The Maxwell equations are the set of four fundamental equations governing electromagnetism (i.e., the behavior of electric and magnetic fields). They were first written down in complete form by physicist James Clerk Maxwell,who added the so-called displacement current term to the final equation, although steady-state forms were known earlier.
For time-varying fields, the differential form of these equations in cgs is




where is the divergence, is the curl, is the constant pi,E is the electric field, B is the magnetic field, is the charge density, c is the speed of light, and J is the vector current density.
In MKS, these become




where is the permittivity of free space and is the permeability of free space.
The equations can also be expressed in integral form. In cgs,





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are known as Gauss's law, Faraday's law, the absence of magnetic monopoles, and Ampere's law (with displacement current).
In MKS, these become





In a dielectric,the Maxwell equations take a slightly modified form with E and B replaced by D and H, respectively. In steady state, a slightly simpler form of the Maxwell equations results.