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We calculate exactly the Casimir force or dispersive force, in thenon-retarded limit, between a spherical nanoparticle and a substrate beyond theLondon's or dipolar approximation. We find that the force is a non-monotonicfunction of the distance between the sphere and the substrate, such that, it isenhanced by several orders of magnitude as the sphere approaches the substrate.Our results do not agree with previous predictions like the Proximity theoremapproach.Comment: 7 pages including 2 figures. Submitted to Europjysics Letter

High-multipolar effects on the Casimir force: The non-retarded limit