With the help of _____________ the surface integral can be converted into a volume integral.

Divergence Theorem:

This theorem is used to convert the surface integral can be converted into a volume integral.

It states that “Total outward flux through any closed surface of a vector is equal to the volume integral of the divergence of that vector”.

\( \oint_{S}^{}\vec{A}.\vec{ds}=\int_{V}^{}(\nabla.\vec{A})dV\)

Gauss Law:

Gauss law states that the net flux of an electric field in a closed surface is directly proportional to the enclosed electric charge.

\(\phi = \oint \vec{E}.\vec{ds} ={Q_{en}\over \epsilon_o}\)

Coulomb's Law:

Coulomb's law states that the electrical force between two charged objects is directly proportional to the product of the quantity of charge on the objects and inversely proportional to the square of the separation distance between the two objects.

\(F = {1\over 4\pi\epsilon_o}{Q_1Q_2 \over R^2}\)

Maxwell Theorem: 

The four Maxwell equations are as follows:

1. \(\nabla .\vec{D} =\rho_v\)
2. \(\nabla .\vec{B} =0\)
3. \(\nabla \times \vec{E} =-{\partial B\over \partial t}\)
4. \(\nabla \times \vec{H} =\vec {J}+{\partial \vec D\over \partial t}\)