Application of the electrostatic mean value theorem to electrostatic sensor electrodes

We present a method for approximating the potential of conducting objects due to a known electrostatic source. The method involves averaging the incident potential over the conductor surface or volume region, which is known to give the exact value for a perfectly conducting sphere. The method is extended to spheroidal geometries, both prolate and oblate, to study the error incurred for deviations from the spherical case. Exact values for the spheroid potentials are derived and compared with those obtained by the mean value approximations. The result for the oblate spheroid is extended to the case of a two-dimensional electrostatic disk. The approximations are proposed as a method for predicting the potential of conducting electrodes used with electrostatic sensors for the measurement of electrostatic field disturbances. In this regard, the mean value approximation is applied to determine the source to electrode mutual capacitance, which is implemented in the model for the sensor system. Electrostatic disk electrodes are used with an electrostatic disturbance sensor to experimentally validate the application of the mean value approximation.