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Update 2022-02-09 07:44

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Jean-Sébastien
2022-02-09 07:44:58 +01:00
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-08 Tue 17:21 -->
<!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1616,7 +1616,7 @@ Table of contents
</ul>
</details>
</nav>
<ul class="navigation-links"><li>Prev:&nbsp;<a href="emsm_esm_fpo_fid.html">The Field Inside a Dielectric&emsp;<small>[emsm.esm.fpo.fid]</small></a></li><li>Next:&nbsp;<a href="emsm_esm_D_bc.html">Boundary Conditions&emsp;<small>[emsm.esm.D.bc]</small></a></li><li>Up:&nbsp;<a href="emsm_esm.html">Electrostatics in matter&emsp;<small>[emsm.esm]</small></a></li></ul>
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="emsm.html">Electromagnetostatics in matter</a></li><li><a class="breadcrumb-link"href="emsm_esm.html">Electrostatics in matter</a></li><li>The Electric Displacement</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="emsm_esm_fpo_fid.html">The Field Inside a Dielectric&emsp;<small>[emsm.esm.fpo.fid]</small></a></li><li>Next:&nbsp;<a href="emsm_esm_D_bc.html">Boundary Conditions&emsp;<small>[emsm.esm.D.bc]</small></a></li><li>Up:&nbsp;<a href="emsm_esm.html">Electrostatics in matter&emsp;<small>[emsm.esm]</small></a></li></ul>
<h4 id="emsm_esm_D">The Electric Displacement<a class="headline-permalink" href="./emsm_esm_D.html#emsm_esm_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"/>
@@ -1626,7 +1626,7 @@ Table of contents
<p>
Field due to polarization: effectively comes from bound surface and volume charges,
</p>
<div class="main div" id="org9531944">
<div class="main div" id="org31dde4c">
<p>
\[
\rho_b = -{\boldsymbol \nabla} \cdot {\bf P}, \hspace{1cm} \sigma_b = {\bf P} \cdot \hat{\bf n}.
@@ -1655,7 +1655,7 @@ Convenient way of writing:
\]
Defining the
</p>
<div class="core div" id="org98901f4">
<div class="core div" id="org05c3963">
<p>
<b>Electric displacement</b> \({\bf D}\)
\[
@@ -1668,7 +1668,7 @@ Defining the
<p>
Gauss's law becomes
</p>
<div class="core div" id="org49dea26">
<div class="core div" id="orgd8cb113">
<p>
\[
{\boldsymbol \nabla} \cdot {\bf D} = \rho_f
@@ -1680,7 +1680,7 @@ Gauss's law becomes
<p>
or in integral form
</p>
<div class="core div" id="orgf2cfa4b">
<div class="core div" id="org331a73a">
<p>
\[
\oint d{\bf a} \cdot {\bf D} = Q_{f_{enc}}
@@ -1690,7 +1690,7 @@ or in integral form
</div>
<div class="example div" id="orgb3982f7">
<div class="example div" id="org3daf0dd">
<p>
\paragraph{Example 4.4:} long straight wire, uniform line charge \(\lambda\), surrounded by rubber insulation
to radius \(a\). Find \({\bf D}\).
@@ -1736,10 +1736,21 @@ There is not 'potential' for \({\bf D}\).
<li><a href="emsm_esm_D_bc.html">Boundary Conditions</a><span class="headline-id">emsm.esm.D.bc</span></li>
</ul>
<hr><div id="postamble" class="status">
<hr>
<div class="license">
<a rel="license noopener" href="https://creativecommons.org/licenses/by/4.0/"
target="_blank" class="m-2">
<img alt="Creative Commons License" style="border-width:0"
src="https://licensebuttons.net/l/by/4.0/80x15.png"/>
</a>
Except where otherwise noted, all content is licensed under a
<a rel="license noopener" href="https://creativecommons.org/licenses/by/4.0/"
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: 2022-02-08 Tue 17:21</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
<p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"></p>
</div>