Commit c41e45b7 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent ba732a5a
Pipeline #17002 canceled with stage
......@@ -288,15 +288,15 @@ $`\mathbf{\forall M \in \mathscr{E}\; , \; B_{\rho}=B_z=0}`$
\right.`$**
* $`\Longrightarrow`$ l'expression du *rotarionnel de $`\overrightarrow{B}`$ se simplifie* en tout point de l'espace :
**$`\mathbf{\overrightarrow{rot}\,\overrightarrow{B}}`$**
<br>
$`\require{\cancel}\begin{align}
\color{brown}{\mathbf{\overrightarrow{rot}\,\overrightarrow{B}}}
&\;=\left(\dfrac{1}{\rho}\,\dfrac{\partial B_z}{\partial\varphi}\;-\;\dfrac{\partial B_{\varphi}}{\partial z}\right)\,\overrightarrow{e_{\rho}}\\
&\;=\left(\xcancel{\dfrac{1}{\rho}\,\dfrac{\partial B_z}{\partial\varphi}}\;-\;\xcancel{\dfrac{\partial B_{\varphi}}{\partial z}}\right)\,\overrightarrow{e_{\rho}}\\
\\
&\quad\; +\left(\dfrac{\partial B_{\rho}}{\partial z}\;-\;\dfrac{\partial B_z}{\partial \rho}\right)\,\overrightarrow{e_{\varphi}}\\
&\quad\; +\left(\xcancel{\dfrac{\partial B_{\rho}}{\partial z}}\;-\;\xcancel{\dfrac{\partial B_z}{\partial \rho}}\right)\,\overrightarrow{e_{\varphi}}\\
\\
&\quad\; +
\,\dfrac{1}{\rho}\,\left(\dfrac{\partial (\,\rho\,B_{\varphi})}{\partial \rho}\;-\;\dfrac{\partial B_{\rho}}{\partial \varphi}\right)
\,\dfrac{1}{\rho}\,\left(\dfrac{\partial (\,\rho\,B_{\varphi})}{\partial \rho}\;-\;\xcancel{\dfrac{\partial B_{\rho}}{\partial \varphi}}\right)
\,\overrightarrow{e_z}
\end{align}`$**
......
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