Application of Gauss Law : Metallic charged sphere

                Gauss Law states that “Total electric field in a body is equal to the total electric charge enclosed in a body by electric permittivity in vacuum.”

Mathematically,              

Ø = Electric field

q = total charge enclosed

E₀ = Electric permittivity in vacuum

Now,

                By Gauss Law, finding the electric field enclosed in a body. A sphere with radius r and having charge q. Let us create a Gaussian surface and the radius of created surface is r. The charge enclosed in a body is +q.

Then,

Total Electric field passing through the Gaussian surface is

Ø = E x A = E x 4πv²

Again,

By Gauss Law,

Ø = q/ E₀

or,  E x A = q/ E₀

or, E x 4πv² = q/ E₀

or, E = q/4πr² E₀