c26968">
|
||||
<ul class="org-ul">
|
||||
<li>Gr4(2.21)</li>
|
||||
</ul>
|
||||
|
|
@ -1755,7 +1750,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1616,7 +1611,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1607,14 +1602,14 @@ which \(r\) is the distance from the chosen origin,
|
|||
The usual Cartesian coordinates relate to spherical coordinates
|
||||
according to
|
||||
</p>
|
||||
<div class="eqlabel" id="orgbcfbea1">
|
||||
<div class="eqlabel" id="org27681c3">
|
||||
<p>
|
||||
<a id="sph_xyz"></a><a href="./c_m_cs_sph.html#sph_xyz"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org71b8aed">
|
||||
<div class="alteqlabels" id="org41dfc3e">
|
||||
|
||||
</div>
|
||||
|
||||
|
|
@ -1639,14 +1634,14 @@ A generic vector can be expressed as
|
|||
where the explicit relation between spherical and
|
||||
Cartesian unit vectors is
|
||||
</p>
|
||||
<div class="eqlabel" id="org6e45fd1">
|
||||
<div class="eqlabel" id="org8bd9d3d">
|
||||
<p>
|
||||
<a id="sph_uv"></a><a href="./c_m_cs_sph.html#sph_uv"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org5b78c82">
|
||||
<div class="alteqlabels" id="orga7940d0">
|
||||
|
||||
</div>
|
||||
|
||||
|
|
@ -1669,14 +1664,14 @@ and \(\hat{\boldsymbol \varphi} (\theta, \varphi)\).
|
|||
<p>
|
||||
An infinitesimal displacement \(d{\bf l}\) can be written as
|
||||
</p>
|
||||
<div class="eqlabel" id="org673b085">
|
||||
<div class="eqlabel" id="org3750477">
|
||||
<p>
|
||||
<a id="sph_dl"></a><a href="./c_m_cs_sph.html#sph_dl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org77c531c">
|
||||
<div class="alteqlabels" id="orge80cb83">
|
||||
|
||||
</div>
|
||||
|
||||
|
|
@ -1692,14 +1687,14 @@ d{\bf l} = dr ~\hat{\boldsymbol r} + r d\theta ~\hat{\boldsymbol \theta} + r\sin
|
|||
<p>
|
||||
Infinitesimal volume element:
|
||||
</p>
|
||||
<div class="eqlabel" id="org1dbbdd5">
|
||||
<div class="eqlabel" id="orgf70b76f">
|
||||
<p>
|
||||
<a id="sph_dtau"></a><a href="./c_m_cs_sph.html#sph_dtau"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org00dd06e">
|
||||
<div class="alteqlabels" id="orgceda545">
|
||||
|
||||
</div>
|
||||
|
||||
|
|
@ -1720,14 +1715,14 @@ Infinitesimal surface element: depends on situation.
|
|||
<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>
|
||||
<div class="outline-text-6" id="text-c_m_cs_sph_grad">
|
||||
<div class="eqlabel" id="org80c4f55">
|
||||
<div class="eqlabel" id="org4246420">
|
||||
<p>
|
||||
<a id="sph_grad"></a><a href="./c_m_cs_sph.html#sph_grad"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org0ea0f03">
|
||||
<div class="alteqlabels" id="org25d124f">
|
||||
|
||||
</div>
|
||||
|
||||
|
|
@ -1744,14 +1739,14 @@ Infinitesimal surface element: depends on situation.
|
|||
<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>
|
||||
<div class="outline-text-6" id="text-c_m_cs_sph_div">
|
||||
<div class="eqlabel" id="orgfe29a0f">
|
||||
<div class="eqlabel" id="org2e86b9a">
|
||||
<p>
|
||||
<a id="sph_div"></a><a href="./c_m_cs_sph.html#sph_div"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org5b16e24">
|
||||
<div class="alteqlabels" id="org7267db3">
|
||||
|
||||
</div>
|
||||
|
||||
|
|
@ -1768,14 +1763,14 @@ Infinitesimal surface element: depends on situation.
|
|||
<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>
|
||||
<div class="outline-text-6" id="text-c_m_cs_sph_curl">
|
||||
<div class="eqlabel" id="orga4479e8">
|
||||
<div class="eqlabel" id="orgeedbe30">
|
||||
<p>
|
||||
<a id="sph_curl"></a><a href="./c_m_cs_sph.html#sph_curl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org557f5ed">
|
||||
<div class="alteqlabels" id="org5abe4c1">
|
||||
|
||||
</div>
|
||||
|
||||
|
|
@ -1794,14 +1789,14 @@ Infinitesimal surface element: depends on situation.
|
|||
<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>
|
||||
<div class="outline-text-6" id="text-c_m_cs_sph_lap">
|
||||
<div class="eqlabel" id="orgecfce1d">
|
||||
<div class="eqlabel" id="org515dcfa">
|
||||
<p>
|
||||
<a id="sph_Lap"></a><a href="./c_m_cs_sph.html#sph_Lap"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org01d6eb3">
|
||||
<div class="alteqlabels" id="orgbb072b6">
|
||||
|
||||
</div>
|
||||
|
||||
|
|
@ -1835,7 +1830,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1607,7 +1602,7 @@ Table of contents
|
|||
<li><a href="c_m_dc_del.html">The \({\boldsymbol \nabla}\) Operator</a><span class="headline-id">c.m.dc.del</span></li>
|
||||
<li><a href="c_m_dc_div.html">The Divergence</a><span class="headline-id">c.m.dc.div</span></li>
|
||||
<li><a href="c_m_dc_curl.html">The Curl</a><span class="headline-id">c.m.dc.curl</span></li>
|
||||
<li><a href="c_m_dc_pr.html">Product Rules</a><span class="headline-id">c.m.dc.pr</span></li>
|
||||
<li><a href="c_m_dc_pr.html">Product arguments</a><span class="headline-id">c.m.dc.pr</span></li>
|
||||
<li><a href="c_m_dc_d2.html">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span></li>
|
||||
</ul>
|
||||
|
||||
|
|
@ -1626,7 +1621,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1591,7 +1586,7 @@ Table of contents
|
|||
</ul>
|
||||
</details>
|
||||
</nav>
|
||||
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_dc.html">Differential Calculus</a></li><li>The Curl</li></ul><ul class="navigation-links"><li>Prev: <a href="c_m_dc_div.html">The Divergence <small>[c.m.dc.div]</small></a></li><li>Next: <a href="c_m_dc_pr.html">Product Rules <small>[c.m.dc.pr]</small></a></li><li>Up: <a href="c_m_dc.html">Differential Calculus <small>[c.m.dc]</small></a></li></ul><div id="outline-container-c_m_dc_curl" class="outline-5">
|
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<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_dc.html">Differential Calculus</a></li><li>The Curl</li></ul><ul class="navigation-links"><li>Prev: <a href="c_m_dc_div.html">The Divergence <small>[c.m.dc.div]</small></a></li><li>Next: <a href="c_m_dc_pr.html">Product arguments <small>[c.m.dc.pr]</small></a></li><li>Up: <a href="c_m_dc.html">Differential Calculus <small>[c.m.dc]</small></a></li></ul><div id="outline-container-c_m_dc_curl" class="outline-5">
|
||||
<h5 id="c_m_dc_curl">The Curl<a class="headline-permalink" href="./c_m_dc_curl.html#c_m_dc_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="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"/>
|
||||
|
|
@ -1613,7 +1608,7 @@ v_x & v_y & v_z \end{array} \right| \nonumber \\
|
|||
|
||||
|
||||
|
||||
<br><ul class="navigation-links"><li>Prev: <a href="c_m_dc_div.html">The Divergence <small>[c.m.dc.div]</small></a></li><li>Next: <a href="c_m_dc_pr.html">Product Rules <small>[c.m.dc.pr]</small></a></li><li>Up: <a href="c_m_dc.html">Differential Calculus <small>[c.m.dc]</small></a></li></ul>
|
||||
<br><ul class="navigation-links"><li>Prev: <a href="c_m_dc_div.html">The Divergence <small>[c.m.dc.div]</small></a></li><li>Next: <a href="c_m_dc_pr.html">Product arguments <small>[c.m.dc.pr]</small></a></li><li>Up: <a href="c_m_dc.html">Differential Calculus <small>[c.m.dc]</small></a></li></ul>
|
||||
<br>
|
||||
<hr>
|
||||
<div class="license">
|
||||
|
|
@ -1628,7 +1623,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li class="toc-currentpage">
|
||||
|
|
@ -1591,7 +1586,7 @@ Table of contents
|
|||
</ul>
|
||||
</details>
|
||||
</nav>
|
||||
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_dc.html">Differential Calculus</a></li><li>Second Derivatives</li></ul><ul class="navigation-links"><li>Prev: <a href="c_m_dc_pr.html">Product Rules <small>[c.m.dc.pr]</small></a></li><li>Next: <a href="c_m_ic.html">Integral Calculus <small>[c.m.ic]</small></a></li><li>Up: <a href="c_m_dc.html">Differential Calculus <small>[c.m.dc]</small></a></li></ul><div id="outline-container-c_m_dc_d2" class="outline-5">
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<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_dc.html">Differential Calculus</a></li><li>Second Derivatives</li></ul><ul class="navigation-links"><li>Prev: <a href="c_m_dc_pr.html">Product arguments <small>[c.m.dc.pr]</small></a></li><li>Next: <a href="c_m_ic.html">Integral Calculus <small>[c.m.ic]</small></a></li><li>Up: <a href="c_m_dc.html">Differential Calculus <small>[c.m.dc]</small></a></li></ul><div id="outline-container-c_m_dc_d2" class="outline-5">
|
||||
<h5 id="c_m_dc_d2">Second Derivatives<a class="headline-permalink" href="./c_m_dc_d2.html#c_m_dc_d2"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
|
|
@ -1599,9 +1594,9 @@ Table of contents
|
|||
<div class="outline-text-5" id="text-c_m_dc_d2">
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org48d9aa2" class="outline-6">
|
||||
<h6 id="org48d9aa2"><a href="#org48d9aa2">Divergence of gradient</a></h6>
|
||||
<div class="outline-text-6" id="text-org48d9aa2">
|
||||
<div id="outline-container-org1a142a0" class="outline-6">
|
||||
<h6 id="org1a142a0"><a href="#org1a142a0">Divergence of gradient</a></h6>
|
||||
<div class="outline-text-6" id="text-org1a142a0">
|
||||
<p>
|
||||
\({\boldsymbol \nabla} \cdot ({\boldsymbol \nabla} T) \equiv {\boldsymbol \nabla}^2 T\) 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
|
||||
|
|
@ -1610,36 +1605,36 @@ given by the Laplacian of the corresponding vector elements.
