  In this paper nonhomogeneous deterministic and stochastic Maxwell equations
are used to rigorously formulate the capacity of electromagnetic channels such
as wave guides (cavities, coaxial cables etc). Both distributed, but localized,
and Dirichlet boundary data are considered as the potential input sources. We
prove the existence of a source measure, satisfying certain second order
constraints (equivalent to power constraints), at which the channel capacity is
attained. Further, necessary and sufficient conditions for optimality are
presented.
