Commit 58bc63b0 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent 5b84e3d0
Pipeline #18241 canceled with stage
...@@ -787,16 +787,16 @@ figure à faire ...@@ -787,16 +787,16 @@ figure à faire
$`\displaystyle\hspace{1cm}=\dfrac{\dens^{2D}\,z}{2\epsilon_0} $`\displaystyle\hspace{1cm}=\dfrac{\dens^{2D}\,z}{2\epsilon_0}
\int_{\rho = 0}^R - \Big(\underbrace{-\dfrac{1}{2}}_{\color{blue}{n+1}}\Big)\cdot\underbrace{2\rho}_{\color{blue}{u^{\,'}}}\,\underbrace{(\rho^2+z^2)^{-\,3/2}}_{\color{blue}{u^n}}\,d\rho`$ \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>
$`\displaystyle \hspace{1cm} = - \dfrac{\dens^{2D}\,z}{2\epsilon_0} \big[\underbrace{(\rho^2+z^2)^{-\,1/2}}_{\color{blue}{u^{n+1}}\big]_0^R`$ $`\displaystyle \hspace{1cm} = - \dfrac{\dens^{2D}\,z}{2\epsilon_0} \big[\underbrace{(\rho^2+z^2)^{-\,1/2}}_{\color{blue}{u^{n+1}}}\big]_0^R`$
<br> <br>
$`\color{blue}{\scriptsize{\text{Le signe moins devient plus}}}`$ $`\color{blue}{\scriptsize{\text{Le signe moins devient plus}}}`$
$`\color{blue}{\scriptsize{\text{en inversant les bornes d'intégration}}}`$ $`\color{blue}{\scriptsize{\text{en inversant les bornes d'intégration}}}`$
<br> <br>
$`\displaystyle \hspace{1cm} = +\dfrac{\dens^{2D}\,z}{2\epsilon_0} \big[(\rho^2+z^2)^{-\,1/2}\big]_R^0`$ $`\displaystyle \hspace{1cm} = +\dfrac{\dens^{2D}\,z}{2\epsilon_0} \big[(\rho^2+z^2)^{-\,1/2}\big]_R^0`$
<br> <br>
$`\displaystyle \hspace{1cm} = \dfrac{\dens^{2D}\,z}{2\epsilon_0} \left(\dfrac{1}{\sqrt{z^2}} - \dfrac{1}{\sqrt{\rho^2+z^2}}\right)`$ $`\displaystyle \hspace{1cm} = \dfrac{\dens^{2D}\,z}{2\epsilon_0} \left(\dfrac{1}{\sqrt{z^2}} - \dfrac{1}{\sqrt{R^2+z^2}}\right)`$
<br> <br>
$`\displaystyle \hspace{1cm} = \dfrac{\dens^{2D}\,z}{2\epsilon_0} \left(\dfrac{1}{|z|} - \dfrac{1}{\sqrt{\rho^2+z^2}}\right)`$ $`\displaystyle \hspace{1cm} = \dfrac{\dens^{2D}\,z}{2\epsilon_0} \left(\dfrac{1}{|z|} - \dfrac{1}{\sqrt{R^2+z^2}}\right)`$
<br> <br>
Ainsi le champ électrique s'exprime plus simplement : Ainsi le champ électrique s'exprime plus simplement :
<br> <br>
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