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M3P2
Courses
Commits
21d5ff1d
Commit
21d5ff1d
authored
May 20, 2023
by
Claude Meny
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Update cheatsheet.fr.md
parent
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12.temporary_ins/90.electromagnetism-in-vacuum/20.electromagnetic-waves-vacuum/20.overview/cheatsheet.fr.md
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21d5ff1d
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@@ -191,7 +191,7 @@ puis d'une onde plane progressive monochromatique (OPPM).
<br>
*
L'équation de
*Maxwell-Thomson*
implique
:
*
L'équation de
*Maxwell-Thomson*
implique
dans le vide :
<br>
$
`\left.
\begin{align} &\underbrace{div\,\overrightarrow{B}=0}_{\color{blue}{\text{th. de Maxwell-Thomson}}}\\
...
...
@@ -210,8 +210,38 @@ puis d'une onde plane progressive monochromatique (OPPM).
<br>
*
L'équation de
*Maxwell-Ampère*
implique
:
*
L'équation de
*Maxwell-Ampère*
implique
($
`\overrightarrow{j}=\overrightarrow{0}`
$) :
<br>
$
`\left.
\begin{align}
&\underbrace{\overrightarrow{rot}\,\overrightarrow{B}=
\mu_0\,\overrightarrow{j}+\underbrace{\mu_0\epsilon_0}_{\color{blue}{=\dfrac{1}{c^2}}\,
\dfrac{\partial \overrightarrow{E}}{\partial t}_{\color{blue}{\text{th. de Maxwell-Faraday}
=\dfrac{1}{c^2}\,\dfrac{\partial \overrightarrow{E}}{\partial t}}
}}\\
\\
&\overrightarrow{B}\;uniforme\\
&dans\;tout\;plan\;\perp\overrightarrow{e_z}\end{align}\right\}`
$
<br>
$
`\Longrightarrow\left\{
\begin{align}
&\dfrac{\partial B_z}{\partial y}-\dfrac{\partial B_y}{\partial z}=\dfrac{\partial E_x}{\partial t}\\
&\dfrac{\partial E_x}{\partial z}-\dfrac{\partial E_z}{\partial x}=-\dfrac{\partial B_y}{\partial t}\\
&\dfrac{\partial E_y}{\partial x}-\dfrac{\partial E_x}{\partial y}=-\dfrac{\partial B_z}{\partial t}\\
\\
&\dfrac{\partial E_z}{\partial y}=\dfrac{\partial E_y}{\partial z}=\dfrac{\partial E_x}{\partial z}\\
&\quad =\dfrac{\partial E_z}{\partial x}=\dfrac{\partial E_y}{\partial x}=\dfrac{\partial E_x}{\partial y}=0
\end{align}\right.`
$
<br>
*
$
`\Longrightarrow\left\{
\begin{align}
&\dfrac{\partial B_x}{\partial t}=- \dfrac{\partial E_y}{\partial z}\\
\\
&\dfrac{\partial B_y}{\partial t}=- \dfrac{\partial E_x}{\partial z}\\
\\
&\dfrac{\partial B_z}{\partial t}=0
\end{align}\right.`
$
*
schéma de démonstration à faire, puis modifier :
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