Electrostatic force between a charged sphere and a planar surface: A general solution for dielectric materials

Using the bispherical coordinate system, an analytical solution describing the electrostatic force between a charged dielectric sphere and a planar dielectric surface is presented. This new solution exhibits excellent numerical convergence, and is sufficiently general as to allow for the presence of charge on both the sphere and the surface. The solution has been applied to two examples of sphere-plane interactions chosen from the literature, namely, (i) a charged lactose sphere interacting with a neutral glass surface and (ii) a charged polystyrene sphere interacting with a neutral graphite surface. Theory suggests that in both cases the electrostatic force makes a major contribution to the experimentally observed attraction at short sphere-plane separations, and that the force is much longer ranged than previously suggested.