Maxwell’s Equations and Constitutive Relations


            The equations on this page represent time-harmonic derivations with an  time dependence.  A subscript “i” means “impressed current”, “c” means “conduction current”, “m” means magnetic charge”, “e” means “electric charge”, “s” means “surface”, and “v” means “volume”.  Sometimes subscripts are combined.  The source for much of the following is


            Balanis, C.  Advanced Engineering Electromagnetics, John Wiley & Sons, 1989.


Differential Form







Integral Form







Boundary Equations






Constitutive Relations and Fundamental Constants





             (computed from the speed of light)


Power Relations


                Supplied complex power (W)

                                   Exiting complex power (W)

                                       Dissipated real power (W)

                                    Time-average magnetic energy (J)

                                      Time-average electric energy (J)