Maxwell's Equations

Maxwell's equations are the system of partial differential equations describing classical electromagnetism and therefore of central importance in physics. In the so-called cgs system of units, Maxwell's equations are given by

			(1)
			(2)
			(3)
			(4)

where  is the electric displacement field,  is the free charge density,  is the electric field,  is the speed of light, is the magnetic field,  is the magnetizing field, and  is the free current density (cf. Purcell 1985, p. 330, 381, and 432; Jackson 1998, p. 818). As usual,  is the divergence and  is the curl.

In the MKS system of units, the equations are written

			(5)
			(6)
			(7)
			(8)

supplemented by

			(9)
			(10)

where  is the permittivity of free space,  is the permeability of free space,  is the electric polarization, and  is the magnetic polarization or "magnetization" (Griffiths 1998, pp. 278-279).

REFERENCES:

Griffiths, D. J. Introduction to Electrodynamics, 3rd ed. Englewood Cliffs, NJ: Prentice-Hall, pp. 279 and 295, 1998.

Jackson, J. D. Table 2 in Classical Electrodynamics, 3rd ed. New York: Wiley, p. 818, 1998.

Purcell, E. M. Electricity and Magnetism, 2nd ed. New York: McGraw-Hill, 1985.