Commit c9050df0 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent 883bfccb
Pipeline #16329 canceled with stage
......@@ -656,14 +656,26 @@ $`\mathbf{div\,\big(\overrightarrow{U}\land\overrightarrow{V}\big)=\overrightarr
$`\mathbf{div\,\big(\overrightarrow{E}\land\overrightarrow{B}\big)
=\overrightarrow{E}\cdot\big(\underbrace{\overrightarrow{rot}\,\overrightarrow{B}}_{\color{blue}{=\mu_0\,\vec{j}+\mu_0\epsilon_0\frac{\partial \vec{E}}{\partial t}}}\big)\,
-\,\overrightarrow{B}\cdot\big(\underbrace{\overrightarrow{rot}\,\overrightarrow{E}}_{
\color{brown}{=-\frac{\partial \vec{B}}{\partial t}}}\big)}`$
\color{blue}{=-\frac{\partial \vec{B}}{\partial t}}}\big)}`$
<br>
$`\mathbf{
div\,\big(\overrightarrow{E}\land\overrightarrow{B}\big)
=\mu_0\,\vec{j}\cdot\overrightarrow{E}\,+\,\mu_0\epsilon_0\frac{\partial \vec{E}}{\partial t}\cdot\overrightarrow{E}
=\mu_0\,\vec{j}\cdot\overrightarrow{E}\,+\,\mu_0\,\epsilon_0\dfrac{\partial \vec{E}}{\partial t}\cdot\overrightarrow{E}
\,
-\,\overrightarrow{B}\cdot -\frac{\partial \vec{B}}{\partial t}\big)
+\,\overrightarrow{B}\cdot \dfrac{\partial \vec{B}}{\partial t}\big)
}`$
<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>
$`\mathbf{
div\,\big(\overrightarrow{E}\land\overrightarrow{B}\big)
=\mu_0\,\vec{j}\cdot\overrightarrow{E}\,+\,\mu_0\,\epsilon_0\dfrac{\partial E^2}{\partial t}
\,
+\,\dfrac{\partial B^2}{\partial t}
}`$
<br>
<br>
* A partir des équations de Maxwell, on montre avec une combinaison d'opérateur adéquate (à faire) que cette
densité volumique $`\dens_{énergie-EM}^{3D}`$ *possède deux composantes* :
......
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