|
|||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org527fbc8" class="outline-6">
|
||||
<h6 id="org527fbc8"><a href="#org527fbc8">Curl of a gradient</a></h6>
|
||||
<div class="outline-text-6" id="text-org527fbc8">
|
||||
<div id="outline-container-org16039ac" class="outline-6">
|
||||
<h6 id="org16039ac"><a href="#org16039ac">Curl of a gradient</a></h6>
|
||||
<div class="outline-text-6" id="text-org16039ac">
|
||||
<p>
|
||||
This always vanishes.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org9758e01" class="outline-6">
|
||||
<h6 id="org9758e01"><a href="#org9758e01">Gradient of the divergence</a></h6>
|
||||
<div class="outline-text-6" id="text-org9758e01">
|
||||
<div id="outline-container-orgd64b31f" class="outline-6">
|
||||
<h6 id="orgd64b31f"><a href="#orgd64b31f">Gradient of the divergence</a></h6>
|
||||
<div class="outline-text-6" id="text-orgd64b31f">
|
||||
<p>
|
||||
\({\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v})\) does not appear often in physics. No special name.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org5e919b4" class="outline-6">
|
||||
<h6 id="org5e919b4"><a href="#org5e919b4">Divergence of a curl</a></h6>
|
||||
<div class="outline-text-6" id="text-org5e919b4">
|
||||
<div id="outline-container-orgf932975" class="outline-6">
|
||||
<h6 id="orgf932975"><a href="#orgf932975">Divergence of a curl</a></h6>
|
||||
<div class="outline-text-6" id="text-orgf932975">
|
||||
<p>
|
||||
This always vanishes.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org0eb22e6" class="outline-6">
|
||||
<h6 id="org0eb22e6"><a href="#org0eb22e6">Curl of curl</a></h6>
|
||||
<div class="outline-text-6" id="text-org0eb22e6">
|
||||
<div id="outline-container-orgcb842e5" class="outline-6">
|
||||
<h6 id="orgcb842e5"><a href="#orgcb842e5">Curl of curl</a></h6>
|
||||
<div class="outline-text-6" id="text-orgcb842e5">
|
||||
<p>
|
||||
\[
|
||||
{\boldsymbol \nabla} \times ({\boldsymbol \nabla} \times {\bf v}) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v}) - {\boldsymbol \nabla}^2 {\bf v}
|
||||
|
|
@ -1651,7 +1646,7 @@ This always vanishes.
|
|||
</div>
|
||||
|
||||
|
||||
<br><ul class="navigation-links"><li>Prev: <a href="c_m_dc_pr.html">Product Rules <small>[c.m.dc.pr]</small></a></li><li>Next: <a href="c_m_ic.html">Integral Calculus <small>[c.m.ic]</small></a></li><li>Up: <a href="c_m_dc.html">Differential Calculus <small>[c.m.dc]</small></a></li></ul>
|
||||
<br><ul class="navigation-links"><li>Prev: <a href="c_m_dc_pr.html">Product arguments <small>[c.m.dc.pr]</small></a></li><li>Next: <a href="c_m_ic.html">Integral Calculus <small>[c.m.ic]</small></a></li><li>Up: <a href="c_m_dc.html">Differential Calculus <small>[c.m.dc]</small></a></li></ul>
|
||||
<br>
|
||||
<hr>
|
||||
<div class="license">
|
||||
|
|
@ -1666,7 +1661,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1627,7 +1622,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1624,7 +1619,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1648,7 +1643,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li class="toc-currentpage">
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1591,14 +1586,177 @@ Table of contents
|
|||
</ul>
|
||||
</details>
|
||||
</nav>
|
||||
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_dc.html">Differential Calculus</a></li><li>Product Rules</li></ul><ul class="navigation-links"><li>Prev: <a href="c_m_dc_curl.html">The Curl <small>[c.m.dc.curl]</small></a></li><li>Next: <a href="c_m_dc_d2.html">Second Derivatives <small>[c.m.dc.d2]</small></a></li><li>Up: <a href="c_m_dc.html">Differential Calculus <small>[c.m.dc]</small></a></li></ul><div id="outline-container-c_m_dc_pr" class="outline-5">
|
||||
<h5 id="c_m_dc_pr">Product Rules<a class="headline-permalink" href="./c_m_dc_pr.html#c_m_dc_pr"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="c.html">Compendium</a></li><li><a class="breadcrumb-link"href="c_m.html">Mathematics</a></li><li><a class="breadcrumb-link"href="c_m_dc.html">Differential Calculus</a></li><li>Product arguments</li></ul><ul class="navigation-links"><li>Prev: <a href="c_m_dc_curl.html">The Curl <small>[c.m.dc.curl]</small></a></li><li>Next: <a href="c_m_dc_d2.html">Second Derivatives <small>[c.m.dc.d2]</small></a></li><li>Up: <a href="c_m_dc.html">Differential Calculus <small>[c.m.dc]</small></a></li></ul><div id="outline-container-c_m_dc_pr" class="outline-5">
|
||||
<h5 id="c_m_dc_pr">Product arguments<a class="headline-permalink" href="./c_m_dc_pr.html#c_m_dc_pr"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a><span class="headline-id">c.m.dc.pr</span></h5>
|
||||
<div class="outline-text-5" id="text-c_m_dc_pr">
|
||||
<p>
|
||||
Six product rules (on inside front cover of Gr).
