Boundary Conditions
To get a full description of an electromagnetics problem, boundary conditions must be specified at material interfaces and physical boundaries. At interfaces between two media, the boundary conditions can be expressed mathematically as
(2-4)
where ρs and Js denote surface charge density and surface current density, respectively, and n2 is the outward normal from medium two.
The boundary condition for the current density, derived from Equation 2-4, is expressed as
Interface Between a Dielectric and a Perfect Conductor
A perfect conductor has infinite electrical conductivity and thus no internal electric field. Otherwise, it would produce an infinite current density according to the third fundamental constitutive relation. At an interface between a dielectric and a perfect conductor, the boundary conditions for the E and D fields are simplified. Assume that subscript 1 corresponds to a perfect conductor; then D1 = 0 and E1 = 0 in the relationships just given. If it is a time-varying case, then B1 = 0 and H1 = 0 as well, as a consequence of Maxwell’s equations. The result is the following set of boundary conditions for the fields in the dielectric medium for the time-varying case:
(2-5)