The Electrostatic Force on a Dielectric Sphere Resting on a Conducting Substrate

Abstract

The electrostatic force of removal is calculated for a sphere in contact with a grounded plane in an externally applied electric field that is normal to the plane. The electrostatic force is given by the sum of the Lorentz force QE₀ , where Q is the free charge on the sphere and E₀ is the applied electric field, and the electrical force between the sphere and the plane. The force between the sphere and the plane can be described by the interaction between the bound and free charges on the sphere, whose distribution is strongly influenced by the polarization of the sphere, and their images in the plane. The polarization charge distribution of the sphere is described by a linear multipole expansion. The multipole terms are calculated by a simple, iterative, self-consistent scheme, in which the externally applied field and the image charges induce the polarization of the sphere. The net electrostatic force on the sphere is given by the sum of the force on each linear multipole in the expansion. Two novel results of this force computation are found. The force on the higher order multipoles increases with the applied electric field more rapidly than the Lorentz force. For a given charge level, a field magnitude exists above which the net electric force is adhesional. Furthermore, an optimum charge level exists that minimizes the field required for electrostatic removal.