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.