Update 2022-02-21 10:35
This commit is contained in:
Jean-Sébastien
+34
-39
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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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<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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@@ -1607,14 +1602,14 @@ which \(r\) is the distance from the chosen origin,
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The usual Cartesian coordinates relate to spherical coordinates
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according to
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</p>
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<div class="eqlabel" id="orgbcfbea1">
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<div class="eqlabel" id="org27681c3">
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<p>
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<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">
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<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
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<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
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</svg></a>
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</p>
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<div class="alteqlabels" id="org71b8aed">
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<div class="alteqlabels" id="org41dfc3e">
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</div>
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@@ -1639,14 +1634,14 @@ A generic vector can be expressed as
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where the explicit relation between spherical and
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Cartesian unit vectors is
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</p>
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<div class="eqlabel" id="org6e45fd1">
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<div class="eqlabel" id="org8bd9d3d">
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<p>
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<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">
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<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
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<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
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</svg></a>
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</p>
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<div class="alteqlabels" id="org5b78c82">
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<div class="alteqlabels" id="orga7940d0">
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</div>
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@@ -1669,14 +1664,14 @@ and \(\hat{\boldsymbol \varphi} (\theta, \varphi)\).
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<p>
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An infinitesimal displacement \(d{\bf l}\) can be written as
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</p>
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<div class="eqlabel" id="org673b085">
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<div class="eqlabel" id="org3750477">
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<p>
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<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">
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<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
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<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
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</svg></a>
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</p>
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<div class="alteqlabels" id="org77c531c">
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<div class="alteqlabels" id="orge80cb83">
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</div>
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@@ -1692,14 +1687,14 @@ d{\bf l} = dr ~\hat{\boldsymbol r} + r d\theta ~\hat{\boldsymbol \theta} + r\sin
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<p>
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Infinitesimal volume element:
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</p>
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<div class="eqlabel" id="org1dbbdd5">
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<div class="eqlabel" id="orgf70b76f">
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<p>
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<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">
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<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
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<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
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</svg></a>
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</p>
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<div class="alteqlabels" id="org00dd06e">
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<div class="alteqlabels" id="orgceda545">
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</div>
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@@ -1720,14 +1715,14 @@ Infinitesimal surface element: depends on situation.
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<div id="outline-container-c_m_cs_sph_grad" class="outline-6">
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<h6 id="c_m_cs_sph_grad"><a href="#c_m_cs_sph_grad">Gradient</a></h6>
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<div class="outline-text-6" id="text-c_m_cs_sph_grad">
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<div class="eqlabel" id="org80c4f55">
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<div class="eqlabel" id="org4246420">
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<p>
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<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">
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<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
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<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
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</svg></a>
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</p>
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<div class="alteqlabels" id="org0ea0f03">
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<div class="alteqlabels" id="org25d124f">
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</div>
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@@ -1744,14 +1739,14 @@ Infinitesimal surface element: depends on situation.
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<div id="outline-container-c_m_cs_sph_div" class="outline-6">
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<h6 id="c_m_cs_sph_div"><a href="#c_m_cs_sph_div">Divergence</a></h6>
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<div class="outline-text-6" id="text-c_m_cs_sph_div">
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<div class="eqlabel" id="orgfe29a0f">
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<div class="eqlabel" id="org2e86b9a">
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<p>
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<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">
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<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
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<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
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</svg></a>
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</p>
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<div class="alteqlabels" id="org5b16e24">
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<div class="alteqlabels" id="org7267db3">
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</div>
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@@ -1768,14 +1763,14 @@ Infinitesimal surface element: depends on situation.
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<div id="outline-container-c_m_cs_sph_curl" class="outline-6">
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<h6 id="c_m_cs_sph_curl"><a href="#c_m_cs_sph_curl">Curl</a></h6>
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<div class="outline-text-6" id="text-c_m_cs_sph_curl">
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<div class="eqlabel" id="orga4479e8">
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<div class="eqlabel" id="orgeedbe30">
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<p>
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<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">
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<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
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<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
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</svg></a>
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</p>
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<div class="alteqlabels" id="org557f5ed">
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<div class="alteqlabels" id="org5abe4c1">
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</div>
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@@ -1794,14 +1789,14 @@ Infinitesimal surface element: depends on situation.
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<div id="outline-container-c_m_cs_sph_lap" class="outline-6">
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<h6 id="c_m_cs_sph_lap"><a href="#c_m_cs_sph_lap">Laplacian</a></h6>
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<div class="outline-text-6" id="text-c_m_cs_sph_lap">
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<div class="eqlabel" id="orgecfce1d">
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<div class="eqlabel" id="org515dcfa">
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<p>
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<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">
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<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
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<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
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</svg></a>
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</p>
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<div class="alteqlabels" id="org01d6eb3">
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<div class="alteqlabels" id="orgbb072b6">
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</div>
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@@ -1835,7 +1830,7 @@ 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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