|
||||
When applied to arguments which are products of scalar/vector fields,
|
||||
the action of \(\nabla\), \(\nabla \cdot\) and \(\nabla \times\) can be
|
||||
explicited as follows:
|
||||
</p>
|
||||
|
||||
<p>
|
||||
<b>Gradient of a product</b>:
|
||||
</p>
|
||||
<div class="eqlabel" id="org77098c1">
|
||||
<p>
|
||||
<a id="grad_prod"></a><a href="./c_m_dc_pr.html#grad_prod"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org098750f">
|
||||
<ul class="org-ul">
|
||||
<li>Gr (3)</li>
|
||||
<li>W (1-111)</li>
|
||||
</ul>
|
||||
|
||||
</div>
|
||||
|
||||
</div>
|
||||
<p>
|
||||
\[
|
||||
\nabla (uv) = u \nabla v + v \nabla u
|
||||
\tag{grad_prod}\label{grad_prod}
|
||||
\]
|
||||
</p>
|
||||
|
||||
<br>
|
||||
<p>
|
||||
<b>Gradient of a scalar product</b>:
|
||||
</p>
|
||||
<div class="eqlabel" id="org623c0b6">
|
||||
<p>
|
||||
<a id="grad_sprod"></a><a href="./c_m_dc_pr.html#grad_sprod"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org9c465bf">
|
||||
<ul class="org-ul">
|
||||
<li>Gr (4)</li>
|
||||
<li>W (1-112)</li>
|
||||
</ul>
|
||||
|
||||
</div>
|
||||
|
||||
</div>
|
||||
<p>
|
||||
\[
|
||||
\nabla ({\bf a} \cdot {\bf b}) = ({\bf a} \cdot \nabla) {\bf b} + ({\bf b} \cdot \nabla) {\bf a} + {\bf a} \times (\nabla \times {\bf b}) + {\bf b} \times (\nabla \times {\bf a})
|
||||
\tag{grad_sprod}\label{grad_sprod}
|
||||
\]
|
||||
</p>
|
||||
|
||||
<br>
|
||||
<p>
|
||||
<b>Divergence of a product</b>:
|
||||
</p>
|
||||
<div class="eqlabel" id="org27a4a20">
|
||||
<p>
|
||||
<a id="div_prod"></a><a href="./c_m_dc_pr.html#div_prod"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org3259c68">
|
||||
<ul class="org-ul">
|
||||
<li>Gr (5)</li>
|
||||
<li>W (1-115)</li>
|
||||
</ul>
|
||||
|
||||
</div>
|
||||
|
||||
</div>
|
||||
<p>
|
||||
\[
|
||||
\nabla (\psi {\bf a}) = {\bf a} \cdot \nabla \psi + \psi \nabla \cdot {\bf a}
|
||||
\tag{div_prod}\label{div_prod}
|
||||
\]
|
||||
</p>
|
||||
|
||||
<br>
|
||||
<p>
|
||||
<b>Divergence of a cross product</b>:
|
||||
</p>
|
||||
<div class="eqlabel" id="orgaa0862c">
|
||||
<p>
|
||||
<a id="div_xprod"></a><a href="./c_m_dc_pr.html#div_xprod"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org1672361">
|
||||
<ul class="org-ul">
|
||||
<li>Gr (6)</li>
|
||||
<li>W (1-116)</li>
|
||||
</ul>
|
||||
|
||||
</div>
|
||||
|
||||
</div>
|
||||
<p>
|
||||
\[
|
||||
\nabla \cdot ({\bf a} \times {\bf b}) = {\bf b} \cdot (\nabla \times {\bf a}) - {\bf a} \cdot (\nabla \times {\bf b})
|
||||
\tag{div_xprod}\label{div_xprod}
|
||||
\]
|
||||
</p>
|
||||
|
||||
<br>
|
||||
<p>
|
||||
<b>Curl of a product</b>:
|
||||
</p>
|
||||
<div class="eqlabel" id="org8a2530a">
|
||||
<p>
|
||||
<a id="curl_prod"></a><a href="./c_m_dc_pr.html#curl_prod"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="orgdb6a233">
|
||||
<ul class="org-ul">
|
||||
<li>Gr (7)</li>
|
||||
<li>W (1-118)</li>
|
||||
</ul>
|
||||
|
||||
</div>
|
||||
|
||||
</div>
|
||||
<p>
|
||||
\[
|
||||
\nabla \times (\psi {\bf a}) = \nabla \psi \times {\bf a} + \psi \nabla \times {\bf a}
|
||||
\tag{curl_prod}\label{curl_prod}
|
||||
\]
|
||||
</p>
|
||||
|
||||
<br>
|
||||
<p>
|
||||
<b>Curl of a cross product</b>:
|
||||
</p>
|
||||
<div class="eqlabel" id="org21daf74">
|
||||
<p>
|
||||
<a id="curl_xprod"></a><a href="./c_m_dc_pr.html#curl_xprod"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org87e2222">
|
||||
<ul class="org-ul">
|
||||
<li>Gr (8)</li>
|
||||
<li>W (1-119)</li>
|
||||
</ul>
|
||||
|
||||
</div>
|
||||
|
||||
</div>
|
||||
<p>
|
||||
\[
|
||||
\nabla ({\bf a} \times {\bf b}) = {\bf a} (\nabla \cdot {\bf b}) - {\bf b} (\nabla \cdot {\bf a}) + ({\bf b} \cdot \nabla) {\bf a} - ({\bf a} \cdot \nabla) {\bf b}
|
||||
\tag{curl_xprod}\label{curl_xprod}
|
||||
\]
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
|
|
@ -1606,6 +1764,11 @@ Six product rules (on inside front cover of Gr).
|
|||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
<br><ul class="navigation-links"><li>Prev: <a href="c_m_dc_curl.html">The Curl <small>[c.m.dc.curl]</small></a></li><li>Next: <a href="c_m_dc_d2.html">Second Derivatives <small>[c.m.dc.d2]</small></a></li><li>Up: <a href="c_m_dc.html">Differential Calculus <small>[c.m.dc]</small></a></li></ul>
|
||||
<br>
|
||||
<hr>
|
||||
|
|
@ -1621,7 +1784,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1623,7 +1618,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1635,7 +1630,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1620,14 +1615,14 @@ Resolution of divergence of \(\hat{\bf r}/r^2\) paradox:
|
|||
More generally,
|
||||
</p>
|
||||
|
||||
<div class="eqlabel" id="org53bf72e">
|
||||
<div class="eqlabel" id="org42fce11">
|
||||
<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">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="orgf5950bf">
|
||||
<div class="alteqlabels" id="org7526e1a">
|
||||
<ul class="org-ul">
|
||||
<li>Gr (1.100)</li>
|
||||
</ul>
|
||||
|
|
@ -1646,14 +1641,14 @@ More generally,
|
|||
Since
|
||||
</p>
|
||||
|
||||
<div class="eqlabel" id="org95ea3a2">
|
||||
<div class="eqlabel" id="org204d0c0">
|
||||
<p>
|
||||
<a id="div1or"></a><a href="./c_m_dd_3d.html#div1or"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org173d151">
|
||||
<div class="alteqlabels" id="orgd677a10">
|
||||
<ul class="org-ul">
|
||||
<li>Gr (1.101)</li>
|
||||
</ul>
|
||||
|
|
@ -1669,14 +1664,14 @@ Since
|
|||
<p>
|
||||
we have that
|
||||
</p>
|
||||
<div class="eqlabel" id="orgf8803cf">
|
||||
<div class="eqlabel" id="orgb31b1d6">
|
||||
<p>
|
||||
<a id="Lap1or"></a><a href="./c_m_dd_3d.html#Lap1or"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="orgaa458a9">
|
||||
<div class="alteqlabels" id="orgc762b5a">
|
||||
<ul class="org-ul">
|
||||
<li>Gr (1.102)</li>
|
||||
</ul>
|
||||
|
|
@ -1708,7 +1703,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1641,7 +1636,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1626,7 +1621,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1624,7 +1619,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1633,7 +1628,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1627,7 +1622,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1634,7 +1629,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1599,9 +1594,9 @@ Table of contents
|
|||
<div class="outline-text-5" id="text-c_m_ic_lsv">
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org524bc35" class="outline-6">
|
||||
<h6 id="org524bc35"><a href="#org524bc35">Line Integrals</a></h6>
|
||||
<div class="outline-text-6" id="text-org524bc35">
|
||||
<div id="outline-container-org89b219e" class="outline-6">
|
||||
<h6 id="org89b219e"><a href="#org89b219e">Line Integrals</a></h6>
|
||||
<div class="outline-text-6" id="text-org89b219e">
|
||||
<p>
|
||||
\[
|
||||
{\int_{\bf a}^{\bf b}}_{\cal P} {\bf v} \cdot d{\bf l}
|
||||
|
|
@ -1630,9 +1625,9 @@ Integral over a closed loop:
|
|||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org0cc38e3" class="outline-6">
|
||||
<h6 id="org0cc38e3"><a href="#org0cc38e3">Surface Integrals</a></h6>
|
||||
<div class="outline-text-6" id="text-org0cc38e3">
|
||||
<div id="outline-container-org44f2fbc" class="outline-6">
|
||||
<h6 id="org44f2fbc"><a href="#org44f2fbc">Surface Integrals</a></h6>
|
||||
<div class="outline-text-6" id="text-org44f2fbc">
|
||||
<p>
|
||||
\[
|
||||
\int_{\cal S} {\bf v} \cdot d{\bf a}
|
||||
|
|
@ -1652,9 +1647,9 @@ Over a closed surface:
|
|||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org9857c59" class="outline-6">
|
||||
<h6 id="org9857c59"><a href="#org9857c59">Volume Integrals</a></h6>
|
||||
<div class="outline-text-6" id="text-org9857c59">
|
||||
<div id="outline-container-org66b01fe" class="outline-6">
|
||||
<h6 id="org66b01fe"><a href="#org66b01fe">Volume Integrals</a></h6>
