Commit b04f9755 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent 1ea7f281
Pipeline #17033 canceled with stage
......@@ -328,20 +328,21 @@ $`\require{\cancel}\begin{align}
* L'étude des invariances de la distribution de courants implique en tout point de l'espace :
*$`\boldsymbol{\mathbf{\overrightarrow{B}=\overrightarrow{B}(\rho)}=B_{\varphi}(\rho)\,\overrightarrow{e_\varphi}}`$*
Cela s'applique à toutes les composantes de $`\overrightarrow{B}`$, donc en particulier à
*$`\boldsymbol{\mathbf{\overrightarrow{B}=\overrightarrow{B}(\rho)}}`$*
Cela s'applique à toutes les composantes de $`\overrightarrow{B}`$, donc en particulier à la
composante selon $`\varphi`$, ce qui implique :
$`\boldsymbol{\mathbf{B_{\varphi} =B_{\varphi}(\rho)}}`$
ce qui entraîne
**$`\boldsymbol{\mathbf{\dfrac{\partial B_{\varphi}}{\partial z} = 0}}`$**.
**$`\Longrightarrow\boldsymbol{\mathbf{\color{brown}{\dfrac{\partial B_{\varphi}}{\partial z} = 0}}}`$**.
<br>
Ainsi :
<br>
$`\require{\cancel}\begin{align}
\color{brown}{\mathbf{\overrightarrow{rot}\,\overrightarrow{B}}}
&\;=-\,\xcancel{\dfrac{\partial B_{\varphi}}{\partial z}}}\,\overrightarrow{e_{\rho}\,+\,
\dfrac{1}{\rho}\,\dfrac{\partial \,(\,\rho\,B_{\varphi})}{\partial \rho}\,\overrightarrow{e_z}}}\\
&\;=-\,\xcancel{\dfrac{\partial B_{\varphi}}{\partial z}}\,\overrightarrow{e_{\rho}}}\,+\,
\dfrac{1}{\rho}\,\dfrac{\partial \,(\,\rho\,B_{\varphi})}{\partial \rho}\,\overrightarrow{e_z}\\
\\
&\color{brown}{\boldsymbol{\mathbf{\;=+\,
\dfrac{1}{\rho}\,\dfrac{\partial \,(\,\rho\,B_{\varphi})}{\partial \rho}\,\overrightarrow{e_z}}}
\dfrac{1}{\rho}\,\dfrac{\partial \,(\,\rho\,B_{\varphi})}{\partial \rho}\,\overrightarrow{e_z}}}}
end{align}`$
* Dans l'espression $`\dfrac{\partial\left(\rho\,B_{\varphi}(\rho)\right)}{\partial\,\rho}`$, le terme **$`\rho\,B_{\varphi}(\rho)`$**
......
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