Maxwell's equations

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Maxwell's equations are a set of four partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These in turn underlie the present radio-, television-, phone-, and information-technologies.

Maxwell's equations have two major variants. The "microscopic" set of Maxwell's equations uses total charge and total current including the difficult to calculate atomic level charges and currents in materials. The "macroscopic" set of Maxwell's equations defines two new auxiliary fields that can sidestep having to know these 'atomic' sized charges and currents.

Maxwell's equations are named after the Scottish physicist and mathematician James Clerk Maxwell, since they are all found in a four-part paper, On Physical Lines of Force, which he published between 1861 and 1862. The mathematical form of the Lorentz force law also appeared in this paper.

It is often useful to write Maxwell's equations in other forms which are often called Maxwell's equations as well. A relativistic formulation in terms of covariant field tensors is used in special relativity. While, in quantum mechanics, a version based on the electric and magnetic potentials is preferred.

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