In this paper, we consider an electromagnetic obstacle scattering
problem in a piecewise homogeneous medium. We assume that the incident
field is the electromagnetic plane wave and the obstacle consists of
metallic and nonmetallic parts. We firstly establish uniqueness and
existence for the solution to the electromagnetic obstacle scattering
problem. Then we prove that the electric far field pattern satisfies the
reciprocity relation and the set of electric far field patterns is
complete in a Hilbert space. These results have an important bearing on
the solution of the inverse electromagnetic scattering problem i.e.
determination of the shape of the obstacle from the knowledge of the
electric far field patterns.