Maxwell's equations

In electromagnetism, Maxwell's equations are a set of equations first presented as a distinct group in the later half of the nineteenth century by James Clerk Maxwell. They describe the interrelationship between electric fields, magnetic fields, electric charge, and electric current.

Although Maxwell himself was not the originator of the individual equations, he derived them again independently in conjunction with his molecular vortex model of Faraday's lines of force, and he was the person who first grouped these equations all together into a coherent set. Most importantly, he introduced an extra term to Ampère's Circuital Law. This extra term is the time derivative of electric field and is known as Maxwell's displacement current. Maxwell's modified version of Ampère's Circuital Law enables the set of equations to be combined together to derive the electromagnetic wave equation.

Although Maxwell's equations were known before special relativity, they can be derived from Coulomb's law and special relativity if one assumes invariance of electric charge.

This in turn leads to a very interesting parallel with gravity in that the same reasoning can be applied to Newton's law of gravitation leading to a gravitational equivalent of Maxwell's equations. See gravitomagnetism for more information.