Commit af6f98d4 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent 07512b13
Pipeline #17000 canceled with stage
......@@ -279,7 +279,7 @@ leur valeur nulle ne varie pas d'un point à un autre point voisin par translati
Donc *les dérivées partiellles de $`\mathbf{B_{\rho}\text{ et }B_z}`$ par
rapport à $`\mathbf{\rho\,,\,\varphi\text{ et }z}`$ sont nulles* :
<br>
$`\mathbf{\forall M \in \mathscr{B}\, , B_{\rho}=B_z=0}`$
$`\mathbf{\forall M \in \mathscr{E}\; , \; B_{\rho}=B_z=0}`$
**$` \Longrightarrow\left\{
\begin{array}{l}
\boldsymbol{\mathbf{\dfrac{\partial B_{\rho}}{\partial\rho}=\dfrac{\partial B_{\rho}}{\partial\varphi}=\dfrac{\partial B_{\rho}}{\partial z}=0}} \\
......@@ -289,12 +289,12 @@ $`\mathbf{\forall M \in \mathscr{B}\, , B_{\rho}=B_z=0}`$
* $`\Longrightarrow`$ l'expression du *rotarionnel de $`\overrightarrow{B}`$ se simplifie* en tout point de l'espace :
**$`\mathbf{\overrightarrow{rot}\,\overrightarrow{B}}`$**
\begin{align}
&\boldsymbol{\mathbf{\;&=\left(\dfrac{1}{\rho}\,\dfrac{\partial B_z}{\partial\varphi}\;-\;\dfrac{\partial B_{\varphi}}{\partial z}\right)\,\overrightarrow{e_{\rho}}}}\\
$`\begin{align}
&\boldsymbol{\mathbf{\;=\left(\dfrac{1}{\rho}\,\dfrac{\partial B_z}{\partial\varphi}\;-\;\dfrac{\partial B_{\varphi}}{\partial z}\right)\,\overrightarrow{e_{\rho}}}}\\
\\
&\boldsymbol{\mathbf{&\quad\; +\left(\dfrac{\partial B_{\rho}}{\partial z}\;-\;\dfrac{\partial B_z}{\partial \rho}\right)\,\overrightarrow{e_{\varphi}}}}\\
&\boldsymbol{\mathbf{\quad\; +\left(\dfrac{\partial B_{\rho}}{\partial z}\;-\;\dfrac{\partial B_z}{\partial \rho}\right)\,\overrightarrow{e_{\varphi}}}}\\
\\
&\boldsymbol{\mathbf{&\quad\; +
&\boldsymbol{\mathbf{\quad\; +
\,\dfrac{1}{\rho}\,\left(\dfrac{\partial (\,\rho\,B_{\varphi})}{\partial \rho}\;-\;\dfrac{\partial B_{\rho}}{\partial \varphi}\right)
\,\overrightarrow{e_z}}}
\end{align}`$**
......
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