Approximations useful for the prediction of electrostatic discharges for electrode geometries

This paper provides approximations for estimating the capacitance and the ratio of electric field strength to potential for a certain class of electrode geometries. The geometry consists of an electrode near a grounded plane, with the electrode being a surface of revolution about the perpendicular to the plane. Some examples that show the accuracy of the capacitance estimate and the accuracy of the estimate of electric field over potential can be found in the appendix. When it is possible to estimate the potential of the electrode, knowing the ratio of electric field to potential will help to determine if an electrostatic discharge is likely to occur. Knowing the capacitance will help to determine the strength of the discharge (the energy released by it) if it does occur. The medium between the electrode and the grounded plane may be a neutral gas, a vacuum, or an uncharged homogeneous isotropic dielectric.<>