That is, it is assumed that there is no other matter in the system than the charges and currents accounted for in the equations the charges and currents are located in empty space. There are two sets of Maxwell's equations, the most basic ones are the microscopic equations, which describe the electric field E and the magnetic field B in vacuo, together with their sources (charge- and current-densities). In modern textbooks Maxwell's equations are presented as four fairly elaborate vector equations, involving abstract mathematical notions as curl and divergence. Maybe, the lack of fame of Maxwell's equations is due to the fact that they cannot be caught in a simple iconic equation like E=mc 2. Without knowledge and understanding of these waves we would not have radio, radar, television, cell phones, global positioning systems, etc. Maxwell was the first to see that his equations predict the existence of electromagnetic waves. This is somewhat surprising, because the applications of Maxwell's equations have far-reaching impact on society. Yet, among the general, well-educated, public, Clerk Maxwell does not have the same fame as the other three physicists. The Maxwell equations are still considered to be valid, even in quantum electrodynamics where the electromagnetic fields are reinterpreted as quantum mechanical operators satisfying canonical commutation relations, see the article quantization of the electromagnetic field.Īmong physicists, the Maxwell equations take a place of importance equal to Newton's equation F=ma, Einstein's equation E=mc 2, and Schrödinger's equation Hψ=Eψ. The equations are named after the Scottish physicist James Clerk Maxwell, who published them (in a somewhat old-fashioned notation) in 1865.
In physics, the Maxwell equations are the mathematical equations that describe how electric and magnetic fields are created by electric charges and electric currents and in addition they give relationships between these fields.