Maxwell Equations -- from Eric Weisstein's World of Physics

Maxwell Equations

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, Eric Weisstein's World of Biography 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

(1)

(2)

(3)

(4)

where is the divergence, Eric Weisstein's World of Math is the curl, Eric Weisstein's World of Math is the constant pi, Eric Weisstein's World of Math 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.

Conductor, Dielectric, Maxwell Equations--Dielectric, Maxwell Equations--Steady State

References

Jackson, J. D. Classical Electrodynamics, 3rd ed. New York: Wiley, p. 177, 1998.

Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 138, 1997.