Three-dimensional electromechanical analysis of a conducting prolate spheroid on a grounded plane

Abstract

This paper presents a 3D analysis of the electromechanics for a conducting prolate spheroid on a grounded plane under electric field. The objective of the analysis is to clarify the roles of tilt angle α between the particle and the plane on the electrostatic force and torque on the spheroid, which are the fundamentals of particle behavior in various applications. The method of multipole images and multipole re-expansion for the prolate spheroidal coordinates are applied to electric field calculation. The electrostatic force and torque on the spheroid are then determined. The calculation results show that the maximal field takes place at or near the higher pole of the spheroid for nonzero tilt angles. The electrostatic force is minimal and maximal when the spheroid lies and stands on the plane, respectively. We present empirical formulae for estimating the minimal and maximal force with error smaller than 1% for the major-to-minor axis ratio between 1 and 10. The electrostatic torque is in the increasing α direction, and it is magnified with increasing α from 0 to about 45°, and then reduces to zero at α = 90°. The torque variation may be estimated by a quadratic relationship. When the gravitational force of the particle is taken into account, the electromechanical behavior can be classified into three regimes, depending on the externally applied field and the tilt angle. The presence of the electrostatic torque enhances the probability of a spheroid particle to be lifted from the grounded plane by the electric field.