Update 2022-02-21 10:35
This commit is contained in:
Jean-Sébastien
+28
-33
@@ -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>
|
||||
@@ -1642,14 +1637,14 @@ sphere of radius \(r\) around the charge,
|
||||
<p>
|
||||
so by superposition, we obtain
|
||||
</p>
|
||||
<div class="eqlabel" id="org18e4ac7">
|
||||
<div class="eqlabel" id="orgc841a96">
|
||||
<p>
|
||||
<a id="Gl_i"></a><a href="./ems_es_ef_Gl.html#Gl_i"><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="org6f891e3">
|
||||
<div class="alteqlabels" id="orgca2a767">
|
||||
<ul class="org-ul">
|
||||
<li>Gr (2.13)</li>
|
||||
</ul>
|
||||
@@ -1657,7 +1652,7 @@ so by superposition, we obtain
|
||||
</div>
|
||||
|
||||
</div>
|
||||
<div class="core div" id="org8aa0959">
|
||||
<div class="core div" id="org479eebf">
|
||||
<p>
|
||||
<b>Gauss' law (in integral form)</b>
|
||||
</p>
|
||||
@@ -1689,14 +1684,14 @@ By applying the divergence theorem,
|
||||
and using \(Q_{\mbox{enc}} = \int_{\cal V} \rho d\tau\), and using the fact the the choice of volume
|
||||
is arbitrary, we get
|
||||
</p>
|
||||
<div class="eqlabel" id="org2625b7f">
|
||||
<div class="eqlabel" id="orga0658c7">
|
||||
<p>
|
||||
<a id="Gl_d"></a><a href="./ems_es_ef_Gl.html#Gl_d"><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="orgd3a84db">
|
||||
<div class="alteqlabels" id="orgf538ceb">
|
||||
<ul class="org-ul">
|
||||
<li>Gr (2.14)</li>
|
||||
</ul>
|
||||
@@ -1704,7 +1699,7 @@ is arbitrary, we get
|
||||
</div>
|
||||
|
||||
</div>
|
||||
<div class="core div" id="org398d11a">
|
||||
<div class="core div" id="org82e4552">
|
||||
<p>
|
||||
<b>Gauss' law in differential form</b>
|
||||
</p>
|
||||
@@ -1763,7 +1758,7 @@ cylindrical or plane symmetry.
|
||||
Gaussian surfaces: respectively, concentric sphere, coaxial cylinder, pillbox.
|
||||
</p>
|
||||
|
||||
<div class="example div" id="org6574b9f">
|
||||
<div class="example div" id="org8f38038">
|
||||
<p>
|
||||
<b>Example 2.2</b>: Field outside a uniformly charged sphere of radius \(R\) and total charge \(q\).
|
||||
</p>
|
||||
@@ -1794,7 +1789,7 @@ Same as point charge at origin!
|
||||
|
||||
</div>
|
||||
|
||||
<div class="example div" id="org21bf00b">
|
||||
<div class="example div" id="orgd106ac8">
|
||||
<p>
|
||||
<b>Example 2.3</b>: infinitely long cylinder carrying charge density \(\rho = k s\) for some constant \(k\). Find \({\bf E}\) within the cylinder.
|
||||
</p>
|
||||
@@ -1833,7 +1828,7 @@ Therefore,
|
||||
</div>
|
||||
|
||||
|
||||
<div class="example div" id="org02f609a">
|
||||
<div class="example div" id="org3361637">
|
||||
<p>
|
||||
<b>Example 2.4</b>: infinite plane (defined by \(z = 0\)) with uniform surface charge density \(\sigma\). Find \({\bf E}\).
|
||||
</p>
|
||||
@@ -1859,7 +1854,7 @@ where \(\hat{\bf n}\) is a unit vector extending away from the plane. Independe
|
||||
|
||||
</div>
|
||||
|
||||
<div class="example div" id="org84fb124">
|
||||
<div class="example div" id="orgf505f9f">
|
||||
<p>
|
||||
<b>Example 2.5</b>: two infinite planes (put them vertical) carrying equal but opposite uniform surface charge densities \(\pm \sigma\).
|
||||
</p>
|
||||
@@ -1889,7 +1884,7 @@ 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>
|
||||
|
||||
|
||||
Reference in New Issue
Block a user