State and prove Gauss theorem in electrostatics.

State and prove Gauss theorem in electrostatics.

**Statement of Gauss"s Theorem :** The net-outward normal electric flux through any closed surface of any shape is equal to

1/ε0 times the total charge contained within that surface , i.e.,

over the whole of the closed surface, q is the algebraic sum of all the charges (i.e., net charge in coulombs) enclosed by surface S.

**Proof of Gauss"s Theorem :**

Let a point charge +q coulomb be placed at O within the closed surface. Let E be the electric field strength at P. Let

OP= r and the permittivity of free space or vaccuum be ε0.