Update cheatsheet.fr.md

12.temporary_ins/90.electromagnetism-in-vacuum/30.maxwell-electromagnetism-potentials/cheatsheet.fr.md

@@ -112,17 +112,17 @@ RÉSUMÉ
 
 --------------->
 
-* $`div\,\overrightarrow{B} = 0\quad`$ (Maxwell-Thomson)   
+* *$`div\,\overrightarrow{B} = 0\quad`$ (Maxwell-Thomson)*   
 <br>
 $`\color{blue}{\scriptsize{\left.\begin{align} &\forall \overrightarrow{V}\,,\, 
   div \,(\overrightarrow{rot}\,\overrightarrow{V})=0\\
   &div\,\overrightarrow{U}=0\end{align}\right\}\Longrightarrow
   \exists\overrightarrow{V}\,,\, \overrightarrow{U}=\overrightarrow{rot}\,\overrightarrow{V}}}`$   
 <br>
-$`\exists\overrightarrow{A}\,,\, \overrightarrow{B}=\overrightarrow{rot}\,\overrightarrow{A}`$
+$`\exists\overrightarrow{A}\,,\, \large{\color{brown}{\overrightarrow{B}=\overrightarrow{rot}\,\overrightarrow{A}}}`$
 
 
-* $`\overrightarrow{rot}\,\overrightarrow{E}=-\dfrac{\partial \overrightarrow{B}}{\partial t}\quad`$(Maxwell-Faraday)   
+* *$`\overrightarrow{rot}\,\overrightarrow{E}=-\dfrac{\partial \overrightarrow{B}}{\partial t}\quad`$(Maxwell-Faraday)*   
 <br>
 $`\quad\quad\;=-\dfrac{\partial \big(\overrightarrow{rot}\,\overrightarrow{A}\big)}{\partial t}`$   
 <br>
@@ -142,21 +142,12 @@ $`\color{blue}{\scriptsize{\left.\begin{align} &\forall \phi\,,\,
 <br>
 $`\exists V\,,\, \overrightarrow{E}+\dfrac{\partial \overrightarrow{A}}{\partial t}=-\,\overrightarrow{grad}\,V`$   
 <br>
+$`\color{blue}{\scriptsize{\text{soit :}}}`$ 
+<br>
 **$`\large{\mathbf{\overrightarrow{E}=-\,\overrightarrow{grad}\,V-\dfrac{\partial \overrightarrow{A}}{\partial t}}}`$**
 
 
-$`\Longrightarrow \overrightarrow{rot}\,\left(\overrightarrow{E}+\dfrac{\partial \overrightarrow{A}
-}{\partial t}\right)=\overrightarrow{0}`$
-
-$`\quad = A\cdot 
-\;\underbrace{cos \Big[\,\Big(\omega t - \vec{k}\cdot\vec{r}  + \varphi'\Big) - \dfrac{\pi}{2}}_{\color{blue}{cos(a-\pi/2)\\\;=cos(a)\,cos(\pi/2)+sin(a)\,sin(\pi/2)\\=\;sin(a)}}\Big]`$
 
- $`\color{blue}{\scriptsize{\left.\begin{align} \quad\quad &cos(a+b)=cos(a)cos(b)-sin(a)sin(b)\\
-                     &cos(a-b)=cos(a)cos(b)+sin(a)sin(b)\end{align}
-               \right\}\Longrightarrow\\
-        \quad\quad cos^2(a)=cos(a)cos(a)=\dfrac{1}{2}[cos(a+a)+cos(a-a)]\\
-        \quad\quad\quad\quad=\dfrac{1}{2}[1 + cos(2a)]}}`$   
-        
 <!-------------
 
 $`\color{blue}{\scriptsize{\quad\quad