|
||||
<div class="outline-text-6" id="text-org66b01fe">
|
||||
<p>
|
||||
\[
|
||||
\int_{\cal V} T d\tau
|
||||
|
|
@ -1695,7 +1690,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1597,14 +1592,14 @@ 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"/>
|
||||
</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="eqlabel" id="orgc6d532c">
|
||||
<div class="eqlabel" id="orgc8b92ac">
|
||||
<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">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org6c9bf8e">
|
||||
<div class="alteqlabels" id="org7dca564">
|
||||
<ul class="org-ul">
|
||||
<li>Gr (1.57)</li>
|
||||
</ul>
|
||||
|
|
@ -1649,7 +1644,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1623,7 +1618,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1636,7 +1631,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1636,7 +1631,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1639,7 +1634,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1625,7 +1620,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1654,7 +1649,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1649,7 +1644,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1683,7 +1678,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1649,7 +1644,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1696,7 +1691,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1622,7 +1617,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1641,7 +1636,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1668,7 +1663,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
45
build/d.html
45
build/d.html
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1598,8 +1593,8 @@ Table of contents
|
|||
</svg></a><span class="headline-id">d</span></h2>
|
||||
|
||||
<div class="outline-text-2" id="text-d">
|
||||
<details class="objectives" id="org060fffc">
|
||||
<summary id="org324a296">
|
||||
<details class="objectives" id="org5b81bb5">
|
||||
<summary id="org3f2d119">
|
||||
Objectives
|
||||
</summary>
|
||||
|
||||
|
|
@ -1663,7 +1658,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1643,7 +1638,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1638,7 +1633,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1641,7 +1636,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1638,7 +1633,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1660,7 +1655,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1643,7 +1638,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1640,7 +1635,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1643,7 +1638,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1641,7 +1636,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1651,7 +1646,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1645,7 +1640,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1598,8 +1593,8 @@ Table of contents
|
|||
</svg></a><span class="headline-id">emd</span></h2>
|
||||
|
||||
<div class="outline-text-2" id="text-emd">
|
||||
<details class="prereq" id="org9fd257c">
|
||||
<summary id="org03c921a">
|
||||
<details class="prereq" id="orgb2dc4db">
|
||||
<summary id="org0ce70b2">
|
||||
Prerequisites
|
||||
</summary>
|
||||
<ul class="org-ul">
|
||||
|
|
@ -1608,8 +1603,8 @@ Prerequisites
|
|||
</ul>
|
||||
</details>
|
||||
|
||||
<details class="objectives" id="orgde2512c">
|
||||
<summary id="org1721848">
|
||||
<details class="objectives" id="org1795145">
|
||||
<summary id="orgbb33e19">
|
||||
Objectives
|
||||
</summary>
|
||||
<ul class="org-ul">
|
||||
|
|
@ -1650,7 +1645,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1624,7 +1619,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1638,7 +1633,7 @@ Empirically: the changing magnetic field induces an electric current around
|
|||
the circuit. This current is really driven by an electric field having a component
|
||||
along the wire. The line integral of this field is called the
|
||||
</p>
|
||||
<div class="core div" id="org48bd452">
|
||||
<div class="core div" id="org33fe3db">
|
||||
<p>
|
||||
<b>Electromotive force (or electromotance)</b>,
|
||||
\[
|
||||
|
|
@ -1660,7 +1655,7 @@ to the rate of change of the magnetic flux,
|
|||
\]
|
||||
so we obtain
|
||||
</p>
|
||||
<div class="core div" id="orgb48b333">
|
||||
<div class="core div" id="org7ae72ba">
|
||||
<p>
|
||||
<b>Faraday's law</b> (integral form <i>N.B.: for a stationary loop</i>)
|
||||
\[
|
||||
|
|
@ -1678,7 +1673,7 @@ for any loop (on a wire or not). Using Stokes' theorem,
|
|||
\]
|
||||
we obtain
|
||||
</p>
|
||||
<div class="core div" id="org7ffdde2">
|
||||
<div class="core div" id="org9b15297">
|
||||
<p>
|
||||
<b>Faraday's law</b> (differential form)
|
||||
\[
|
||||
|
|
@ -1715,7 +1710,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1657,7 +1652,7 @@ 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
|
||||
</p>
|
||||
<div class="core div" id="org05103f7">
|
||||
<div class="core div" id="orgca61a8b">
|
||||
<p>
|
||||
\[
|
||||
W_{mag} = \frac{1}{2\mu_0} \int d\tau B^2
|
||||
|
|
@ -1678,7 +1673,7 @@ 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)}
|
||||
\end{align}
|
||||
|
||||
<div class="example div" id="orgfe6530a">
|
||||
<div class="example div" id="org97b1250">
|
||||
<p>
|
||||
\paragraph{Example 7.13:} coaxial cable (inner cylinder radius \(a\), outer \(b\)) carries current \(I\).
|
||||
Find energy stored in section of length \(l\).
|
||||
|
|
@ -1717,7 +1712,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1637,7 +1632,7 @@ M_{12} = M_{21}
|
|||
\]
|
||||
</p>
|
||||
|
||||
<div class="example div" id="org8c11522">
|
||||
<div class="example div" id="org60345e2">
|
||||
<p>
|
||||
\paragraph{Example 7.10:}
|
||||
short solenoid (length \(l\), radius \(a\), \(n_1\) turns per unit length) lies concentrically inside
|
||||
|
|
@ -1687,7 +1682,7 @@ Inductance: measured in {\bf henries} (\(H\)). \(H = V s/A\).
|
|||
</p>
|
||||
|
||||
|
||||
<div class="example div" id="org9c04d6d">
|
||||
<div class="example div" id="org13c54cb">
|
||||
<p>
|
||||
\paragraph{Example 7.11:} find self-inductance of toroidal coil with
|
||||
rectangular cross-section (inner radius \(a\), outer radius \(b\), height \(h\))
|
||||
|
|
@ -1714,7 +1709,7 @@ Total flux: \(N\) times this, so self-inductance is
|
|||
Inductance (like capacitance) is intrinsically positive. Use Lenz law. Think of {\bf back EMF}.
|
||||
</p>
|
||||
|
||||
<div class="example div" id="org856ea2f">
|
||||
<div class="example div" id="org9ccd19a">
|
||||
<p>
|
||||
\paragraph{Example 7.12:} circuit with inductance \(L\), resistor \(R\) and battery \({\cal E}_0\).
|
||||
What is the current ?
|
||||
|
|
@ -1753,7 +1748,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1621,7 +1616,7 @@ law in integral form:
|
|||
|
||||
|
||||
|
||||
<div class="example div" id="org9995269">
|
||||
<div class="example div" id="orgbe4cbfb">
|
||||
<p>
|
||||
{\bf Example 7.7:}
|
||||
\({\bf B}(t)\) points up in circular region of radius \(R\). What is the induced \({\bf E}(t)\) ?
|
||||
|
|
@ -1637,7 +1632,7 @@ Increasing \({\bf B}\): clockwise (viewed from above) \({\bf E}\) from Lenz.
|
|||
</div>
|
||||
|
||||
|
||||
<div class="example div" id="org10525d2">
|
||||
<div class="example div" id="orge1cb85e">
|
||||
<p>
|
||||
{\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 \(a < b\),
|
||||
|
|
@ -1671,7 +1666,7 @@ called the {\bf quasistatic} approximation, and works provided we deal with
|
|||
'slow enough' phenomena.
|
||||
</p>
|
||||
|
||||
<div class="example div" id="orga3b651f">
|
||||
<div class="example div" id="org20dbc12">
|
||||
<p>
|
||||
{\bf Example 7.9:} infinitely long straight wire carries \(I(t)\). Find
|
||||
induced \({\bf E}\) field as a function of distance \(s\) from wire.
