Commit 1c782564 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent fe1e80e8
Pipeline #16001 canceled with stage
......@@ -138,14 +138,13 @@ puis d'une onde plane progressive monochromatique (OPPM).
\dfrac{\partial B_x}{\partial x}=\dfrac{\partial B_y}{\partial x}=\dfrac{\partial B_z}{\partial x}
=\dfrac{\partial B_x}{\partial y}=\dfrac{\partial B_y}{\partial y}=\dfrac{\partial B_z}{\partial y}=0`$
<br>
* Pour le **champ électrique** $`\overrightarrow{E}`$ :
<br>
* Le théorème de *Maxwell-Gauss* implique dans le vide ($`\dens=0`$) :
* Le théorème de *Maxwell-Gauss* implique dans le vide ($`\dens=0`$) :
<br>
$`\left.
\begin{align} &\underbrace{div(\overrightarrow{E}=\dfrac{\dens}{\epsilon_0}=0}_{\color{blue}{\text{th. de Gauss}
\text{\\dans le vide}}}\\
\begin{align} &\underbrace{div\,\overrightarrow{E}=\dfrac{\dens}{\epsilon_0}=0}_{\color{blue}{\text{th. de Maxwell-Gauss}\\
\text{dans le vide}}}\\
\\
&\overrightarrow{E}\;uniforme\\
&dans\;tout\;plan\;\perp\overrightarrow{e_z}\end{align}\right\}`$
......@@ -157,12 +156,37 @@ puis d'une onde plane progressive monochromatique (OPPM).
\\
&\dfrac{\partial E_x}{\partial x}=\dfrac{\partial E_y}{\partial y}=0
\end{align}\right\}`$
$`\Longrightarrow\;\dfrac{\partial E_z}{\partial z}=0`$
*$`\Longrightarrow\;\dfrac{\partial E_z}{\partial z}=0`$*
<br>
* Le théorème de *Maxwell-Faraday* implique :
<br>
* Le théorème de *Maxwell-Faraday* implique dans le vide :
$`\left.
\begin{align} &\underbrace{\overrightarrow{rot}\,\overrightarrow{E}=-\dfrac{\partial \overrightarrow{B}}{\partial t}}_{\color{blue}{\text{th. de Maxwell-Faraday}}\\
\\
&\overrightarrow{E}\;uniforme\\
&dans\;tout\;plan\;\perp\overrightarrow{e_z}\end{align}\right\}`$
<br>
$`\Longrightarrow\left\{
\begin{align}
&\dfrac{\partial E_x}{\partial x}+\dfrac{\partial E_y}{\partial y}
+\dfrac{\partial E_z}{\partial z}=0\\
\\
&\dfrac{\partial E_x}{\partial x}=\dfrac{\partial E_y}{\partial y}=0
\end{align}\right\}`$
*$`\Longrightarrow\;\dfrac{\partial E_z}{\partial z}=0`$*
<br>
$`\begin{align} \color{blue}{\overrightarrow{rot}\,overrightarrow{E} &= -\dfrac{\partial \overrightarrow{B}}{\partial t}} \\
$`\begin{align} \color{blue}{\overrightarrow{rot}\,\overrightarrow{E} &= -\dfrac{\partial \overrightarrow{B}}{\partial t}} \\
\\
\quad\left(\begin{matrix}
&\Longrightarrow\;\dfrac{\partial E}{\partial x} + \dfrac{\partial E}{\partial y} + \dfrac{\partial E}{\partial y}=0 \\
......
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