Motion of a sphere in non-uniform electrostatic field

Abstract

A mathematical expression for the electric force acting on a sphere placed in a non-uniform electrostatic field is derived taking into account the conductivity and permittivity of both the sphere and the medium, as well as the initial velocity and charge of the spherical particle. The expression demonstrates a time-dependent variation of the force in a non-uniform field. New formulae are given for calculating the particle charge and the electric field strength inside and outside the sphere. An example is given of particle motion in a field with constant gradient in a direction normal to the field vector. It is demonstrated that oscillatory motion of the sphere in a non-uniform field is possible at certain sphere parameters and field strength gradients as a result of instability of the equilibrium state of the system.