Update 2022-02-14 20:42
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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>
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<!-- 2022-02-13 Sun 21:20 -->
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<!-- 2022-02-14 Mon 20:35 -->
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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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@@ -1598,18 +1598,23 @@ Table of contents
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</svg></a><span class="headline-id">ems.ca.fe</span></h4>
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<div class="outline-text-4" id="text-ems_ca_fe">
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<ul class="org-ul altsecnrs">
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<li>Gr 3.1</li>
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</ul>
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<p>
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A generic configuration of static charges coupled via the Coulomb interaction
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defines an electrostatic problem, whose solution is in principle obtained
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from calculating either the field according to <a href="./ems_es_ef_ccd.html#E_vcd">E_vcd</a>
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</p>
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<div class="main div" id="org98cdfd8">
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<div class="main div" id="orgfccec5d">
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<p>
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</p>
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\begin{equation*}
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{\bf E} ({\bf r}) = \frac{1}{4\pi\varepsilon_0} \int_{\mathbb{R}^3} d\tau' \rho({\bf r}') \frac{{\bf r} - {\bf r}'}{|{\bf r} - {\bf r}'|^3}
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{\bf E} ({\bf r}) = \frac{1}{4\pi\varepsilon_0} \int_{\mathbb{R}^3} d\tau' \rho({\bf r}') \frac{{\bf r} - {\bf r}'}{|{\bf r} - {\bf r}'|^3}
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\end{equation*}
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</div>
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@@ -1617,7 +1622,7 @@ from calculating either the field according to <a href="./ems_es_ef_ccd.html#E_v
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or (often simpler) by calculating the electrostatic potential, using either the
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explicit construction <a href="./ems_es_ep_d.html#p_vcd">p_vcd</a>
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</p>
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<div class="main div" id="org12e97ac">
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<div class="main div" id="org5194654">
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<p>
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</p>
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@@ -1637,7 +1642,7 @@ condition <a href="./ems_es_ef_cE.html#curlE0">curlE0</a> can be expressed as th
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<a href="./ems_es_ep_PL.html#Poi">🐟</a>
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</p>
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<div class="core div" id="orgcacf446">
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<div class="core div" id="org765eb12">
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<p>
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</p>
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@@ -1653,7 +1658,7 @@ condition <a href="./ems_es_ef_cE.html#curlE0">curlE0</a> can be expressed as th
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<p>
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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>
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</p>
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<div class="core div" id="orgea7b7e8">
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<div class="core div" id="org025bcf6">
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<p>
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</p>
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@@ -1691,7 +1696,7 @@ 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: 2022-02-13 Sun 21:20</p>
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<p class="date">Created: 2022-02-14 Mon 20:35</p>
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<p class="validation"></p>
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</div>
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