Maxwell's equations are the four equations formulated by James Clerk Maxwell, a British physicist, that explain all classical electromagnetic phenomena. They are a set of differential equations that describe and predict the behavior of electromagnetic waves in dielectrics, free space and at the boundary of conductors and dielectric materials. Maxwell's equations unify the laws of Gauss, Ampere, and Faraday in concise statements concerning the fundamentals of electricity and magnetism. They embody a high level of mathematical sophistication and are usually found in advanced courses. The laws are usually written in the form of equations in the absence of magnetic or polarizable media.

The first of Maxwell's equations is a form of Gauss' law for electricity. Written in differential form it is: ∇E = /ε₀, where E is the electric field vector, is the density of electric charge and ε₀ is the permittivity of a vacuum. Basically...