Update cheatsheet.fr.md

12.temporary_ins/90.electromagnetism-in-vacuum/10.maxwell-equations/20.overview/cheatsheet.fr.md

@@ -676,9 +676,7 @@ $`\mathbf{div\,\big(\overrightarrow{U}\land\overrightarrow{V}\big)=
   \text{Identifie les termes } \overrightarrow{rot}\,\overrightarrow{E} \text{ et } \overrightarrow{rot}\,\overrightarrow{B}}}`$ 
   $`\color{blue}{\scriptsize{\text{ à leurs causes avec respectivement}}}`$   
   $`\color{blue}{\scriptsize{\text{les équations de Maxwell-Faraday et Maxwell Ampère}}}`$   
-  <br><br>
-  @@@@@@@@@@@@@
-  <br><br>
+  <br>
   $`div\,\big(\overrightarrow{E}\land\overrightarrow{B}\big)
   =\overrightarrow{B}\cdot
   \big(
@@ -691,19 +689,21 @@ $`\mathbf{div\,\big(\overrightarrow{U}\land\overrightarrow{V}\big)=
   <br><br>
   $`
   div\,\big(\overrightarrow{E}\land\overrightarrow{B}\big)
-  =\mu_0\,\vec{j}\cdot\overrightarrow{E}\,+\,\mu_0\,\epsilon_0\dfrac{\partial \vec{E}}{\partial t}\cdot\overrightarrow{E}
+  =-\,\mu_0\,\vec{j}\cdot\overrightarrow{E}\,-\,\mu_0\,\epsilon_0\dfrac{\partial \vec{E}}{\partial t}\cdot\overrightarrow{E}
   \,
-  +\,\overrightarrow{B}\cdot \dfrac{\partial \vec{B}}{\partial t}\big)
+  -\,\overrightarrow{B}\cdot \dfrac{\partial \vec{B}}{\partial t}\big)
   `$   
-  <br><br><br>
+  <br><br>
+  @@@@@@@@@@@@@
+  <br><br>
   $`\color{blue}{\scriptsize{
   \text{Souviens-toi que } \vec{u}\dfrac{\partial \vec{u}}{\partial t}=\dfrac{1}{2}\,\dfrac{\partial (\vec{u}\cdot\vec{u})}{\partial t}=\dfrac{1}{2}\,\dfrac{\partial u^2}{\partial t}}}`$   
   <br>
   $`
   div\,\big(\overrightarrow{E}\land\overrightarrow{B}\big)
-  =\mu_0\,\vec{j}\cdot\overrightarrow{E}\,+\,\dfrac{\mu_0\,\epsilon_0}{2}\,\dfrac{\partial E^2}{\partial t}
+  =-\,\mu_0\,\vec{j}\cdot\overrightarrow{E}\,-\,\dfrac{\mu_0\,\epsilon_0}{2}\,\dfrac{\partial E^2}{\partial t}
   \,
-  +\,\dfrac{1}{2}\,\dfrac{\partial B^2}{\partial t}
+  -\,\dfrac{1}{2}\,\dfrac{\partial B^2}{\partial t}
   `$   
   <br>
     $`\color{blue}{\scriptsize{\text{La reconnaissance du terme d'effet Joule }\vec{j}\cdot\vec{E}=\dfrac{d\mathcal{P}_{cédée}}{d\tau}}}`$   
@@ -712,23 +712,23 @@ $`\mathbf{div\,\big(\overrightarrow{U}\land\overrightarrow{V}\big)=
   <br>
   $`
   div\,\left(\dfrac{\overrightarrow{E}\land\overrightarrow{B}}{\mu_0}\right) 
-  = \underbrace{
+  = -\,\underbrace{
   \vec{j}\cdot\overrightarrow{E}
   }_{
   \color{blue}{=\frac{d\mathcal{P}_{cédée}}{d\tau}}
   }
-  \,+\,\dfrac{\epsilon_0}{2}\,\dfrac{\partial E^2}{\partial t}
+  \,-\,\dfrac{\epsilon_0}{2}\,\dfrac{\partial E^2}{\partial t}
   \,
-  +\,\dfrac{1}{2\,\mu_0}\,\dfrac{\partial B^2}{\partial t}
+  -\,\dfrac{1}{2\,\mu_0}\,\dfrac{\partial B^2}{\partial t}
   `$   
   <br>
     $`\color{blue}{\scriptsize{\text{que tu peux réécrire :}}}`$   
   <br>
   **$`\mathbf{
   div\,\left(\dfrac{\overrightarrow{E}\land\overrightarrow{B}}{\mu_0}\right)
-  = \vec{j}\cdot\overrightarrow{E}
-  \,+\,\dfrac{\partial}{\partial t}\,\left(
-  \dfrac{\epsilon_0\,E^2}{2}\,+\,\dfrac{B^2}{2\,\mu_0}
+  = -\,\vec{j}\cdot\overrightarrow{E}
+  \,-\,\dfrac{\partial}{\partial t}\,\left(
+  \dfrac{\epsilon_0\,E^2}{2}\,-\,\dfrac{B^2}{2\,\mu_0}
   \right)
   }`$**