Fringing fields in disc capacitors

The results of a high accuracy numerical study of the uniformity of the electric field between parallel disc electrodes are reported. Simple analytical expressions are derived describing the field behaviour at points on the electrodes near the edges of the discs and also at points between the electrodes remote from the edges. These expressions are consistent with the numerical results. A simple approximation for the fringing capacitance of parallel-plate electrode systems of arbitrary shape is also given. This expression leads to a first-order approximation for the total capacitance which, for disc electrodes, has superior accuracy to similar published approximations for radii up to five times the disc separation. A higher-order approximation for the capacitance is shown to have markedly better accuracy than any first-order approximation.