Commit a0e1f4d5 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent 91ba0010
Pipeline #17029 failed with stage
......@@ -298,21 +298,25 @@ leur valeur nulle ne varie pas d'un point à un autre point voisin par translati
Donc *les dérivées partiellles de $`\mathbf{B_{\rho}\text{ et }B_{\varphi}}`$ par
rapport à $`\mathbf{\rho\,,\,\varphi\text{ et }z}`$ sont nulles* :
<br>
$`\mathbf{\forall M \in \mathscr{E}\; , \; B_{\rho}=B_z=0}`$
$`\mathbf{\forall M \in \mathscr{E}\; , \; B_{\rho}=B_{\varphi}=0}`$
**$` \Longrightarrow\left\{
\begin{array}{l}
\boldsymbol{\mathbf{\dfrac{\partial B_{\rho}}{\partial\rho}=\dfrac{\partial B_{\rho}}{\partial\varphi}=\dfrac{\partial B_{\rho}}{\partial z}=0}} \\
\boldsymbol{\mathbf{\dfrac{\partial B_{\varphi}}{\partial\rho}=\dfrac{\partial B_{\varphi}}{\partial\varphi}=\dfrac{\partial B_{\varphi}}{\partial z}=0}} \\
\end{array}
\right.`$**
Suite en construction
<!----------------------
* $`\Longrightarrow`$ l'expression du *rotationnel de $`\overrightarrow{B}`$ se simplifie* en tout point de l'espace :
<br>
$`\require{\cancel}\begin{align}
\color{brown}{\mathbf{\overrightarrow{rot}\,\overrightarrow{B}}}
&\;=\left(\xcancel{\dfrac{1}{\rho}\,\dfrac{\partial B_z}{\partial\varphi}}\;-\;\xcancel{\dfrac{\partial B_{\varphi}}{\partial z}}\right)\,\overrightarrow{e_{\rho}}\\
&\;=\left(\dfrac{1}{\rho}\,\dfrac{\partial B_z}{\partial\varphi}\;-\;\xcancel{\dfrac{\partial B_{\varphi}}{\partial z}}\right)\,\overrightarrow{e_{\rho}}\\
\\
&\quad\; +\left(\xcancel{\dfrac{\partial B_{\rho}}{\partial z}}\;-\;\xcancel{\dfrac{\partial B_z}{\partial \rho}}\right)\,\overrightarrow{e_{\varphi}}\\
&\quad\; +\left(\xcancel{\dfrac{\partial B_{\rho}}{\partial z}}\;-\;\dfrac{\partial B_z}{\partial \rho}\right)\,\overrightarrow{e_{\varphi}}\\
\\
&\quad\; +
\,\dfrac{1}{\rho}\,\left(\dfrac{\partial (\,\rho\,B_{\varphi})}{\partial \rho}\;-\;\xcancel{\dfrac{\partial B_{\rho}}{\partial \varphi}}\right)
......@@ -387,4 +391,6 @@ $`\quad\Longrightarrow`$ **$`\displaystyle\boldsymbol{\mathbf{\rho_M\,B_{\varphi
À faire
--------------->
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