  We study the interaction between a neutral atom or molecule and a
conductor-patched dielectric surface. We model this system by a perfectly
reflecting disc lying atop of a non-dispersive dielectric half-space, both
interacting with the neutral atom or molecule. We assume the interaction to be
non-retarded and at zero temperature. We find an exact solution to this
problem. In addition we generate a number of other useful results. For the case
of no substrate we obtain the exact formula for the van der Waals interaction
energy of an atom near a perfectly conducting disc. We show that the
Casimir-Polder force acting on an atom that is polarized in the direction
normal to the surface of the disc displays intricate behaviour. This part of
our results is directly relevant to recent matter-wave experiments in which
cold molecules are scattered by a radially symmetric object in order to study
diffraction patterns and the so-called Poisson spot. Furthermore, we give an
exact expression for the non-retarded limit of the Casimir-Polder interaction
between an atom and a perfectly-conducting bowl.
