Re: Electric current components at boundaries between two materials

For simplicity, we consider harmonic EM field with time dependence of
exp(j*w*t) at the interface between two lossy media. The first medium is
characterized by a real positive permittivity eps1 and a real positive
conductivity sigma1. The second medium is characterized by a real positive
permittivity eps2 and a real positive conductivity sigma2. The first medium
is equivalent to a dielectric with complex permittivity eps1-sigma1/(j*w).
The second medium is equivalent to a dielectric with complex permittivity
eps2-sigma2/(j*w). Since the normal component of electric flux density is
continuous across the interface, it is easy to know the normal component of
electric current density is also continuous across the interface. The
tangential component of current density is not continuous if sigma1 is not
equal to sigma2 since the tangential component of E is continous.