Update cheatsheet.fr.md

12.temporary_ins/10.electrostatics-vacuum/20.causes-stationary-electric-field/20.overview/cheatsheet.fr.md

@@ -594,7 +594,7 @@ $`\hspace{2.3cm}=\quad\dfrac{\dens^{1D}\cdot R\,d\varphi}{4\pi\epsilon_0}\cdot\d
 ! <br>
 ! $`dE_z = \dfrac{\dens^{2D}}{2\epsilon_0}\cdot\dfrac{\rho\,z}{(\rho^2+z^2)^{\,3/2}}\,d\rho`$ <br>
 ! <br>
-! $`\hspace{1cm} = \dfrac{\dens^{2D}\,z}{2\epsilon_0}\cdot \rho\,(\rho^2+z^2)^{-\,3/2}\,d\rho`$<br>
+! $`\hspace{0.5 cm} = \dfrac{\dens^{2D}\,z}{2\epsilon_0}\cdot \rho\,(\rho^2+z^2)^{-\,3/2}\,d\rho`$<br>
 ! <br>
 ! Calculons $`E_z`$ :<br>
 ! <br>
@@ -607,16 +607,16 @@ $`\hspace{2.3cm}=\quad\dfrac{\dens^{1D}\cdot R\,d\varphi}{4\pi\epsilon_0}\cdot\d
 ! $`\displaystyle\hspace{1cm}=\dfrac{\dens^{2D}\,z}{2\epsilon_0}  
 ! \int_{\rho = 0}^R - \Big(\underbrace{-\dfrac{1}{2}}_{\color{blue}{n+1}}\Big)\cdot\underbrace{2\rho}_{\color{blue}{u^{\,'}}}\,\underbrace{(\rho^2+z^2)^{-\,3/2}}_{\color{blue}{u^n}}\,d\rho`$<br>
 ! <br>
-! $`\displaystyle \hspace{1cm} =  - \dfrac{\dens^{2D}\,z}{2\epsilon_0} \big[\underbrace{(\rho^2+z^2)^{-\,1/2}}_{\color{blue}{u^{n+1}}}\big]_0^R`$<br>
+! $`\displaystyle \hspace{0.5 cm} =  - \dfrac{\dens^{2D}\,z}{2\epsilon_0} \big[\underbrace{(\rho^2+z^2)^{-\,1/2}}_{\color{blue}{u^{n+1}}}\big]_0^R`$<br>
 ! <br>
 ! $`\color{blue}{\scriptsize{\text{Le signe moins devient plus}}}`$<br>
 ! $`\color{blue}{\scriptsize{\text{en inversant les bornes d'intégration}}}`$<br>   
 ! <br>
-! $`\displaystyle \hspace{1cm} = +\dfrac{\dens^{2D}\,z}{2\epsilon_0} \big[(\rho^2+z^2)^{-\,1/2}\big]_R^0`$<br>
+! $`\displaystyle \hspace{0.5cm} = +\dfrac{\dens^{2D}\,z}{2\epsilon_0} \big[(\rho^2+z^2)^{-\,1/2}\big]_R^0`$<br>
 ! <br>
-! $`\displaystyle \hspace{1cm} =  \dfrac{\dens^{2D}\,z}{2\epsilon_0} \left(\dfrac{1}{\sqrt{z^2}} - \dfrac{1}{\sqrt{R^2+z^2}}\right)`$<br>   
+! $`\displaystyle \hspace{0.5 cm} =  \dfrac{\dens^{2D}\,z}{2\epsilon_0} \left(\dfrac{1}{\sqrt{z^2}} - \dfrac{1}{\sqrt{R^2+z^2}}\right)`$<br>   
 ! <br>
-! $`\displaystyle \hspace{1cm} =  \dfrac{\dens^{2D}\,z}{2\epsilon_0} \left(\dfrac{1}{|z|} - \dfrac{1}{\sqrt{R^2+z^2}}\right)`$<br>   
+! $`\displaystyle \hspace{0.5 cm} =  \dfrac{\dens^{2D}\,z}{2\epsilon_0} \left(\dfrac{1}{|z|} - \dfrac{1}{\sqrt{R^2+z^2}}\right)`$<br>   
 ! <br>
 ! Ainsi le champ électrique s'exprime plus simplement :<br>   
 ! <br>
@@ -625,26 +625,7 @@ $`\hspace{2.3cm}=\quad\dfrac{\dens^{1D}\cdot R\,d\varphi}{4\pi\epsilon_0}\cdot\d
 ! <br>
 ! Pour $`z>0`$ :<br>   
 ! $`\overrightarrow{E}(z) =  \dfrac{\dens^{2D}\,z}{2\epsilon_0} \left(- 1 - \dfrac{z}{\sqrt{\rho^2+z^2}}\right)\,\overrightarrow{e_z}`$<br>
-!
-!
-! $`\displaystyle E_z = \int_{\rho = 0}^R \dfrac{\dens^{2D}\,z}{2\epsilon_0}\cdot \rho\,(\rho^2+z^2)^{-\,3/2}\,d\rho`$<br>
-! <br>
-! $`\displaystyle \hspace{1cm} =  \dfrac{\dens^{2D}\,z}{2\epsilon_0} \int_{\rho = 0}^R\dfrac{1}{2}\times
-! \underbrace{2\rho}_{u^{\,'}}\,\underbrace{(\rho^2+z^2)^{-\,3/2}}_{u^n}\,d\rho`$<br>
-! <br>
-! $`\displaystyle \hspace{1cm} =  \dfrac{\dens^{2D}\,z}{2\epsilon_0} \big[\underbrace{\dfrac{1}{2}\times\dfrac{1}{-3/2+1}}
-! _{=\frac{1}{2}\,\times \,(-2) \,=\, -1}(\rho^2+z^2)^{-\,1/2}\big]_0^R`$<br>
-! <br>
-! $`\displaystyle \hspace{1cm} =  \dfrac{\dens^{2D}\,z}{2\epsilon_0} \left(\dfrac{1}{|z|} - \dfrac{1}{\sqrt{\rho^2+z^2}}\right)`$<br>
-! <br>
-! Ainsi le champ électrique s'exprime plus simplement :<br>
-! <br>
-! Pour $`z>0`$ :<br>
-! $`\overrightarrow{E}(z) =  \dfrac{\dens^{2D}\,z}{2\epsilon_0} \left(1 - \dfrac{z}{\sqrt{\rho^2+z^2}}\right)\,\overrightarrow{e_z}`$<br>
-! <br>
-! Pour $`z>0`$ :<br>
-! $`\overrightarrow{E}(z) =  \dfrac{\dens^{2D}\,z}{2\epsilon_0} \left(- 1 - \dfrac{z}{\sqrt{\rho^2+z^2}}\right)\,\overrightarrow{e_z}`$
-! </details>
+!! </details>