|
||||
|
|
@ -1719,7 +1714,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1624,7 +1619,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1600,7 +1595,7 @@ Table of contents
|
|||
<p>
|
||||
Full set of equations for the electromagnetic field:
|
||||
</p>
|
||||
<div class="core div" id="orgb65b34c">
|
||||
<div class="core div" id="org05c5b38">
|
||||
<p>
|
||||
{\bf Maxwell's equations} {\it (in vacuum)}
|
||||
</p>
|
||||
|
|
@ -1616,7 +1611,7 @@ Full set of equations for the electromagnetic field:
|
|||
<p>
|
||||
Complement:
|
||||
</p>
|
||||
<div class="core div" id="orga966eba">
|
||||
<div class="core div" id="orgdcc1f4c">
|
||||
<p>
|
||||
{\bf Force law}
|
||||
\[
|
||||
|
|
@ -1640,7 +1635,7 @@ take divergence of \((iv)\).
|
|||
<p>
|
||||
Better way of writing: all fields on left, all sources on right,
|
||||
</p>
|
||||
<div class="core div" id="org660ec71">
|
||||
<div class="core div" id="org26036d7">
|
||||
\begin{align}
|
||||
(i) &{\boldsymbol \nabla} \cdot {\bf E} = \frac{\rho}{\varepsilon_0},
|
||||
&(iii) {\boldsymbol \nabla} \times {\bf E} + \frac{\partial {\bf B}}{\partial t} = 0, \\
|
||||
|
|
@ -1670,7 +1665,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1607,7 +1602,7 @@ the continuity equation as
|
|||
\]
|
||||
The extra term would thus be eliminated if we were to put
|
||||
</p>
|
||||
<div class="core div" id="orgf32f14b">
|
||||
<div class="core div" id="orgba85b39">
|
||||
<p>
|
||||
\[
|
||||
{\boldsymbol \nabla} \times {\bf B} = \mu_0 {\bf J} + \mu_0 \varepsilon_0 \frac{\partial {\bf E}}{\partial t}
|
||||
|
|
@ -1631,7 +1626,7 @@ Real confirmation of Maxwell's theory: 1888, Hertz's experiments on propagation
|
|||
<p>
|
||||
Maxwell baptized this term the
|
||||
</p>
|
||||
<div class="core div" id="orgf353887">
|
||||
<div class="core div" id="org1bb49a0">
|
||||
<p>
|
||||
{\bf Displacement current}
|
||||
\[
|
||||
|
|
@ -1679,7 +1674,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1649,7 +1644,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1647,7 +1642,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1598,8 +1593,8 @@ Table of contents
|
|||
</svg></a><span class="headline-id">emd.ce</span></h3>
|
||||
|
||||
<div class="outline-text-3" id="text-emd_ce">
|
||||
<details class="prereq" id="orgd0bc04d">
|
||||
<summary id="org26554fe">
|
||||
<details class="prereq" id="org1758e01">
|
||||
<summary id="org85b5990">
|
||||
Prerequisites
|
||||
</summary>
|
||||
<ul class="org-ul">
|
||||
|
|
@ -1607,8 +1602,8 @@ Prerequisites
|
|||
</ul>
|
||||
</details>
|
||||
|
||||
<details class="objectives" id="org41b8c54">
|
||||
<summary id="orgeccfbac">
|
||||
<details class="objectives" id="org2078622">
|
||||
<summary id="org8bbb395">
|
||||
Objectives
|
||||
</summary>
|
||||
<ul class="org-ul">
|
||||
|
|
@ -1646,7 +1641,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1600,7 +1595,7 @@ Table of contents
|
|||
<p>
|
||||
The angular momentum of EM fields is directly given by
|
||||
</p>
|
||||
<div class="main div" id="org5125785">
|
||||
<div class="main div" id="orgeb9f3aa">
|
||||
<p>
|
||||
{\bf Angular momentum of EM fields}
|
||||
\[
|
||||
|
|
@ -1630,7 +1625,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1619,7 +1614,7 @@ This means that
|
|||
\]
|
||||
Since this is true for any volume, we have (re)derived the
|
||||
</p>
|
||||
<div class="core div" id="org3a26ba8">
|
||||
<div class="core div" id="org9d0437e">
|
||||
<p>
|
||||
{\bf Continuity equation}
|
||||
\[
|
||||
|
|
@ -1660,7 +1655,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1612,7 +1607,7 @@ in which the first integral can be interpreted as the momentum stored in the EM
|
|||
<p>
|
||||
This is thus simply a conservation law for momentum, with
|
||||
</p>
|
||||
<div class="main div" id="org908691c">
|
||||
<div class="main div" id="orga925365">
|
||||
<p>
|
||||
{\bf Momentum density in the EM fields}
|
||||
\[
|
||||
|
|
@ -1624,7 +1619,7 @@ This is thus simply a conservation law for momentum, with
|
|||
<p>
|
||||
In a region in which the mechanical momentum is not changing due to external influences, we then have the
|
||||
</p>
|
||||
<div class="main div" id="org1908c28">
|
||||
<div class="main div" id="org5972f3c">
|
||||
<p>
|
||||
{\bf Continuity equation for EM momentum}
|
||||
\[
|
||||
|
|
@ -1653,7 +1648,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1654,7 +1649,7 @@ and similarly for \({\boldsymbol B}\). We thus get
|
|||
<p>
|
||||
This expression can be greatly simplified by introducing the
|
||||
</p>
|
||||
<div class="main div" id="orgf914cc8">
|
||||
<div class="main div" id="org8af3b6f">
|
||||
<p>
|
||||
{\bf Maxwell stress tensor}
|
||||
\[
|
||||
|
|
@ -1677,7 +1672,7 @@ The element \(T_{ij}\) represents the force per unit area in the $i$th direction
|
|||
<p>
|
||||
We then obtain
|
||||
</p>
|
||||
<div class="main div" id="orgb679cf4">
|
||||
<div class="main div" id="orgaca85e5">
|
||||
<p>
|
||||
{\bf EM force per unit volume}
|
||||
\[
|
||||
|
|
@ -1689,7 +1684,7 @@ We then obtain
|
|||
<p>
|
||||
where \({\boldsymbol S}\) is the Poynting vector. Integrating, we obtain the
|
||||
</p>
|
||||
<div class="main div" id="org4a6eed2">
|
||||
<div class="main div" id="org9271f22">
|
||||
<p>
|
||||
{\bf Total force on charges in volume}
|
||||
\[
|
||||
|
|
@ -1718,7 +1713,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1666,7 +1661,7 @@ so we get
|
|||
Substituting this in \ref{Gr(8.6)} and using the divergence theorem,
|
||||
we obtain
|
||||
</p>
|
||||
<div class="main div" id="orgc46594c">
|
||||
<div class="main div" id="orgd161684">
|
||||
<p>
|
||||
{\bf Poynting's theorem}
|
||||
\[
|
||||
|
|
@ -1691,7 +1686,7 @@ energy is carried by EM fields out of \({\cal V}\) across its boundary surface.
|
|||
<p>
|
||||
Energy per unit time, per unit area carried by EM fields:
|
||||
</p>
|
||||
<div class="core div" id="org499e389">
|
||||
<div class="core div" id="org90e3d26">
|
||||
<p>
|
||||
{\bf Poynting vector}
|
||||
\[
|
||||
|
|
@ -1704,7 +1699,7 @@ Energy per unit time, per unit area carried by EM fields:
|
|||
<p>
|
||||
We can thus express Poynting's theorem more compactly:
|
||||
</p>
|
||||
<div class="core div" id="org47309b1">
|
||||
<div class="core div" id="orgc1eb716">
|
||||
<p>
|
||||
{\bf Poynting's theorem}
|
||||
\[
|
||||
|
|
@ -1717,7 +1712,7 @@ We can thus express Poynting's theorem more compactly:
|
|||
<p>
|
||||
where we have defined the total
|
||||
</p>
|
||||
<div class="core div" id="org06b3424">
|
||||
<div class="core div" id="orgac7f9d9">
|
||||
<p>
|
||||
{\bf Energy in electromagnetic fields}
|
||||
\[
|
||||
|
|
@ -1740,7 +1735,7 @@ Then,
|
|||
\]
|
||||
so we get the
|
||||
</p>
|
||||
<div class="core div" id="org3934004">
|
||||
<div class="core div" id="orgf8675a9">
|
||||
<p>
|
||||
{\bf Poynting theorem (differential form)}
|
||||
\[
|
||||
|
|
@ -1757,7 +1752,7 @@ and has a similar for to the continuity equation
|
|||
|
||||
|
||||
|
||||
<div class="example div" id="orgb4eafb2">
|
||||
<div class="example div" id="org0fdb2d9">
|
||||
<p>
|
||||
\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
|
||||
|
|
@ -1802,7 +1797,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1598,8 +1593,8 @@ Table of contents
|
|||
</svg></a><span class="headline-id">emd.emw</span></h3>
|
||||
|
||||
<div class="outline-text-3" id="text-emd_emw">
|
||||
<details class="prereq" id="org078565b">
|
||||
<summary id="org8eb1ce8">
|
||||
<details class="prereq" id="orgd0c1190">
|
||||
<summary id="org39fb2fc">
|
||||
Prerequisites
|
||||
</summary>
|
||||
<ul class="org-ul">
|
||||
|
|
@ -1608,8 +1603,8 @@ Prerequisites
|
|||
</ul>
|
||||
</details>
|
||||
|
||||
<details class="objectives" id="orgaefc9c9">
|
||||
<summary id="org4dd81e4">
|
||||
<details class="objectives" id="org9925619">
|
||||
<summary id="org4ccd34a">
|
||||
Objectives
|
||||
</summary>
|
||||
<ul class="org-ul">
|
||||
|
|
@ -1650,7 +1645,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1628,7 +1623,7 @@ so for a monochromatic EM plan wave,
|
|||
\]
|
||||
or more succinctly:
|
||||
</p>
|
||||
<div class="main div" id="orgbc4e836">
|
||||
<div class="main div" id="org0eacbcf">
|
||||
<p>
|
||||
{\bf Poynting vector of a monochromatic EM wave}
|
||||
\[
|
||||
|
|
@ -1644,7 +1639,7 @@ This has a transparent physical interpretation: the energy density \(u\) flows w
|
|||
<p>
|
||||
Similary, we get the
|
||||
</p>
|
||||
<div class="main div" id="org1beac86">
|
||||
<div class="main div" id="org05fac46">
|
||||
<p>
|
||||
{\bf Momentum density of a monochromatic EM wave}
|
||||
\[
|
||||
|
|
@ -1695,7 +1690,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1629,7 +1624,7 @@ B_0 = \frac{k}{\omega} E_0 = \frac{1}{c} E_0.
