Electric field analysis using image charges of spheroidal harmonics and its application to the calculation of field in cavities

This paper describes a method of electric field analysis for configurations consisting of oblate spheroidal objects. In the method, electric potential is expressed as a sum of oblate spheroidal harmonics. The method utilizes the re-expansion and the image schemes of a dielectric oblate spheroid and a conducting plane to determine the solution of potential that satisfies all the boundary conditions involved. Electric field is calculated for an oblate spheroidal void enclosed in a solid dielectric near an electrode. The object of the calculation is to clarify the electric field inside the void which varies with (1) the separation between the void and the electrode, (2) the ratio of the major to minor axes of the void and (3) the dielectric constant of the solid dielectric. The results show that the effect of the electrode on the field inside the void is negligible when the separation is greater than the major semi-axis of the void. The presence of the electrode near the void mitigates the electric field on the axis of symmetry of the void. However, higher field stress exists at the region away from the axis, and the field maximum is not significantly reduced by decreasing the separation, in particular for flatter voids. In order to present the potential induced by the void, higher order multipoles must be incorporated. The effect of the planar electrode on the equivalent multipole moments of the void is also discussed.