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Update 2022-02-08 17:21

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Jean-Sébastien
2022-02-08 17:21:33 +01:00
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-08 Tue 06:55 -->
<!-- 2022-02-08 Tue 17:21 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -272,6 +272,10 @@ Table of contents
</summary>
<ul>
<li>
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
</li>
<li>
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
</li>
@@ -736,7 +740,7 @@ Table of contents
</li>
<li>
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
</li>
<li>
@@ -1612,7 +1616,7 @@ Table of contents
</ul>
</details>
</nav>
<ul class="navigation-links"><li>Prev:&nbsp;<a href="emsm_esm_d.html">Dielectrics&emsp;<small>[emsm.esm.d]</small></a></li><li>Next:&nbsp;<a href="emsm_esm_fpo_pibc.html">Physical Interpretation of Bound Charges&emsp;<small>[emsm.esm.fpo.pibc]</small></a></li><li>Up:&nbsp;<a href="emsm_esm.html">Electrostatics in matter&emsp;<small>[emsm.esm]</small></a></li></ul>
<ul class="navigation-links"><li>Prev:&nbsp;<a href="emsm_esm_di.html">Dielectrics&emsp;<small>[emsm.esm.di]</small></a></li><li>Next:&nbsp;<a href="emsm_esm_fpo_pibc.html">Physical Interpretation of Bound Charges&emsp;<small>[emsm.esm.fpo.pibc]</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_fpo">The Field of a Polarized Object<a class="headline-permalink" href="./emsm_esm_fpo.html#emsm_esm_fpo"><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"/>
@@ -1662,7 +1666,7 @@ V({\bf r}) = \frac{1}{4\pi\varepsilon_0} \oint_{\cal S} d{\bf a}' ⋅ \frac{{\bf
\]
Interpretation: first terms is like contribution of a surface charge,
</p>
<div class="main div" id="org5c31a10">
<div class="main div" id="org0db0ed1">
<p>
\[
\sigma_b({\bf r}) = {\bf P} ({\bf r}) \cdot \hat{\bf n}
@@ -1674,7 +1678,7 @@ Interpretation: first terms is like contribution of a surface charge,
<p>
and second term looks like contribution of a volume charge,
</p>
<div class="main div" id="org2c0c9b0">
<div class="main div" id="orgf6835b7">
<p>
\[
\rho_b ({\bf r}) = -{\boldsymbol \nabla} \cdot {\bf P} ({\bf r})
@@ -1686,7 +1690,7 @@ and second term looks like contribution of a volume charge,
<p>
Using these definitions,
</p>
<div class="main div" id="orgec07570">
<div class="main div" id="orgaff40e6">
<p>
\[
V({\bf r}) = \frac{1}{4\pi\varepsilon_0} \oint_{\cal S} d{\bf a}' ⋅ \frac{σ_b ({\bf r}')}{|{\bf r} - {\bf r}'|}
@@ -1705,7 +1709,7 @@ These {\bf bound charges} faithfully represent the object's sources for electric
</p>
<div class="example div" id="org3291100">
<div class="example div" id="orgd5d2cc0">
<p>
\paragraph{Example 4.2:} electric field produced by uniformly polarized sphere of radius \(R\).
\paragraph{Solution:} put \(z\) axis along \({\bf P}\). Since \({\bf P}\) is uniform, \(\rho_b = 0\).
@@ -1751,7 +1755,7 @@ where the total dipole moment is simply the integral over the polarization,
<hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 06:55</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>
</div>