Commit 745d38ba authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent 8c5ca763
Pipeline #18917 canceled with stage
...@@ -676,19 +676,19 @@ $`\mathbf{div\,\big(\overrightarrow{U}\land\overrightarrow{V}\big)= ...@@ -676,19 +676,19 @@ $`\mathbf{div\,\big(\overrightarrow{U}\land\overrightarrow{V}\big)=
\text{Identifie les termes } \overrightarrow{rot}\,\overrightarrow{E} \text{ et } \overrightarrow{rot}\,\overrightarrow{B}}}`$ \text{Identifie les termes } \overrightarrow{rot}\,\overrightarrow{E} \text{ et } \overrightarrow{rot}\,\overrightarrow{B}}}`$
$`\color{blue}{\scriptsize{\text{ à leurs causes avec respectivement}}}`$ $`\color{blue}{\scriptsize{\text{ à leurs causes avec respectivement}}}`$
$`\color{blue}{\scriptsize{\text{les équations de Maxwell-Faraday et Maxwell Ampère}}}`$ $`\color{blue}{\scriptsize{\text{les équations de Maxwell-Faraday et Maxwell Ampère}}}`$
<br> <br><br><br>
$`div\,\big(\overrightarrow{E}\land\overrightarrow{B}\big) $`div\,\big(\overrightarrow{E}\land\overrightarrow{B}\big)
=\,\overrightarrow{B}\cdot\big(\underbrace{\overrightarrow{rot}\,\overrightarrow{E}} =\overrightarrow{E}\cdot\big(\underbrace{\overrightarrow{rot}\,\overrightarrow{B}}_{\color{blue}{=\mu_0\,\vec{j}+\mu_0\epsilon_0\frac{\partial \vec{E}}{\partial t}}}\big)\,
_{\color{blue}{=-\frac{\partial \vec{B}}{\partial t}}\big)\, -\,\overrightarrow{B}\cdot\big(\underbrace{\overrightarrow{rot}\,\overrightarrow{E}}_{
- \color{blue}{=-\frac{\partial \vec{B}}{\partial t}}}\big)`$
\overrightarrow{E}\cdot\big(\underbrace{\overrightarrow{rot}\,\overrightarrow{B}} <br>
_{\color{blue}{=\mu_0\,\vec{j}+\mu_0\epsilon_0\frac{\partial \vec{E}}{\partial t}}\big)`$
<br> ok
$` $`
div\,\big(\overrightarrow{E}\land\overrightarrow{B}\big) div\,\big(\overrightarrow{E}\land\overrightarrow{B}\big)
=\,-\,\overrightarrow{B}\cdot \dfrac{\partial \vec{B}}{\partial t}\,-\, \mu_0\,\vec{j}\cdot\overrightarrow{E}\, =\mu_0\,\vec{j}\cdot\overrightarrow{E}\,+\,\mu_0\,\epsilon_0\dfrac{\partial \vec{E}}{\partial t}\cdot\overrightarrow{E}
-\,\mu_0\,\epsilon_0\dfrac{\partial \vec{E}}{\partial t}\cdot\overrightarrow{E}`$ \,
<br> +\,\overrightarrow{B}\cdot \dfrac{\partial \vec{B}}{\partial t}\big)
`$
<br><br><br>
$`\color{blue}{\scriptsize{ $`\color{blue}{\scriptsize{
\text{Souviens-toi que } \vec{u}\dfrac{\partial \vec{u}}{\partial t}=\dfrac{1}{2}\,\dfrac{\partial (\vec{u}\cdot\vec{u})}{\partial t}=\dfrac{1}{2}\,\dfrac{\partial u^2}{\partial t}}}`$ \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> <br>
......
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