|
|||
Generalizing to propagation in the direction of an arbitrary wavevector
|
||||
\({\boldsymbol k}\) and (transverse) polarization vector \(\hat{\boldsymbol n}\), we have the
|
||||
</p>
|
||||
<div class="core div" id="orgc712ee1">
|
||||
<div class="core div" id="org304040f">
|
||||
<p>
|
||||
{\bf E and B fields for a monochromatic EM plane wave}
|
||||
\[
|
||||
|
|
@ -1673,7 +1668,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1626,7 +1621,7 @@ These take the form of coupled first-order partial differential equations for \(
|
|||
Since \({\boldsymbol \nabla} \cdot {\bf E} = 0\) and \({\boldsymbol \nabla} \cdot {\bf B} = 0\),
|
||||
we get the
|
||||
</p>
|
||||
<div class="core div" id="orgafd96cf">
|
||||
<div class="core div" id="org5f3e8fb">
|
||||
<p>
|
||||
{\bf Wave equations for electric and magnetic fields in vacuum}
|
||||
\[
|
||||
|
|
@ -1682,7 +1677,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1622,7 +1617,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1622,7 +1617,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1633,7 +1628,7 @@ dI = \frac{\partial \sigma_b}{\partial t} da_{\perp} = \frac{\partial P}{\partia
|
|||
\]
|
||||
We therefore have the
|
||||
</p>
|
||||
<div class="core div" id="orge4132f2">
|
||||
<div class="core div" id="org9309d43">
|
||||
<p>
|
||||
{\bf Polarization current density}
|
||||
\[
|
||||
|
|
@ -1651,7 +1646,7 @@ the polarization current is the result of linear motion of charge when
|
|||
polarization changes). We can check consistency with the continuity equation
|
||||
associated to the conservation of bound charges:
|
||||
</p>
|
||||
<aside id="orgcbc08fb">
|
||||
<aside id="org37f623e">
|
||||
<p>
|
||||
Note the unfortunate labelling: it would have been nicer to have \(\rho_b\) be the charge associated to current
|
||||
\({\boldsymbol J}_b\) but this is not the convention used here.
|
||||
|
|
@ -1674,7 +1669,7 @@ 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,
|
||||
{\it free} and {\it bound}:
|
||||
</p>
|
||||
<div class="main div" id="org5d3e365">
|
||||
<div class="main div" id="org29f863b">
|
||||
<p>
|
||||
\[
|
||||
\rho = \rho_f + \rho_b = \rho_f - {\boldsymbol \nabla} \cdot {\bf P}
|
||||
|
|
@ -1687,7 +1682,7 @@ 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
|
||||
{\it polarization}:
|
||||
</p>
|
||||
<div class="main div" id="org385196e">
|
||||
<div class="main div" id="org851bf9b">
|
||||
<p>
|
||||
\[
|
||||
{\bf J} = {\bf J}_f + {\bf J}_b + {\bf J}_p = {\bf J}_f + {\boldsymbol ∇} × {\bf M}
|
||||
|
|
@ -1711,7 +1706,7 @@ Gauss's law: can be rewritten
|
|||
\]
|
||||
where (as in static case)
|
||||
</p>
|
||||
<div class="core div" id="org94769a9">
|
||||
<div class="core div" id="org358a7bd">
|
||||
<p>
|
||||
\[
|
||||
{\bf D} \equiv \varepsilon_0 {\bf E} + {\bf P}
|
||||
|
|
@ -1737,7 +1732,7 @@ or
|
|||
\]
|
||||
where as before
|
||||
</p>
|
||||
<div class="core div" id="org4d90031">
|
||||
<div class="core div" id="org64d8ed7">
|
||||
<p>
|
||||
\[
|
||||
{\bf H} \equiv \frac{1}{\mu_0} {\bf B} - {\bf M}
|
||||
|
|
@ -1755,7 +1750,7 @@ bound parts, since they don't involve \(\rho\) or \({\bf J}\).
|
|||
<p>
|
||||
In terms of free charges and currents, we thus get
|
||||
</p>
|
||||
<div class="core div" id="org52f1ad1">
|
||||
<div class="core div" id="org5222e7f">
|
||||
<p>
|
||||
{\bf Maxwell's equations {\it (in matter)}}
|
||||
</p>
|
||||
|
|
@ -1781,7 +1776,7 @@ Must be complemented by the {\bf constitutive relations} giving \({\bf D}\) and
|
|||
in terms of \({\bf E}\) and \({\bf B}\).
|
||||
For the restricted case of linear media:
|
||||
</p>
|
||||
<div class="main div" id="org7bab0fe">
|
||||
<div class="main div" id="org9f37a42">
|
||||
<p>
|
||||
\[
|
||||
{\bf P} = \varepsilon_0 \chi_e {\bf E}, \hspace{1cm}
|
||||
|
|
@ -1818,7 +1813,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1600,7 +1595,7 @@ Table of contents
|
|||
<p>
|
||||
Discontinuities between different media, deduced from
|
||||
</p>
|
||||
<div class="core div" id="org9ce00cc">
|
||||
<div class="core div" id="orgdfc4211">
|
||||
<p>
|
||||
{\bf Maxwell's equations {\it (in matter)}, integral form}
|
||||
</p>
|
||||
|
|
@ -1691,7 +1686,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1625,7 +1620,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1621,7 +1616,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1717,7 +1712,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1635,7 +1630,7 @@ v = \frac{1}{\sqrt{\mu \varepsilon}} = \frac{c}{n}
|
|||
\]
|
||||
where the index of refraction of the material is defined as
|
||||
</p>
|
||||
<div class="main div" id="org3ccae9b">
|
||||
<div class="main div" id="orgfca4f9b">
|
||||
<p>
|
||||
{\bf Index of refraction}
|
||||
\[
|
||||
|
|
@ -1692,7 +1687,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1636,7 +1631,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1616,7 +1611,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1617,7 +1612,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1708,7 +1703,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1635,7 +1630,7 @@ These forms for incident, reflected and transmitted wave can be substituted in t
|
|||
<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
|
||||
</p>
|
||||
<div class="core div" id="org77887dc">
|
||||
<div class="core div" id="org909fdf0">
|
||||
<p>
|
||||
{\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.
