The electrostatic force between a charged dielectric particle and a conducting plane

Abstract

The electrostatic force between a uniformly charged dielectric particle and a conducting plane was carefully calculated including the effect of higher-order polarizations. The potential distribution problem was solved using spherical coordinates by considering the symmetry of the image and using a re-expansion technique of the Legendre functions. On the basis of the results, the electrostatic force was calculated using the orthogonality of the Legendre terms. In this method, numerical calculations are required for each condition, such as the contact gaps and the dielectric constants of the particle. This would be avoidable if an approximate formula was available. Thus, for convenience, an approximate formula was searched for by trial and error, and F e =F e (d=0)/{1 + (d/a) α } β was found to be a good approximation. This was the simple expansion of the contact gap dependence of the particle with a relative dielectric constant ε = 1, i. e., with no effect of polarization.