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Jean-Sébastien
2022-03-15 10:07:27 +01:00
parent 4808df71e6
commit 55f0de8197
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-03-07 Mon 20:38 -->
<!-- 2022-03-15 Tue 08:10 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1310,10 +1310,6 @@ Table of contents
</summary>
<ul>
<li>
<a href="./d_m.html#d_m">Diagnostics: Mathematical Preliminaries</a><span class="headline-id">d.m</span>
</li>
<li>
<a href="./d_ems.html#d_ems">Diagnostics: Electromagnetostatics</a><span class="headline-id">d.ems</span>
</li>
@@ -1352,6 +1348,10 @@ Table of contents
<li>
<a href="./d_red.html#d_red">Diagnostics: Relativistic Electrodynamics</a><span class="headline-id">d.red</span>
</li>
<li>
<a href="./d_m.html#d_m">Diagnostics: Compendium - Mathematics</a><span class="headline-id">d.m</span>
</li>
</ul>
@@ -1620,14 +1620,14 @@ field is independent of the path, and that it is proportional to the test charge
We can thus define a function representing the work per unit charge and
called the <b>electrostatic potential</b>
</p>
<div class="eqlabel" id="org9a20fdf">
<div class="eqlabel" id="orgfcac90f">
<p>
<a id="p"></a><a href="./ems_es_ep_d.html#p"><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="org2d11a20">
<div class="alteqlabels" id="orgab3c157">
<ul class="org-ul">
<li>Gr (2.21)</li>
</ul>
@@ -1643,7 +1643,7 @@ called the <b>electrostatic potential</b>
\]
</p>
<aside id="orgd5384a2">
<aside id="orgc523465">
<p>
\(\phi\) carries as unit: Newton-meters per coulomb or joules per coulomb, which is called a <b>volt</b>.
In the SI system where the ampere is a base unit, a volt is a \(kg m^2/s^3 A\).
@@ -1660,14 +1660,14 @@ want; it's energy <i>differences</i> which matter).
The potential difference between two arbitrary points \({\bf a}\) and \({\bf b}\) is
well-defined without the need to specify the reference point,
</p>
<div class="eqlabel" id="org4f4ddb1">
<div class="eqlabel" id="orge35b00f">
<p>
<a id="p_diff"></a><a href="./ems_es_ep_d.html#p_diff"><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="orga46dee2">
<div class="alteqlabels" id="org21f750c">
<ul class="org-ul">
<li>Gr (2.21)</li>
</ul>
@@ -1675,7 +1675,7 @@ well-defined without the need to specify the reference point,
</div>
</div>
<div class="main div" id="org95c6d71">
<div class="main div" id="orgfcd367f">
<p>
\[
\phi({\bf b}) - \phi({\bf a}) = - \int_{\bf a}^{\bf b} {\bf E} \cdot d{\bf l}
@@ -1692,14 +1692,14 @@ The reference point is typically put at infinity. The electrostatic potential c
point charge \(q\) at the origin can then be calculated (taking for convenience \(d{\bf l} = \hat{\bf r} dr\),
<i>i.e.</i> moving in purely radially) as
</p>
<div class="eqlabel" id="org68094ea">
<div class="eqlabel" id="org7062925">
<p>
<a id="p_pc"></a><a href="./ems_es_ep_d.html#p_pc"><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="org18beaa0">
<div class="alteqlabels" id="org35b2cdc">
<ul class="org-ul">
<li>FLS II (4.20,4.23)</li>
<li>Gr (2.26)</li>
@@ -1722,14 +1722,14 @@ point charge \(q\) at the origin can then be calculated (taking for convenience
The electrostatic potential moreover inherits the superposition principle from the electric field,
so for a distribution of point charges \(q_i\) at positions \({\bf r}_i\), we have
</p>
<div class="eqlabel" id="org39c7fae">
<div class="eqlabel" id="orgf111ed3">
<p>
<a id="p_pcd"></a><a href="./ems_es_ep_d.html#p_pcd"><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="org7b5d232">
<div class="alteqlabels" id="org89071e0">
<ul class="org-ul">
<li>FLS II (4.24)</li>
<li>Gr (2.27)</li>
@@ -1739,7 +1739,7 @@ so for a distribution of point charges \(q_i\) at positions \({\bf r}_i\), we ha
</div>
</div>
<div class="core div" id="org177c6aa">
<div class="core div" id="org4ac5fc6">
<p>
</p>
@@ -1755,14 +1755,14 @@ so for a distribution of point charges \(q_i\) at positions \({\bf r}_i\), we ha
<p>
For a continuous charge density in a volume \({\cal V}\), we have
</p>
<div class="eqlabel" id="org84a07be">
<div class="eqlabel" id="orgd4c214c">
<p>
<a id="p_vcd"></a><a href="./ems_es_ep_d.html#p_vcd"><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="orgb95597d">
<div class="alteqlabels" id="org8fb75e5">
<ul class="org-ul">
<li>Gr (2.29)</li>
<li>PM (2.18)</li>
@@ -1771,7 +1771,7 @@ For a continuous charge density in a volume \({\cal V}\), we have
</div>
</div>
<div class="main div" id="org4f9dae7">
<div class="main div" id="org0561934">
<p>
</p>
@@ -1788,14 +1788,14 @@ For a continuous charge density in a volume \({\cal V}\), we have
<p>
whereas for a surface or line charge distribution, respectively,
</p>
<div class="eqlabel" id="org9b4933a">
<div class="eqlabel" id="org886392d">
<p>
<a id="p_scd"></a><a href="./ems_es_ep_d.html#p_scd"><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="orgce60f21">
<div class="alteqlabels" id="org488ec6b">
<ul class="org-ul">
<li>Gr (2.30)b</li>
</ul>
@@ -1803,7 +1803,7 @@ whereas for a surface or line charge distribution, respectively,
</div>
</div>
<div class="main div" id="orgde978cb">
<div class="main div" id="org21be33b">
<p>
\[
\phi({\bf r}) = \frac{1}{4\pi \varepsilon_0} \int_{\cal S} da' \frac{\sigma({\bf r}')}{|{\bf r} - {\bf r}'|}
@@ -1813,14 +1813,14 @@ whereas for a surface or line charge distribution, respectively,
</div>
<div class="eqlabel" id="org2dc0be7">
<div class="eqlabel" id="orgf80de2f">
<p>
<a id="p_lcd"></a><a href="./ems_es_ep_d.html#p_lcd"><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="orgd8cf363">
<div class="alteqlabels" id="orgc67dd5f">
<ul class="org-ul">
<li>Gr (2.30)a</li>
</ul>
@@ -1828,7 +1828,7 @@ whereas for a surface or line charge distribution, respectively,
</div>
</div>
<div class="main div" id="orgeaaa789">
<div class="main div" id="orgaeed524">
<p>
</p>
@@ -1861,7 +1861,7 @@ 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: 2022-03-07 Mon 20:38</p>
<p class="date">Created: 2022-03-15 Tue 08:10</p>
<p class="validation"></p>
</div>