Potential distribution for a spheroidal cell having a conductive membrane in an electric field

When a cell is situated in a uniform electric field, the field is modified due to the relatively low conductance of the cell membrane compared to that of the surrounding fluids. In certain cases, such as in the estimation of internal and external electrokinetic forces, one requires a means of estimating the magnitude of the electric field inside and outside the cell. Most treatments consider the case when the membrane has zero conductivity, or the case of only a spherical cell. We solve Laplace's equation for the electric potential distribution inside and outside a cell having a prolate spheroidal shape and having a membrane with a finite, nonzero conductivity.