Gauss Law

Electric Flux

Electric Flux refers to the amount of electric field passing through a given area.

${\Phi }_E=\vec{E}\cdot \vec{n}=|\vec{E}||\vec{n}|\cos (\theta )$

• $\vec{E}$ is the electric field
• $\vec{n}$ is the surface normal vector

units of flux is in $\frac{N}{C}{m}^2$

Electric Flux applies everywhere, whether it is an open or a closed surface. 

For non-uniform fields, we must divide the surface into small pieces $dS$.

If we are interested in finding the flux through a closed surface with an enclosed net charge, ${\Phi }_E={\oint }_{surface}\vec{E}\cdot d\vec{S}$

This is super important to understand for solving Electric Flux Problems

We have 3 scenarios

1. Electric Flux
   1. No need for anything, open surface works, standalone concept
2. Gauss Law for charge → flux = Q/$ϵ$
   1. Closed surface
3. Gauss Law with electric field
   1. Closed surface
   2. Gaussian symmetry