Force exerted on a conducting spherical particle near the plate of a plane capacitor

The potential energy and the interaction force of a conducting spherical particle and a similarly charged plane plate are calculated for relatively small distances. The force is calculated from the potential energy and the plate is represented as a conducting sphere whose radius is 100 times greater than the radius of the particle. It is assumed that the particle is not charged by the plate. The domains of parameters in which the particle is always repulsed from the plate and in which the attraction takes place are determined.