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)