Electric Flux and Gauss law

Electric Flux

dφ=E.da
da is the area vector to the surface and it is taken +ve along the outward normal to the surface
dφ=Edacosθ

φ=∫ E.da

For closed surface
φ=∫ E.da

Guass Theorem

Flux in closed surface is equal net charge inside divided by ε

E.da=qin

Some points:
a. E is the electric field present due to all charges in the ssystem not just the charge inside

b.Flux crossing a closed surface does not depend on the shapes and size of gaussian surface

Electric Potential energy of a charge
=qV where V is the potential there

Others important things
1. ∫ E.dl over closed path is zero
2.Electric potential in the spherical charge conductor is Q/4πεR where R is the radius of the shell and the potential is same everywhere in the conductor
3 Conductor surface is a equipotential surface