Bipolar charging and discharging of a perfectly conducting sphere in a lossy medium stressed by a uniform electric field

Abstract

Generalized analysis is presented extending recent work of the charging of a perfectly conducting sphere from a single charge carrier to two charge carriers of opposite polarity, with different values of volume charge density and mobility and including an ohmic lossy dielectric region surrounding a perfectly conducting sphere. Specific special cases treated are: (1) unipolar positive or negative charging and discharging and (2) bipolar charging and discharging; both cases treating zero and nonzero conductivity of the dielectric region surrounding a sphere. It is found that there exists a theoretical limit to the amount of charge, either positive or negative, that can accumulate on a perfectly conducting sphere for a specific applied electric field magnitude, permittivity of the surrounding medium, and sphere size. However, in practice this saturation charge limit is not reached and the sphere is charged to a lower value due to the nonzero conductivity of the surrounding medium and the existence of both positive and negative mobile carriers. Moreover, it is the respective effective conductivities of these positive and negative carriers, as well as the conductivity of the surrounding medium, which strongly influences the sphere’s lowered saturation charge limit, charge polarity, charging rate, and discharging rate.