Update cheatsheet.fr.md

12.temporary_ins/20.magnetostatics-vacuum/40.ampere-theorem-applications/30.cylindrical-current-distributions/10.rectilinear-current/10.ampere-integral/20.overview/cheatsheet.fr.md

@@ -199,19 +199,23 @@ Image à faire
 * Si **$`\mathbf{\overrightarrow{dl}=+\,\rho_M\,\overrightarrow{e_{\varphi}}}`$** :   
 <br>
 **$`\mathbf{\oint_{\Gamma_A}\overrightarrow{B}\cdot\overrightarrow{dl}}`$**   
-$`\quad=\oint_{\varphi=0}^{\varphi=2\pi}\big(B_{\varphi}(\rho_M)\,\overrightarrow{e_{\varphi}}\big)\cdot \big(+\rho_M\,d\varphi\,\overrightarrow{e_{\varphi}}\big)`$   
-$`\displaystyle\quad=\oint_{\varphi=0}^{\varphi=2\pi}\big(B_{\varphi}(\rho_M)\,\overrightarrow{e_{\varphi}}\big)\cdot \big(\rho_M\,d\varphi\,\overrightarrow{e_{\varphi}}\big)`$   
-$`\displaystyle\quad=\oint_{\varphi=0}^{\varphi=2\pi}B_{\varphi}(\rho_M)\,\rho_M\,\big(\overrightarrow{e_{\varphi}}\cdot \overrightarrow{e_{\varphi}}\big) d\varphi`$   
-$`\displaystyle\quad=\rho_M\,B_{\varphi}(\rho_M)\,\oint_{\varphi=0}^{\varphi=2\pi}d\varphi`$   
+$`\quad=\oint_{\varphi=0}^{\varphi=2\pi}\big(B_{\varphi}(\rho_M)\,\overrightarrow{e_{\varphi}}\big)\cdot \big(+\rho_M\,d\varphi\,\overrightarrow{e_{\varphi}}\big)`$    
+   
+$`\displaystyle\quad=\oint_{\varphi=0}^{\varphi=2\pi}B_{\varphi}(\rho_M)\,\rho_M\,\big(\overrightarrow{e_{\varphi}}\cdot \overrightarrow{e_{\varphi}}\big) d\varphi`$      
+   
+$`\displaystyle\quad=\rho_M\,B_{\varphi}(\rho_M)\,\oint_{\varphi=0}^{\varphi=2\pi}d\varphi`$    
+   
 **$`\mathbf{\displaystyle\quad= 2\pi\,\rho_M\, B_{\varphi}(\rho_M)}`$**
 
-* Si *$`\mathbf{\overrightarrow{dl}=-\,\rho_M\,\overrigharrow{e_{\varphi}}}`$* :   
+* Si *$`\mathbf{\overrightarrow{dl}=-\,\rho_M\,\overrightarrow{e_{\varphi}}}`$* :   
 <br>
 *$`\mathbf{\oint_{\Gamma_A}\overrightarrow{B}\cdot\overrightarrow{dl}}`$*
-$`\displaystyle\quad=\oint_{\varphi=0}^{\varphi=2\pi}\big(B_{\varphi}(\rho_M)\,\overrightarrow{e_{\varphi}}\big)\cdot \big(-\rho_M\,d\varphi\,\overrightarrow{e_{\varphi}}\big)   
-$`\displaystyle\quad=-\oint_{\varphi=0}^{\varphi=2\pi}\big(B_{\varphi}(\rho_M)\,\overrightarrow{e_{\varphi}}\big)\cdot \big(\rho_M\,d\varphi\,\overrightarrow{e_{\varphi}}\big)`$   
+$`\displaystyle\quad=\oint_{\varphi=0}^{\varphi=2\pi}\big(B_{\varphi}(\rho_M)\,\overrightarrow{e_{\varphi}}\big)\cdot \big(-\rho_M\,d\varphi\,\overrightarrow{e_{\varphi}}\big)`$      
+   
 $`\displaystyle\quad=-\oint_{\varphi=0}^{\varphi=2\pi}B_{\varphi}(\rho_M)\,\rho_M\,\big(\overrightarrow{e_{\varphi}}\cdot \overrightarrow{e_{\varphi}}\big) d\varphi`$   
+   
 $`\displaystyle\quad=-\rho_M\,B_{\varphi}(\rho_M)\,\oint_{\varphi=0}^{\varphi=2\pi}d\varphi`$   
+   
 *$`\mathbf{\displaystyle\quad= -\,2\pi\,\rho_M\, B_{\varphi}(\rho_M)}`$*