We calculate exactly the Casimir force or dispersive force, in the non-retarded limit, between a spherical nanoparticle and a substrate beyond the Londons or dipolar approximation. We find that the force is a non-monotonic function of the distance between the sphere and the substrate, such that, it is enhanced by several orders of magnitude as the sphere approaches the substrate. Our results do not agree with previous predictions like the Proximity theorem approach.
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