where $\phi$ is the angle between the electric field and the normal vector $\hat n$. $E\cos\phi$ is the perpendicular component of the electric field with respect to the surface.
- A surface has two sides, so there will be two possible signs of the flux: positive when the electric field has a component along the normal, and negative otherwise. The limit case when the electric field is parallel to the surface produces a zero flux.
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#General Expression
The way to generalize the previous expression to general electric fields and surfaces is to integrate the contribution of infinitesimal surfaces. Mathematically speaking, we are defining a surface integral.
$$ \Phi_{E}=\int_S \vec E \cdot d \vec A=\int_S E \cos \phi dA $$ $$ d \vec{A}=\hat{n} d A $$- flux is a scalar
- This expression gives an average value of the perpendicular component of the electric field (multiplied by a factor: the area of the surface).
- The SI unit is $Nm^2/C$
Electric Dipole