|
||||
|
|
@ -1650,7 +1645,7 @@ Specializing (\ref{eq:RTObliquek}) to our notations, we have
|
|||
with the incidence (\(\theta_I\)) and reflection (\(\theta_R\)) angles
|
||||
and the angle of refraction (\(\theta_T\)) obey the following laws:
|
||||
</p>
|
||||
<div class="core div" id="orgff35843">
|
||||
<div class="core div" id="orgee7521f">
|
||||
<p>
|
||||
{\bf Law of reflection}
|
||||
\[
|
||||
|
|
@ -1708,7 +1703,7 @@ while the third equation becomes
|
|||
\]
|
||||
Writing everything in terms of the incident amplitude, we get
|
||||
</p>
|
||||
<div class="main div" id="orgc0d3690">
|
||||
<div class="main div" id="org4ac057c">
|
||||
<p>
|
||||
{\bf Fresnel's equations for reflection and transmission amplitudes (parallel case)}
|
||||
\[
|
||||
|
|
@ -1728,7 +1723,7 @@ Amplitudes for transmitted and reflected wave: depend on angle of incidence:
|
|||
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
|
||||
</p>
|
||||
<div class="main div" id="org40da3bc">
|
||||
<div class="main div" id="org47f16fc">
|
||||
<p>
|
||||
{\bf Brewster's angle {\it (at which the reflected wave amplitude vanishes)}}
|
||||
\[
|
||||
|
|
@ -1778,7 +1773,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1617,7 +1612,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1623,7 +1618,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1643,7 +1638,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1667,7 +1662,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1676,7 +1671,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1598,8 +1593,8 @@ Table of contents
|
|||
</svg></a><span class="headline-id">emf</span></h2>
|
||||
|
||||
<div class="outline-text-2" id="text-emf">
|
||||
<details class="prereq" id="org0117d21">
|
||||
<summary id="orgd0bf86c">
|
||||
<details class="prereq" id="org2fe6b4b">
|
||||
<summary id="orgae4a3d9">
|
||||
Prerequisites
|
||||
</summary>
|
||||
<ul class="org-ul">
|
||||
|
|
@ -1607,8 +1602,8 @@ Prerequisites
|
|||
</ul>
|
||||
</details>
|
||||
|
||||
<details class="objectives" id="orgd14f948">
|
||||
<summary id="orgc1f9363">
|
||||
<details class="objectives" id="org52aa226">
|
||||
<summary id="orgcbd8789">
|
||||
Objectives
|
||||
</summary>
|
||||
<ul class="org-ul">
|
||||
|
|
@ -1644,7 +1639,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1641,7 +1636,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1640,7 +1635,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1613,7 +1608,7 @@ while the equation for \(V\) becomes
|
|||
\]
|
||||
These can be written compactly upon introducing a new operator: the
|
||||
</p>
|
||||
<div class="core div" id="org1bdc3b7">
|
||||
<div class="core div" id="orgb9c49fb">
|
||||
<p>
|
||||
{\bf d'Alembertian operator}
|
||||
\[
|
||||
|
|
@ -1626,7 +1621,7 @@ These can be written compactly upon introducing a new operator: the
|
|||
<p>
|
||||
so we get the
|
||||
</p>
|
||||
<div class="core div" id="org0e31a43">
|
||||
<div class="core div" id="org3dbf083">
|
||||
<p>
|
||||
{\bf Inhomogeneous Maxwell equations (Lorenz gauge)}
|
||||
\[
|
||||
|
|
@ -1676,7 +1671,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1614,7 +1609,7 @@ Useful strategy: represent fields in terms of potentials.
|
|||
<p>
|
||||
Easiest:
|
||||
</p>
|
||||
<div class="core div" id="org04beb23">
|
||||
<div class="core div" id="orgaf6ad03">
|
||||
<p>
|
||||
\[
|
||||
{\boldsymbol B} = {\boldsymbol \nabla} \times {\boldsymbol A}
|
||||
|
|
@ -1630,7 +1625,7 @@ Putting this into Faraday's law gives
|
|||
\]
|
||||
so this can be written as the gradient of a scalar (by choice: \(-{\boldsymbol \nabla} V\)) so we get
|
||||
</p>
|
||||
<div class="core div" id="orgd1c129d">
|
||||
<div class="core div" id="org9a58c0a">
|
||||
<p>
|
||||
\[
|
||||
{\boldsymbol E} = -{\boldsymbol \nabla} V - \frac{\partial {\boldsymbol A}}{\partial t}
|
||||
|
|
@ -1643,7 +1638,7 @@ so this can be written as the gradient of a scalar (by choice: \(-{\boldsymbol \
|
|||
<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
|
||||
</p>
|
||||
<div class="main div" id="orgf163188">
|
||||
<div class="main div" id="org9e766d3">
|
||||
<p>
|
||||
\[
|
||||
{\boldsymbol \nabla}^2 V + \frac{\partial}{\partial t} {\boldsymbol \nabla} \cdot {\boldsymbol A} = -\frac{\rho}{\varepsilon_0}
|
||||
|
|
@ -1659,7 +1654,7 @@ whereas Amp{\`ere}-Maxwell becomes
|
|||
\]
|
||||
which becomes after simple rearrangement and use of the identity \({\boldsymbol \nabla} \times \left({\boldsymbol \nabla} \times {\boldsymbol A}\right) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\boldsymbol A}) - {\boldsymbol \nabla}^2 {\boldsymbol A}\),
|
||||
</p>
|
||||
<div class="main div" id="org2b39ef9">
|
||||
<div class="main div" id="org5364b31">
|
||||
<p>
|
||||
\[
|
||||
\left( {\boldsymbol ∇}^2 {\boldsymbol A} - μ_0 ε_0 \frac{∂^2 {\boldsymbol A}}{∂ t^2} \right)
|
||||
|
|
@ -1695,7 +1690,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1624,7 +1619,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1602,8 +1597,8 @@ Table of contents
|
|||
<li>Gr 3</li>
|
||||
</ul>
|
||||
|
||||
<details class="prereq" id="org97f4b33">
|
||||
<summary id="org8628991">
|
||||
<details class="prereq" id="orgbfc6a9b">
|
||||
<summary id="org8848e57">
|
||||
Prerequisites
|
||||
</summary>
|
||||
<ul class="org-ul">
|
||||
|
|
@ -1611,8 +1606,8 @@ Prerequisites
|
|||
</ul>
|
||||
</details>
|
||||
|
||||
<details class="objectives" id="orgdf0f685">
|
||||
<summary id="org9c3f957">
|
||||
<details class="objectives" id="orgab6b502">
|
||||
<summary id="org1296d42">
|
||||
Objectives
|
||||
</summary>
|
||||
<ul class="org-ul">
|
||||
|
|
@ -1650,7 +1645,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1608,7 +1603,7 @@ A generic configuration of static charges coupled via the Coulomb interaction
|
|||
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>
|
||||
</p>
|
||||
<div class="main div" id="org0a614c7">
|
||||
<div class="main div" id="org8506f8e">
|
||||
<p>
|
||||
|
||||
</p>
|
||||
|
|
@ -1622,7 +1617,7 @@ 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
|
||||
explicit construction <a href="./ems_es_ep_d.html#p_vcd">p_vcd</a>
|
||||
</p>
|
||||
<div class="main div" id="org6e195dd">
|
||||
<div class="main div" id="org5719824">
|
||||
<p>
|
||||
|
||||
</p>
|
||||
|
|
@ -1642,7 +1637,7 @@ condition <a href="./ems_es_ef_cE.html#curlE0">curlE0</a> can be expressed as th
|
|||
<a href="./ems_es_ep_PL.html#Poi">🐟</a>
|
||||
</p>
|
||||
|
||||
<div class="core div" id="orgef7da18">
|
||||
<div class="core div" id="org3f71da0">
|
||||
<p>
|
||||
|
||||
</p>
|
||||
|
|
@ -1658,7 +1653,7 @@ condition <a href="./ems_es_ef_cE.html#curlE0">curlE0</a> can be expressed as th
|
|||
<p>
|
||||
In the specific case where the charge density vanishes, we fall back onto the simpler Laplace equation <a href="./ems_es_ep_PL.html#Lap">Lap</a>
|
||||
</p>
|
||||
<div class="core div" id="orgf5b1b63">
|
||||
<div class="core div" id="org5ce296d">
|
||||
<p>
|
||||
|
||||
</p>
|
||||
|
|
@ -1696,7 +1691,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1614,14 +1609,14 @@ In one dimension, the potential is a single-variable
|
|||
function \(\phi (x)\) and the Laplace equation reads
|
||||
</p>
|
||||
|
||||
<div class="eqlabel" id="org20933f1">
|
||||
<div class="eqlabel" id="org725867f">
|
||||
<p>
|
||||
<a id="Lap_1d"></a><a href="./ems_ca_fe_L.html#Lap_1d"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org1705801">
|
||||
<div class="alteqlabels" id="org2a0a535">
|
||||
|
||||
</div>
|
||||
|
||||
|
|
@ -1636,14 +1631,14 @@ function \(\phi (x)\) and the Laplace equation reads
|
|||
<p>
|
||||
The solution to this is
|
||||
</p>
|
||||
<div class="eqlabel" id="orgc9124d1">
|
||||
<div class="eqlabel" id="orgc6b3d69">
|
||||
<p>
|
||||
<a id="Lap_1d_sol"></a><a href="./ems_ca_fe_L.html#Lap_1d_sol"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org566337b">
|
||||
<div class="alteqlabels" id="org95476d4">
|
||||
<ul class="org-ul">
|
||||
<li>Gr (3.6)</li>
|
||||
</ul>
|
||||
|
|
@ -1702,14 +1697,14 @@ In two dimensions, the potential becomes a function
|
|||
of two variables (here: \(x\) and \(y\)), so Laplace's
|
||||
equation now reads
|
||||
</p>
|
||||
<div class="eqlabel" id="org0af82b1">
|
||||
<div class="eqlabel" id="org061811b">
|
||||
<p>
|
||||
<a id="Lap_2d"></a><a href="./ems_ca_fe_L.html#Lap_2d"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="orgf05a1be">
|
||||
<div class="alteqlabels" id="org4f02882">
|
||||
|
||||
</div>
|
||||
|
||||
|
|
@ -1762,14 +1757,14 @@ a point equals its value averaged over a sphere
|
|||
\(S_R({\bf r})\) of any radius \(R\) centered on this point
|
||||
(and of course not containing any charges),
|
||||
</p>
|
||||
<div class="eqlabel" id="org45554bc">
|
||||
<div class="eqlabel" id="orgdcc647d">
|
||||
<p>
|
||||
<a id="p_ball_avg"></a><a href="./ems_ca_fe_L.html#p_ball_avg"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org242a219">
|
||||
<div class="alteqlabels" id="orgce61baf">
|
||||
|
||||
</div>
|
||||
|
||||
|
|
@ -1781,8 +1776,8 @@ a point equals its value averaged over a sphere
|
|||
\]
|
||||
</p>
|
||||
|
||||
<details id="orgeb8b5b8">
|
||||
<summary id="org92de027">
|
||||
<details id="orge7969c9">
|
||||
<summary id="org65097bb">
|
||||
<strong>Physicist's proof</strong>
|
||||
</summary>
|
||||
<p>
|
||||
|
|
@ -1844,8 +1839,8 @@ proving the theorem.
