Commit ae859294 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent f2739b12
Pipeline #16258 canceled with stage
...@@ -247,7 +247,7 @@ $`\Longrightarrow\quad\overrightarrow{dl} \cdot \overrightarrow{B}=0`$ ...@@ -247,7 +247,7 @@ $`\Longrightarrow\quad\overrightarrow{dl} \cdot \overrightarrow{B}=0`$
**$`\mathbf{\oint_{\Gamma_A}\overrightarrow{B}\cdot\overrightarrow{dl}}`$** **$`\mathbf{\oint_{\Gamma_A}\overrightarrow{B}\cdot\overrightarrow{dl}}`$**
<br> <br>
$`\displaystyle\quad\quad=\int_{DA} \overrightarrow{B}(\rho_{DA})\cdot\overrightarrow{dl}_{DA} + \int_{AB} \underbrace{\overrightarrow{B}\cdot\overrightarrow{dl}_{AB}}_{\color{blue}{\quad\;=\,0\\car\,\vec{B}\,\perp\,\vec{dl}_{AB}}}`$ $`\displaystyle\quad\quad=\int_{DA} \overrightarrow{B}(\rho_{DA})\cdot\overrightarrow{dl}_{DA} + \int_{AB} \underbrace{\overrightarrow{B}\cdot\overrightarrow{dl}_{AB}}_{\color{blue}{\quad\;=\,0\\car\,\vec{B}\,\perp\,\vec{dl}_{AB}}}`$
$`\displaystyle\quad\quad\quad +\int_{BC} \underbrace{\overrightarrow{B}(\rho_{BC})}_{\color{blue}{=\,0}}\cdot\overrightarrow{dl}_{BC} + \int_{CD}\underbrace{\overrightarrow{B}\cdot\overrightarrow{dl}_{CD}}_{\color{blue}{\quad\;=\,0\\car\,\vec{B}\,\perp\,\vec{dl}_{CD}}}`$ $`\displaystyle\quad\quad\quad +\int_{BC} \underbrace{\overrightarrow{B}(\rho_{BC})}_{\color{blue}{=\,\vec{0}}}\cdot\overrightarrow{dl}_{BC} + \int_{CD}\underbrace{\overrightarrow{B}\cdot\overrightarrow{dl}_{CD}}_{\color{blue}{\quad\;=\,0\\car\,\vec{B}\,\perp\,\vec{dl}_{CD}}}`$
<br> <br>
$`\quad\quad\color{blue}{\scriptsize{\quad\text{En se rappellant que :}}}`$ $`\quad\quad\color{blue}{\scriptsize{\quad\text{En se rappellant que :}}}`$
$`\quad\quad\color{blue}{\scriptsize{\quad\text{invariances + symétries }\Longrightarrow \vec{B}=B_z(\rho)\,\vec{e_z}}}`$ $`\quad\quad\color{blue}{\scriptsize{\quad\text{invariances + symétries }\Longrightarrow \vec{B}=B_z(\rho)\,\vec{e_z}}}`$
...@@ -273,7 +273,7 @@ $`\Longrightarrow\quad\overrightarrow{dl} \cdot \overrightarrow{B}=0`$ ...@@ -273,7 +273,7 @@ $`\Longrightarrow\quad\overrightarrow{dl} \cdot \overrightarrow{B}=0`$
*$`\mathbf{\oint_{\Gamma_A}\overrightarrow{B}\cdot\overrightarrow{dl}}`$* *$`\mathbf{\oint_{\Gamma_A}\overrightarrow{B}\cdot\overrightarrow{dl}}`$*
<br> <br>
$`\displaystyle\quad\quad=\int_{DA} \overrightarrow{B}(\rho_{DA})\cdot\overrightarrow{dl}_{DA} + \int_{AB} \underbrace{\overrightarrow{B}\cdot\overrightarrow{dl}_{AB}}_{\color{blue}{\quad\;=\,0}}`$ $`\displaystyle\quad\quad=\int_{DA} \overrightarrow{B}(\rho_{DA})\cdot\overrightarrow{dl}_{DA} + \int_{AB} \underbrace{\overrightarrow{B}\cdot\overrightarrow{dl}_{AB}}_{\color{blue}{\quad\;=\,0}}`$
$`\displaystyle \quad\quad\quad +\int_{BC} \underbrace{\overrightarrow{B}(\rho_{BC})}_{\color{blue}{=\,0}}\cdot\overrightarrow{dl}_{BC} + \int_{CD}\underbrace{\overrightarrow{B}\cdot\overrightarrow{dl}_{CD}}_{\color{blue}{\quad\;=\,0}}`$ $`\displaystyle \quad\quad\quad +\int_{BC} \underbrace{\overrightarrow{B}(\rho_{BC})}_{\color{blue}{=\,\vec{0}}}\cdot\overrightarrow{dl}_{BC} + \int_{CD}\underbrace{\overrightarrow{B}\cdot\overrightarrow{dl}_{CD}}_{\color{blue}{\quad\;=\,0}}`$
<br> <br>
$`\displaystyle\quad\quad = \int_{DA}\big(B_z(\rho_{DA})\overrightarrow{e_z}\big)\cdot\big(-\,dz\,\overrightarrow{e_z}\big)`$ $`\displaystyle\quad\quad = \int_{DA}\big(B_z(\rho_{DA})\overrightarrow{e_z}\big)\cdot\big(-\,dz\,\overrightarrow{e_z}\big)`$
<br> <br>
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