Maxwell equations

In physics, the Maxwell equations are the mathematical equations that describe the interrelationship between electric and magnetic fields and they tell us how the electromagnetic fields are caused by electric charges and electric currents. The equations are named after the Scottish physicist James Clerk Maxwell, who published them (in a somewhat old-fashioned notation) in 1865. The Maxwell equations are still held to be completely valid, even in quantum electrodynamics where the electromagnetic fields are reinterpreted as quantum mechanical operators satisfying canonical commutation relations.

Among physicists, the Maxwell equations take a place of equal importance as Newton's equation F=ma, Einstein's equation E=mc², and Schrödinger's equation Hψ=Eψ. Yet, in the eyes of the general, well-educated, public, Clerk Maxwell does not have the same fame as the other three physicists. This is somewhat surprising, because the applications of Maxwell's equations have far-reaching impact on society. Maxwell was the first to see that his equations predict electromagnetic waves. Without knowledge and understanding of these waves we would not have radio, radar, television, cell phones, global positioning systems, etc. Maybe, the lack of fame of the Maxwell's equations is due to the fact that they cannot be caught in a simple iconic equation like E=mc². In modern textbooks Maxwell's equations are presented as four fairly elaborate vector equations, involving abstract mathematical notions as curl and divergence.