Maxwell's Equations

Maxwell's Equations: We are now in a position to collect together all the laws governing the dynamic of electromagnetic field. These equations are collectively known as Maxwell's equations.

Gauss's Law of Electrostatics :

Gauss's Law of Magnetism :

Faraday's Law:

Ampere-Maxwell Law:

These equations are to be supplemented by Lorentz force equation.

In terms of free charges and currents, the first and the fourth of Maxwell's equations are generally expressed in terms of the vectors and :

with the displacement vector $\vec D$ and the H-vector defined as

The polarization vector and the magnetization vector are related to the vectors and $\vec B$ respectively by constitutive relations