Electric field and force on a conducting sphere in contact with a dielectric solid

This paper presents the analysis of electric field and force on a conducting sphere lying on a dielectric solid under a uniform field. To achieve high accuracy, we have applied the analytical method of successively placing three infinite sequences of point and dipole charges (zero- or first-order multipoles). The electric field is highest at the contact point, called the triple junction, where the conductor, the dielectric solid, and the surrounding medium (gas or vacuum) meet together. Both the contact-point field and the force increase with the permittivity ratio of the solid to that of the surrounding medium. The resulting force always attracts the sphere to the solid, in contrast to the repulsive force in the case of a conducting sphere lying on a plane conductor under an external field. We have given very simple formulae for approximating the contact-point field and the force which agree with the precise values within a difference of 3% for permittivity ratios up to 32 and 64, respectively.