|
|||
</p>
|
||||
</details>
|
||||
|
||||
<details id="org2eee056">
|
||||
<summary id="orgf338007">
|
||||
<details id="orgf16a408">
|
||||
<summary id="orgdc4e491">
|
||||
<strong>Formal proof</strong>
|
||||
</summary>
|
||||
|
||||
|
|
@ -1895,14 +1890,14 @@ we get the following general
|
|||
<p>
|
||||
<b>Theorem</b>:
|
||||
</p>
|
||||
<div class="eqlabel" id="org723ed6d">
|
||||
<div class="eqlabel" id="orgb167571">
|
||||
<p>
|
||||
<a id="dfdR_intLap"></a><a href="./ems_ca_fe_L.html#dfdR_intLap"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org447b5bf">
|
||||
<div class="alteqlabels" id="orgb04c004">
|
||||
|
||||
</div>
|
||||
|
||||
|
|
@ -1955,19 +1950,19 @@ are necessarily positive, we thus require \(f_x > 0\), \(f_y > 0\) and \(f
|
|||
of the \(f_x + f_y + f_z = 0\) condition above.
|
||||
</p>
|
||||
|
||||
<div class="eqlabel" id="org7f931db">
|
||||
<div class="eqlabel" id="org368f926">
|
||||
<p>
|
||||
<a id="Earnshaw"></a><a href="./ems_ca_fe_L.html#Earnshaw"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="orgfc31737">
|
||||
<div class="alteqlabels" id="orgd8486b2">
|
||||
|
||||
</div>
|
||||
|
||||
</div>
|
||||
<div class="info div" id="org181f62a">
|
||||
<div class="info div" id="org74af865">
|
||||
<p>
|
||||
<b>Earnshaw's theorem (physical version)</b> <br>
|
||||
</p>
|
||||
|
|
@ -2086,7 +2081,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<!-- 2022-02-17 Thu 08:42 -->
|
||||
<!-- 2022-02-21 Mon 10:33 -->
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
||||
<title>Pre-Quantum Electrodynamics</title>
|
||||
|
|
@ -602,11 +602,11 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charge</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_lf_c.html#ems_ms_lf_c">Currents</a><span class="headline-id">ems.ms.lf.c</span>
|
||||
<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -614,21 +614,12 @@ Table of contents
|
|||
</details>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
|
||||
|
||||
|
||||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_BS_sc.html#ems_ms_BS_sc">The Magnetic Field issuing from a Steady Current</a><span class="headline-id">ems.ms.BS.sc</span>
|
||||
|
||||
</li>
|
||||
|
||||
</ul>
|
||||
</details>
|
||||
</li>
|
||||
<li>
|
||||
|
||||
|
|
@ -640,11 +631,15 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_sc.html#ems_ms_dcB_sc">Straight-line Currents</a><span class="headline-id">ems.ms.dcB.sc</span>
|
||||
<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_BS.html#ems_ms_dcB_BS">Divergence and Curl of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.BS</span>
|
||||
<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
|
||||
|
||||
</li>
|
||||
|
||||
|
|
@ -661,6 +656,10 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
|
||||
|
||||
</li>
|
||||
|
|
@ -698,10 +697,6 @@ Table of contents
|
|||
</summary>
|
||||
<ul>
|
||||
<li>
|
||||
<a href="./emsm_esm_s.html#emsm_esm_s">A proper definition of "statics"</a><span class="headline-id">emsm.esm.s</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
|
@ -1435,7 +1430,7 @@ Table of contents
|
|||
|
||||
</li>
|
||||
<li>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
|
||||
<a href="./c_m_dc_pr.html#c_m_dc_pr">Product arguments</a><span class="headline-id">c.m.dc.pr</span>
|
||||
|
||||
</li>
|
||||
<li>
|
||||
|
|
@ -1597,11 +1592,11 @@ 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"/>
|
||||
</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="info div" id="org28a8993">
|
||||
<div class="info div" id="orgf2e5cc5">
|
||||
<p>
|
||||
<b>George Green</b>
|
||||
</p>
|
||||
<aside id="org0ab9bd7">
|
||||
<aside id="org5d7a251">
|
||||
<p>
|
||||
See a <a href="https://en.wikipedia.org/wiki/George%5C_Green%5C_(mathematician)">short bio on wikipedia</a>
|
||||
</p>
|
||||
|
|
@ -1634,14 +1629,14 @@ and
|
|||
\]
|
||||
Substituting this in the divergence theorem gives <b>Green's first identity</b>
|
||||
</p>
|
||||
<div class="eqlabel" id="orgbbf64af">
|
||||
<div class="eqlabel" id="org6097b29">
|
||||
<p>
|
||||
<a id="Green1"></a><a href="./ems_ca_fe_g.html#Green1"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="orga3318b9">
|
||||
<div class="alteqlabels" id="orgce16d0c">
|
||||
<ul class="org-ul">
|
||||
<li>J (1.34)</li>
|
||||
</ul>
|
||||
|
|
@ -1659,14 +1654,14 @@ As an aside for now, for completeness, if we do the same thing again but with \(
|
|||
interchanged, and subtract the result, we obtain another useful result known as
|
||||
<b>Green's second identity</b> or <b>Green's theorem</b>
|
||||
</p>
|
||||
<div class="eqlabel" id="org785b1da">
|
||||
<div class="eqlabel" id="org867d0df">
|
||||
<p>
|
||||
<a id="Green2"></a><a href="./ems_ca_fe_g.html#Green2"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
|
||||
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
|
||||
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
|
||||
</svg></a>
|
||||
</p>
|
||||
<div class="alteqlabels" id="org08207ba">
|
||||
<div class="alteqlabels" id="org43111e9">
|
||||
<ul class="org-ul">
|
||||
<li>J (1.35)</li>
|
||||
</ul>
|
||||
|
|
@ -1702,7 +1697,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
|
|||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Jean-Sébastien Caux</p>
|
||||
<p class="date">Created: 2022-02-17 Thu 08:42</p>
|
||||
<p class="date">Created: 2022-02-21 Mon 10:33</p>
|
||||
<p class="validation"></p>
|
||||
</div>
|
||||
|
||||
|
|
|
|||
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Reference in New Issue