  Boyer showed that a perfect electrically conducting slab repels a perfect
magnetically conducting slab, in contrast to the attractive Casimir force
between two identical perfect electrically/magnetically conducting slabs. To
gain insight for the difference between the Boyer force and the Casimir force,
we present the derivation of the Boyer force using the stress tensor method and
then using the method of variation in dielectric. The Green dyadic, in terms of
electric and magnetic Green's functions, is presented for an electric medium
filling half of space and another magnetic medium filling another half of space
such that the two half-spaces are parallel and separated by a distance $a$. We
make the observation that the spectral distribution of scattering in a Boyer
cavity is that of Fermi-Dirac type, while the spectral distribution of
scattering in a Casimir cavity is that of Bose-Einstein type. Based on this
observation we conclude that the difference between the Boyer force and the
Casimir force is governed by the statistics of the possible scattering in the
respective cavities.
