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Update 2022-02-08 17:21

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Jean-Sébastien
2022-02-08 17:21:33 +01:00
parent 077433c40a
commit 3454aba504
207 changed files with 1882 additions and 1097 deletions
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build/c_m_dd_div.html
+12 -12
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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>
@@ -1622,12 +1626,10 @@ Table of contents
Try to calculate this directly:
</p>
<p>
\[
\begin{equation}
{\boldsymbol \nabla} \cdot \frac{\hat{\bf r}}{r^2} = \frac{1}{r^2} \frac{\partial}{\partial r} \left( r^2 \frac{1}{r^2}\right) =^{?} 0
\label{Gr(1.84)}
\]
</p>
\end{equation}
<p>
Now apply the divergence theorem.
@@ -1635,16 +1637,14 @@ Integrate over a sphere of radius \(R\) centered at the origin (Prob. 1.38b):
</p>
<p>
\[
\begin{equation}
\oint \frac{\hat{\bf r}}{r^2} \cdot d{\bf a} = \int \left(\frac{1}{R^2} \hat{\bf r} \right) \cdot \left( R^2 \sin \theta d\theta d\phi ~\hat{\bf r} \right)
= \int_0^{\pi} d\theta \sin \theta \int_0^{2\pi} d\phi = 4\pi
\label{Gr(1.85)}
\]
</p>
\end{equation}
<p>
Problem: in (1.84), we've divided by zero when \(r = 0\).
Problem: in Gr(1.84), we've divided by zero when \(r = 0\).
</p>
</div>
</div>
@@ -1653,7 +1653,7 @@ Problem: in (1.84), we've divided by zero when \(r = 0\).
<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>