Talk:QB/c19ElectricPotentialField SurfaceIntegral

$\Phi ={\vec {E}}\cdot {\vec {A}}$ $\to \int {\vec {E}}\cdot d{\vec {A}}=\int {\vec {E}}\cdot {\hat {n}}\,dA$ = electric flux

$q_{enclosed}=\varepsilon _{0}\oint {\vec {E}}\cdot d{\vec {A}}$

$d\,{\text{Vol}}=dxdydz=r^{2}drdA$ where $dA=r^{2}d\phi d\theta$

$A_{\text{sphere}}=r^{2}\int _{0}^{\pi }\sin \theta d\theta \int _{0}^{2\pi }d\phi =4\pi r^{2}$

Calculating $\int fdA$ and $\int fdV$ with angular symmetry
Cyndrical: $dA=2\pi r\,dz;\,dV=dA\,dr$.  Spherical: $\int dA=4\pi r^{2},\;dV=4\pi r^{2}\,dr$

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