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2022-02-21 20:42:13 +01:00
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-21 Mon 10:33 -->
<!-- 2022-02-21 Mon 20:41 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -706,28 +706,41 @@ Table of contents
</summary>
<ul>
<li>
<a href="./emsm_esm_p.html#emsm_esm_p">Polarization</a><span class="headline-id">emsm.esm.p</span>
</li>
<li>
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
</li>
<li>
<details>
<summary>
<a href="./emsm_esm_fpo.html#emsm_esm_fpo">The Field of a Polarized Object</a><span class="headline-id">emsm.esm.fpo</span>
<a href="./emsm_esm_mE.html#emsm_esm_mE">Matter Bathed in E Fields; Polarization</a><span class="headline-id">emsm.esm.mE</span>
</summary>
<ul>
<li>
<a href="./emsm_esm_fpo_pibc.html#emsm_esm_fpo_pibc">Physical Interpretation of Bound Charges</a><span class="headline-id">emsm.esm.fpo.pibc</span>
<a href="./emsm_esm_mE_o.html#emsm_esm_mE_o">Overview</a><span class="headline-id">emsm.esm.mE.o</span>
</li>
<li>
<a href="./emsm_esm_fpo_fid.html#emsm_esm_fpo_fid">The Field Inside a Dielectric</a><span class="headline-id">emsm.esm.fpo.fid</span>
<a href="./emsm_esm_mE_P.html#emsm_esm_mE_P">Polarization</a><span class="headline-id">emsm.esm.mE.P</span>
</li>
</ul>
</details>
</li>
<li>
<details>
<summary>
<a href="./emsm_esm_po.html#emsm_esm_po">Polarized Objects; Bound Charges</a><span class="headline-id">emsm.esm.po</span>
</summary>
<ul>
<li>
<a href="./emsm_esm_po_pibc.html#emsm_esm_po_pibc">Physical Interpretation of Bound Charges</a><span class="headline-id">emsm.esm.po.pibc</span>
</li>
<li>
<a href="./emsm_esm_po_fid.html#emsm_esm_po_fid">The Field Inside a Dielectric</a><span class="headline-id">emsm.esm.po.fid</span>
</li>
@@ -750,18 +763,34 @@ Table of contents
</ul>
</details>
</li>
<li>
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
</li>
<li>
<details>
<summary>
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
<a href="./emsm_esm_ld.html#emsm_esm_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.ld</span>
</summary>
<ul>
<li>
<a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
<a href="./emsm_esm_ld_sp.html#emsm_esm_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a><span class="headline-id">emsm.esm.ld.sp</span>
</li>
<li>
<a href="./emsm_esm_ld_bvp.html#emsm_esm_ld_bvp">Boundary Value Problems with Linear Dielectrics</a><span class="headline-id">emsm.esm.ld.bvp</span>
</li>
<li>
<a href="./emsm_esm_ld_e.html#emsm_esm_ld_e">Energy in Dielectric Systems</a><span class="headline-id">emsm.esm.ld.e</span>
</li>
<li>
<a href="./emsm_esm_ld_f.html#emsm_esm_ld_f">Forces on Dielectrics</a><span class="headline-id">emsm.esm.ld.f</span>
</li>
@@ -1599,14 +1628,14 @@ 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="org18ed00d">
<div class="eqlabel" id="org5b5f651">
<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="orgc42d135">
<div class="alteqlabels" id="org4ef283a">
<ul class="org-ul">
<li>Gr (2.21)</li>
</ul>
@@ -1622,7 +1651,7 @@ called the <b>electrostatic potential</b>
\]
</p>
<aside id="orgac048a8">
<aside id="orgd60b713">
<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 \(kg m^2/s^3 A\).
@@ -1639,14 +1668,14 @@ 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="orgbfef7ae">
<div class="eqlabel" id="orgaf599a2">
<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="orgaf22da0">
<div class="alteqlabels" id="orgdf03085">
<ul class="org-ul">
<li>Gr (2.21)</li>
</ul>
@@ -1654,7 +1683,7 @@ well-defined without the need to specify the reference point,
</div>
</div>
<div class="main div" id="org07eedf5">
<div class="main div" id="orgd3d3b4f">
<p>
\[
\phi({\bf b}) - \phi({\bf a}) = - \int_{\bf a}^{\bf b} {\bf E} \cdot d{\bf l}
@@ -1671,14 +1700,14 @@ 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="org35b60c7">
<div class="eqlabel" id="org058f8de">
<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="orgcdb33b6">
<div class="alteqlabels" id="org5b551aa">
<ul class="org-ul">
<li>FLS II (4.20,4.23)</li>
<li>Gr (2.26)</li>
@@ -1701,14 +1730,14 @@ 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="org6f1b97d">
<div class="eqlabel" id="org29052c6">
<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="orgde5550c">
<div class="alteqlabels" id="orgec1d1dd">
<ul class="org-ul">
<li>FLS II (4.24)</li>
<li>Gr (2.27)</li>
@@ -1718,7 +1747,7 @@ so for a distribution of point charges \(q_i\) at positions \({\bf r}_i\), we ha
</div>
</div>
<div class="core div" id="orgc76aaae">
<div class="core div" id="orgae68c3f">
<p>
</p>
@@ -1734,14 +1763,14 @@ 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="orgd7f3921">
<div class="eqlabel" id="orge090fa0">
<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="orgbb8f01c">
<div class="alteqlabels" id="org7d3ae3d">
<ul class="org-ul">
<li>Gr (2.29)</li>
<li>PM (2.18)</li>
@@ -1750,7 +1779,7 @@ For a continuous charge density in a volume \({\cal V}\), we have
</div>
</div>
<div class="main div" id="orga9781a0">
<div class="main div" id="orgd67d622">
<p>
</p>
@@ -1767,14 +1796,14 @@ 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="orgf360d4a">
<div class="eqlabel" id="org75e85cc">
<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="org79c6e16">
<div class="alteqlabels" id="org1302ba5">
<ul class="org-ul">
<li>Gr (2.30)b</li>
</ul>
@@ -1782,7 +1811,7 @@ whereas for a surface or line charge distribution, respectively,
</div>
</div>
<div class="main div" id="org0cb4e89">
<div class="main div" id="org061ad18">
<p>
\[
\phi({\bf r}) = \frac{1}{4\pi \varepsilon_0} \int_{\cal S} da' \frac{\sigma({\bf r}')}{|{\bf r} - {\bf r}'|}
@@ -1792,14 +1821,14 @@ whereas for a surface or line charge distribution, respectively,
</div>
<div class="eqlabel" id="orgc2dc6dc">
<div class="eqlabel" id="orgfae56fe">
<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="org560a824">
<div class="alteqlabels" id="orgc9e28fa">
<ul class="org-ul">
<li>Gr (2.30)a</li>
</ul>
@@ -1807,7 +1836,7 @@ whereas for a surface or line charge distribution, respectively,
</div>
</div>
<div class="main div" id="org01cfcbf">
<div class="main div" id="org0bf71ae">
<p>
</p>
@@ -1840,7 +1869,7 @@ 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: 2022-02-21 Mon 10:33</p>
<p class="date">Created: 2022-02-21 Mon 20:41</p>
<p class="validation"></p>
</div>