Commit ba84be07 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent 50b29623
Pipeline #17886 canceled with stage
......@@ -156,19 +156,7 @@ $`\dfrac{\partial \dens}{dt}=\dfrac{\partial \,(\dens_{liée} + \dens_{libre})}{
$`\quad\quad\Longrightarrow \overrightarrow{dF_{mag}}= \dens_{libre} \cdot d\tau \cdot (\overrightarrow{v}_{dér\,/\,dC} \wedge \overrightarrow{B})`$.
* On nomme **force de Laplace** cette *force magnétique $`\overrightarrow{dF_B}`$ exercée sur chaque élément $`dC`$* du circuit :
<br>
$`\begin{align}\color{brown}{\mathbf{\overrightarrow{dF}_{Laplace}}}
&= \dens_{libre} \cdot \underbrace{d\tau}_{\color{blue}{\;\;=\\dS\,dl}}
\cdot (\overrightarrow{v}_{dér\,/\,dC} \wedge \overrightarrow{B})\\
\\
&= \underbrace{(\dens_{libre}\cdot \overrightarrow{v}_{dér\,/\,dC}}_{\color{blue}{=\,\overrightarrow{j}_{cond}}}
\cdot \underbrace{dS}_{\color{blue}{\vec{dS}\parallel\vec{v}}}
\cdot \underbrace{dl}_{\color{blue}{\vec{dl}\parallel\vec{v}}}) \wedge \overrightarrow{B}\\
\\
&= \underbrace{\overrightarrow{j}_{cond}\cdot\overrightarrow{dS}}_{\color{blue}{=\,I}}\;\overrightarrow{dl}\wedge\overrightarrow{B}\\
\\
&\mathbf{\color{brown}{=I\,\overrightarrow{dl}\wedge\overrightarrow{B}}}
\end{align}`$
<br>
$`\begin{align}\color{brown}{\mathbf{\large{\overrightarrow{dF}_{Laplace}}}}
&= \dens_{libre} \cdot \underbrace{d\tau}_{\color{blue}{\;\;=\\dS\,dl}}
......@@ -183,11 +171,6 @@ $`\begin{align}\color{brown}{\mathbf{\large{\overrightarrow{dF}_{Laplace}}}}
&\mathbf{\color{brown}{\large{=I\,\overrightarrow{dl}\wedge\overrightarrow{B}}}}
\end{align}`$
<br>
**$`\mathbf{\large{\overrightarrow{dF}_{Laplace}=I\,\overrightarrow{dl}\wedge\overrightarrow{B}}}`$**
<br>
-----------
......
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