What is the relationship between electric flux and electric field? Electric flux is said to be electric field passing through a particular surface...

The electric field (`E` ) is defined as the electric force per unit charge. The electric flux (`Phi_E` )is defined as the electric field times the normal area vector. 

`Phi_E=E*A cos(theta)`

In Gausses law this quantity is proportional to the amount of charge enclosed by a surface.

`Phi_E=Q_(enc)/epsilon_0`

This is a very useful tool to figure out the electric field of an object when you know the charge, for instance if we have a spherical uniform charge distribution of radius `R` , then whats the electric field at `rgtR` ?

`Phi_E=Q_(enc)/epsilon_0`

`E*A=Q_(enc)/epsilon_0` Since E and A are parallel everywhere in space.

`E(4 pi r^2)=Q_(enc)/epsilon_0`

`E=Q/(4pi epsilon_0 r^2)`

The same as for a point charge at r=0.