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M3P2
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bff10ae2
Commit
bff10ae2
authored
May 20, 2023
by
Claude Meny
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Update cheatsheet.fr.md
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12.temporary_ins/90.electromagnetism-in-vacuum/20.electromagnetic-waves-vacuum/20.overview/cheatsheet.fr.md
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bff10ae2
...
@@ -143,9 +143,22 @@ puis d'une onde plane progressive monochromatique (OPPM).
...
@@ -143,9 +143,22 @@ puis d'une onde plane progressive monochromatique (OPPM).
<br>
<br>
*
Le théorème de
*Maxwell-Gauss*
implique dans le vide ($
`\dens=0`
$) :
*
Le théorème de
*Maxwell-Gauss*
implique dans le vide ($
`\dens=0`
$) :
<br>
<br>
$
`\begin{align} &\color{blue}{div\,\overrightarrow{E} = \dfrac{\dens}{\epsilon_0} = 0} \\
$
`\left.
&\Longrightarrow\;\dfrac{\partial E_x}{\partial x} + \dfrac{\partial E_y}{\partial y} + \dfrac{\partial E_z}{\partial y}=0 \\
\begin{align} &\underbrace{div(\overrightarrow{E}=\dfrac{\dens}{\epsilon_0}=0}_{\color{blue}{\text{th. de Gauss}
&\Longrightarrow\;\color{brown}{\dfrac{\partial E_z}{\partial z}=0}\end{align}`
$
\text{\\dans le vide}}}\\
\\
&\overrightarrow{E}\text{ uniforme}\\
&\text{dans tout plan }\perp\overrightarrow{e_z}\end{align}\right\}`
$
<br>
$
`\Longrightarrow\left\{
\begin{align}
&\dfrac{\partial E_x}{\partial x}+\dfrac{\partial E_y}{\partial y}
+\dfrac{\partial E_x}{\partial x}=0\\
\\
&\dfrac{\partial E_x}{\partial x}=\dfrac{\partial E_y}{\partial y}=0
\end{align}\right\}`
$
$
`\Longrightarrow\;\dfrac{\partial E_z}{\partial z}=0`
$
<br>
<br>
*
Le théorème de
*Maxwell-Faraday*
implique :
*
Le théorème de
*Maxwell-Faraday*
implique :
<br>
<br>
...
@@ -156,20 +169,6 @@ puis d'une onde plane progressive monochromatique (OPPM).
...
@@ -156,20 +169,6 @@ puis d'une onde plane progressive monochromatique (OPPM).
&\Longrightarrow\;\dfrac{\partial E}{\partial z}=0\end{align}`
$
&\Longrightarrow\;\dfrac{\partial E}{\partial z}=0\end{align}`
$
<br>
<br>
$
`\left.
\begin{align} &\underbrace{div(\overrightarrow{E}=\dfrac{\dens}{\epsilon_0}=0}_{\color{blue}{\text{th. de Gauss}
\text{\\dans le vide}}}\\
\\
&\overrightarrow{E}\text{ uniforme}\\
&\text{dans tout plan }\perp\overrightarrow{e_z}\end{align}\right\}`
$
$
`\Longrightarrow\left\{
\begin{align}
&\dfrac{\partial E_x}{\partial x}+\dfrac{\partial E_y}{\partial y}
+\dfrac{\partial E_x}{\partial x}=0\\
\\
&\dfrac{\partial E_x}{\partial x}=\dfrac{\partial E_y}{\partial y}=0
\end{align}\right\}`
$
$
`\Longrightarrow\;\dfrac{\partial E_z}{\partial z}=0`
$
schéma de démonstration à faire, puis modifier :
schéma de démonstration à faire, puis modifier :
...
...
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