Maxwell's equations are,
Where the vectors are defined in the usual way. Also,
Taking a Fourier transform with respect to the time variable, we have,
See ``Electromagnetics" for more.
The integral form is also commonly given.
Energy of the Field
Power Flow into a Volume
The Poynting vector gives the direction of power flow. The Poynting vector is given by,
It has the units, watts per square meter.
The power flow through a differential area id given by . The power flow through a volume is then given by summing up the power flow through the area enclosing that volume, thus:
Expanding by Maxwell's equations,
The first summand is the power density of the vacuum electromagnetic field; the second and third summands, when integrated, are the power dissipation by magnetic and electric dipoles; the fourth summand, when integrated is power dissipation by current.
Reference: ECE525 Lasers and Detectors. notes taken in class, 2010. Instructor: Joyce Poon.