Commit 1636abb8 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent ca796f44
Pipeline #17879 canceled with stage
......@@ -158,23 +158,28 @@ $`\quad\quad\Longrightarrow \overrightarrow{dF_{mag}}= \dens_{libre} \cdot d\tau
* On nomme **force de Laplace** cette *force magnétique $`\overrightarrow{dF_B}`$ exercée sur chaque élément $`dC`$* du circuit :
<br>
**$`\mathbf{\overrightarrow{dF}_{Laplace}}`$** *$`\begin{align}\;
&= \dens_{libre} \cdot \underbrace{d\tau}_{\color{blue}{\;\;=\\dS\,dl}} \cdot (\overrightarrow{v}_{dér\,/\,dC} \wedge \overrightarrow{B})\\
**$`\mathbf{\overrightarrow{dF}_{Laplace}}`$**
$`\begin{align}\;
&= \dens_{libre} \cdot \underbrace{d\tau}_{\color{blue}{\;\;=\\dS\,dl}}
\cdot (\overrightarrow{v}_{dér\,/\,dC} \wedge \overrightarrow{B})\\
\\
&=\underbrace{(\dens_{libre}\cdot \overrightarrow{v}_{dér\,/\,dC}}_{\color{blue}{=\,\overrightarrow{j}_{cond}}}
\cdot \underbrace{dS}_{\color{blue}{\vec{dS}\parallel\vec{v}}}\cdot \underbrace{dl}_{\color{blue}{\vec{dl}\parallel\vec{v}}}) \wedge \overrightarrow{B}\\
&= \underbrace{(\dens_{libre}\cdot \overrightarrow{v}_{dér\,/\,dC}}_{\color{blue}{=\,\overrightarrow{j}_{cond}}}
\cdot \underbrace{dS}_{\color{blue}{\vec{dS}\parallel\vec{v}}}
\cdot \underbrace{dl}_{\color{blue}{\vec{dl}\parallel\vec{v}}}) \wedge \overrightarrow{B}\\
\\
&= \underbrace{\overrightarrow{j}_{cond}}\cdot\overrightarrow{dS}}_{\color{blue}{=\,I}}\;\overrightarrow{dl}\wedge\overrightarrow{B}
&= \underbrace{\overrightarrow{j}_{cond}\cdot\overrightarrow{dS}}_{\color{blue}{=\,I}}\;\overrightarrow{dl}\wedge\overrightarrow{B}
\end{align}`$
**$`\mathbf{\overrightarrow{dF}_{Laplace}}`$** *$`\begin{align}\;
&= \dens_{libre} \cdot \underbrace{d\tau}_{\color{blue}{\;\;=\\dS\,dl}} \cdot (\overrightarrow{v}_{dér\,/\,dC} \wedge \overrightarrow{B})\\
**$`\mathbf{\overrightarrow{dF}_{Laplace}}`$** $`
\begin{align}\;
&= \dens_{libre} \cdot \underbrace{d\tau}_{\color{blue}{\;\;=\\dS\,dl}}
\cdot (\overrightarrow{v}_{dér\,/\,dC} \wedge \overrightarrow{B})\\
\\
&=\underbrace{(\dens_{libre}\cdot \overrightarrow{v}_{dér\,/\,dC}}_{\color{blue}{=\,\overrightarrow{j}_{cond}}}
&= \underbrace{(\dens_{libre}\cdot \overrightarrow{v}_{dér\,/\,dC}}_{\color{blue}{=\,\overrightarrow{j}_{cond}}}
\cdot \underbrace{dS}_{\color{blue}{\vec{dS}\parallel\vec{v}}}\cdot \underbrace{dl}_{\color{blue}{\vec{dl}\parallel\vec{v}}}) \wedge \overrightarrow{B}
\end{align}`$
**$`\mathbf{\overrightarrow{dF}_{Laplace}}`$** *$`\begin{align}\;
**$`\mathbf{\overrightarrow{dF}_{Laplace}}`$** $`\begin{align}\;
&= \dens_{libre} \cdot \underbrace{d\tau}_{\color{blue}{\;\;=\\dS\,dl}} \cdot (\overrightarrow{v}_{dér\,/\,dC} \wedge \overrightarrow{B})
\end{align}`$
......
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