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M3P2
Courses
Commits
faf0a52b
Commit
faf0a52b
authored
May 14, 2024
by
Claude Meny
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Update cheatsheet.fr.md
parent
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cheatsheet.fr.md
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12.temporary_ins/10.electrostatics-vacuum/40.gauss-theorem-applications/25.cylindrical-charge-distributions/20.gauss-local/20.overview/cheatsheet.fr.md
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faf0a52b
...
@@ -424,7 +424,7 @@ le fait que $`\dfrac{d(\rho\,E_{\rho})}{d\rho}=0`$ implique que
...
@@ -424,7 +424,7 @@ le fait que $`\dfrac{d(\rho\,E_{\rho})}{d\rho}=0`$ implique que
<br>
<br>
donne :
donne :
<br>
<br>
**$`\boldsymbol{\mathbf{\rho\, E_{\rho}=\dfrac{Cste\,2}{\epsilon_0}}\quad`$**
(éq.2)}
**$`\boldsymbol{\mathbf{\rho\, E_{\rho}=\dfrac{Cste\,2}{\epsilon_0}}
}
\quad`$**
(éq.2)}
##### Détermination des constantes d'intégration
##### Détermination des constantes d'intégration
...
@@ -445,7 +445,7 @@ $`\left.\begin{align}
...
@@ -445,7 +445,7 @@ $`\left.\begin{align}
& \dfrac{\dens^{3D}_0\,\rho^2}{2\,\epsilon_0} + Cste\,1\\
& \dfrac{\dens^{3D}_0\,\rho^2}{2\,\epsilon_0} + Cste\,1\\
& \rho = 0
& \rho = 0
\end{align}
\end{align}
\right\}\Longrightarrow \mathbf{\color{blue}{Cste\,1=0}}`
$
\right\}\Longrightarrow \mathbf{\color{
Navy
blue}{Cste\,1=0}}`
$
*
Enfin, par
*continuité*
de $
`\overrightarrow{E}=E_r\,\overrightarrow{e_r}`
$ et donc
*
Enfin, par
*continuité*
de $
`\overrightarrow{E}=E_r\,\overrightarrow{e_r}`
$ et donc
continuité de $
`E_r`
$ dans tout l'espace, et donc en particulier
*à la frontière $`\rho=R`$*
,
continuité de $
`E_r`
$ dans tout l'espace, et donc en particulier
*à la frontière $`\rho=R`$*
,
...
@@ -457,7 +457,7 @@ $`\displaystyle\lim_{\rho\rightarrow R\\ \rho\lt R} E_{\rho}=`$
...
@@ -457,7 +457,7 @@ $`\displaystyle\lim_{\rho\rightarrow R\\ \rho\lt R} E_{\rho}=`$
$
`\,=\displaystyle\lim_{\rho\rightarrow R\\ \rho\gt R} E_{\rho}`
$
$
`\,=\displaystyle\lim_{\rho\rightarrow R\\ \rho\gt R} E_{\rho}`
$
*$`\,=\dfrac{Cste\,2}{\epsilon_0\,R}`$*
*$`\,=\dfrac{Cste\,2}{\epsilon_0\,R}`$*
<br>
<br>
$
`\Longrightarrow \boldsymbol{\mathbf{\color{blue}{Cste\,2=\dfrac{\dens^{3D}_0\,R^2}{2\,\epsilon_0}}}}`
$
$
`\Longrightarrow \boldsymbol{\mathbf{\color{
Navy
blue}{Cste\,2=\dfrac{\dens^{3D}_0\,R^2}{2\,\epsilon_0}}}}`
$
...
...
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