This chapter provides a simple physical proof of the reciprocity theorem of classical
electrodynamics in the general case of material media that contain linearly polarizable as well as
linearly magnetizable substances. The excitation source is taken to be a point-dipole, either
electric or magnetic, and the measured field at the observation point can be electric or magnetic,
regardless of the nature of the source dipole. The electric and magnetic susceptibility tensors of
the material system may vary from point to point in space, but they cannot be functions of time.
In the case of spatially non-dispersive media, the only other constraint on the local susceptibility
tensors is that they be symmetric at each and every point. The proof is readily extended to
media that exhibit spatial dispersion: For reciprocity to hold, the electric susceptibility tensor
χE_ mn that relates the complex-valued magnitude of the electric dipole at location rm to the
strength of the electric field at rn must be the transpose of χE_nm. Similarly, the necessary and
sufficient condition for the magnetic susceptibility tensor is χ M_mn=χ T
M_nm.
