EM wave

Four basic laws describe how static and changing electric and magnetic fields relate to the charges and currents that produce them. Gauss' law for electrostatics is essentially a restatement of Coulomb's law: it relates the electric field produced by static charges to the amount of charge enclosed by a surface. Gauss' law for magnetism is its magnetic counterpart, and it makes the important statement that magnetic monopoles -- isolated magnetic charges analogous to electric charges -- do not exist; magnetic poles always occur in north-south pairs, so magnetic field lines never begin or end anywhere but always form continuous closed loops. Faraday's law relates the electromotive force (emf) induced in a circuit to the rate at which the magnetic flux linked with that circuit changes with time. Ampere's law relates the magnetic field induced around a loop to the electric current flowing through that loop.

James Clerk Maxwell (1831-1879) noticed a serious flaw in Ampere's law once fields are allowed to change with time: a changing electric field, not just an electric current, must also be able to generate a magnetic field. In 1861 he repaired the law by adding a new term -- the displacement current -- to account for this. That single addition, extending Ampere's law to what is now called the Ampere-Maxwell law, is what makes electromagnetic waves possible at all: without it, the four laws taken together (now known as Maxwell's equations) would not predict any wave that could sustain itself and travel through space. …