  We calculate the Casimir force or dispersive van der Waals force between a
spherical nanoparticle and a planar substrate, both with arbitrary dielectric
properties. We show that the force between a sphere and a plane can be
calculated through the interacting surface plasmons of the bodies. Using a
Spectral Representation formalism, we show that the 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. We found that the difference
depends on the plasma frequency of the materials, the geometry, and the
distance of separation between sphere and plane. The differences show the
importance of the geometry, and make evident the necessity of realistic
descriptions of the sphere-plane system beyond the Derjaguin Approximation or
Proximity Theorem Approximation.
