Analysis on electrostatic behavior of a conducting prolate spheroid under an electric field

This paper presents the electrostatic analysis of a conducting prolate spheroid under an external electric field in axisymmetric configurations. The configurations consist of a conducting spheroid which is in contact with or separated from a grounded plane. We apply the method of images using multipoles to the electric field calculation. The calculation uses the multipole re-expansion formulae and the equivalent image charges of a prolate conducting spheroid. The induced charge and force are determined from the multipole images. For a spheroid on the grounded plane, the calculation results show that the maximal field increases nonlinearly with the major-to-minor axis ratio of the spheroid. The charge and the force are compared between the spheroids of the same major axis or the same surface area. We propose empirical formulae for approximating the maximal field, charge and force with the errors smaller than 2% for the axis ratio between 1 and 32. We examine the propriety of the approximation of the electric field, charge and force based on a hemispheroidal model. For an uncharged spheroid separated from the grounded plane, we clarify the relationship between the separation and the field intensification at the bottom pole of the spheroid. Based on the critical field strength of a background medium, the position of the spheroid where the partial discharge takes place is estimated. For a charged spheroid, we found that the maximal electric field hardly depends on the separation from the plane.