Electrostatic force behavior of a nonuniformly charged particle on a planar dielectric solid

This paper presents the analysis of the electrostatic force on a nonuniformly charged dielectric particle resting on a dielectric solid. The purpose of the analysis is to clarify the force enhancement caused by the nonuniform charging when the particle is on the dielectric solid, and to examine the role of the dielectric solid on the force behavior in the presence of an external electric field. The method of images using multipoles is applied to electric field calculation, and the electrostatic force is determined from the Maxwell stress. The analytical results show significant force enhancement due to nonuniform charging even in the case where the particle and the dielectric solid have the same dielectric-constant value. However, with an externally applied electric field, the nonuniform charging also results in higher force magnitude for detachment of the particle from the plane in comparison with the case of uniform charging. The roles of the dielectric constants of the media involved on the electrostatic force behavior are investigated. Critical difficulty for the detachment is not found for a particle with dielectric constant equal to 4, which is remarkably different from the corresponding case of a particle lying on a conducting plane.