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Update 2022-02-14 20:42

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Jean-Sébastien
2022-02-14 20:42:37 +01:00
parent 4cfe8cef59
commit 09a8ba5fb6
204 changed files with 1968 additions and 1206 deletions
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build/emsm_esm_fpo.html
+7 -7
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-13 Sun 21:20 -->
<!-- 2022-02-14 Mon 20:35 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1641,7 +1641,7 @@ 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="org2b8e04d">
<div class="main div" id="org0cc2b4e">
<p>
\[
\sigma_b({\bf r}) = {\bf P} ({\bf r}) \cdot \hat{\bf n}
@@ -1653,7 +1653,7 @@ 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="orgfedc24b">
<div class="main div" id="org68ad49c">
<p>
\[
\rho_b ({\bf r}) = -{\boldsymbol \nabla} \cdot {\bf P} ({\bf r})
@@ -1665,7 +1665,7 @@ and second term looks like contribution of a volume charge,
<p>
Using these definitions,
</p>
<div class="main div" id="org92d3761">
<div class="main div" id="org7a8a491">
<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}'|}
@@ -1684,7 +1684,7 @@ These {\bf bound charges} faithfully represent the object's sources for electric
</p>
<div class="example div" id="org2180b05">
<div class="example div" id="org2a54ac2">
<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, \(\rho_b = 0\).
@@ -1692,7 +1692,7 @@ Surface charge:
\[
\sigma_b ({\bf r}) = {\bf P} \cdot \hat{\bf n} = P \cos \theta.
\]
This was computed in Example: surface charge density on a sphere (eq. \ref{eq:PotentialUniformlyPolarizedSphere}):
This was computed in Example: surface charge density on a sphere (eq. <a href="./ems_ca_sv_sph.html#p_uni_ch_sph">p_uni_ch_sph</a>):
\[
V(r, \theta) = \left\{ \begin{array}{cc}
\frac{P}{3\varepsilon_0} r\cos \theta, &amp; r \leq R \\
@@ -1743,7 +1743,7 @@ 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: 2022-02-13 Sun 21:20</p>
<p class="date">Created: 2022-02-14 Mon 20:35</p>
<p class="validation"></p>
</div>