A charge q is placed at the centre of a sphere. Taking outward normal as positive, find the flux of the electric field through the surface of the sphere due to the enclosed charge.

Explanation

Let us take a small element `DeltaS` on the surface of the sphere (Figure 30.3(. The electric field here is radially outward and the magnitude.
`q/4piepsilon_0r^2`
where r is the rasius of the sphere. As the positive normal is also outward,`theta-0` and the flux though this part is
`DeltaPhi=vecEDeltavecS=q/4piepsilon_0r^2` DeltaS`.
Summing over the parts of the spherical surface,
`Phi=sumDeltaPhi=q/4Piepsilon_0r^2 sum DeltaS=q/4phir^1` 4phir^2=q/epsilon_0`.