The calculation of the electric field for an infinite dielectric plate between two spherical electrodes

By considering the equipotential surfaces round two equal and opposite point charges, the electric field for an infinite dielectric plate between two spherical electrodes has been calculated. The solution is given as an infinite series in terms of applied voltage, radius of the electrodes, thickness of the dielectric plate, and permittivities of the plate and the medium. Curves have been derived to show the significance of the dependence of the voltage gradient in the field on the ratio of the plate thickness to the electrode diameter, and the ratio of the permittivity of the plate to that of the medium. The edge effect in the electrical breakdown of solid dielectrics may be attributed to the discharge in the medium, which occurs when the voltage gradient on the electrode surface reaches a value favourable to its breakdown condition.