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Update 2022-03-07 20:40

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Jean-Sébastien
2022-03-07 20:40:36 +01:00
parent 21bf9fdba5
commit 4808df71e6
194 changed files with 1487 additions and 5980 deletions
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build/emdm_emwm_ad_c.html
+6 -14
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-03-02 Wed 15:45 -->
<!-- 2022-03-07 Mon 20:38 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1098,14 +1098,6 @@ Table of contents
<li>
<a href="./emdm_emwm_refl_oi.html#emdm_emwm_refl_oi">Oblique Incidence</a><span class="headline-id">emdm.emwm.refl.oi</span>
</li>
<li>
<a href="./emdm_emwm_refl_Fe.html#emdm_emwm_refl_Fe">Fresnel's Equations</a><span class="headline-id">emdm.emwm.refl.Fe</span>
</li>
<li>
<a href="./emdm_emwm_refl_Ba.html#emdm_emwm_refl_Ba">Brewster's Angle</a><span class="headline-id">emdm.emwm.refl.Ba</span>
</li>
</ul>
@@ -1628,13 +1620,13 @@ We now consider EM waves inside a bulk conductor and will consider nonvanishing
\]
which means that the Maxwell equations reduce to
</p>
\begin{align}
\begin{align*}
{\boldsymbol \nabla} \cdot {\boldsymbol E} &amp;= \frac{\rho_f}{\varepsilon},
\hspace{10mm} &amp;
{\boldsymbol \nabla} \cdot {\boldsymbol B} &amp;= 0, \nonumber\\
{\boldsymbol \nabla} \times {\boldsymbol E} &amp;= -\frac{\partial {\boldsymbol B}}{\partial t} &amp;
{\boldsymbol \nabla} \times {\boldsymbol B} &amp;= \mu \sigma {\boldsymbol E} + \mu \varepsilon \frac{\partial {\boldsymbol E}}{\partial t}.
\end{align}
\end{align*}
<p>
Putting together the continuity equation for free charge
\[
@@ -1660,7 +1652,7 @@ After the free charge has dissipated, we have
{\boldsymbol \nabla} \times {\boldsymbol B} &amp;= \mu \sigma {\boldsymbol E} + \mu \varepsilon \frac{\partial {\boldsymbol E}}{\partial t}
\end{align}
<p>
Applying ${\boldsymbol ∇} × $ to the curl equations gives the modified wave equations
Applying \({\boldsymbol \nabla} \times\) to the curl equations gives the modified wave equations
\[
{\boldsymbol \nabla}^2 {\boldsymbol E} = \mu \varepsilon \frac{\partial^2 {\boldsymbol E}}{\partial t^2} + \mu \sigma \frac{\partial {\boldsymbol E}}{\partial t}, \hspace{10mm}
{\boldsymbol \nabla}^2 {\boldsymbol B} = \mu \varepsilon \frac{\partial^2 {\boldsymbol B}}{\partial t^2} + \mu \sigma \frac{\partial {\boldsymbol B}}{\partial t}
@@ -1684,7 +1676,7 @@ The wave can thus be written (letting \(\hat{\boldsymbol k}\) represent the dire
{\boldsymbol E} ({\boldsymbol r}, t) = {\boldsymbol E}_0 e^{-{\boldsymbol \kappa} \cdot {\boldsymbol r}} e^{i ({\boldsymbol k} \cdot {\boldsymbol r} - \omega t)}
\]
with a similar solution for \({\boldsymbol B}\).
The quantity \(d = \frac{1}{\kappa}\) is known as the {\bf skin depth}.
The quantity \(d = \frac{1}{\kappa}\) is known as the <b>skin depth</b>.
</p>
<p>
@@ -1741,7 +1733,7 @@ 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: 2022-03-02 Wed 15:45</p>
<p class="date">Created: 2022-03-07 Mon 20:38</p>
<p class="validation"></p>
</div>