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

           

           

           

             (defined)

             (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)