  We calculate exactly the Casimir force between a spherical particle and a
plane, both with arbitrary dielectric properties, in the non-retarded limit.
Using a Spectral Representation formalism, we show that the Casimir force of a
sphere made of a material A and a plane made of a material B, differ from the
case when the sphere is made of B, and the plane is made of A. The differences
in energy and force show the importance of the geometry, and make evident the
necessity of realistic descriptions of the sphere-plane system beyond the
Proximity Theorem approximation.
