Measuring surface charge with a noncontacting voltmeter

The problem of using a noncontacting electrostatic voltmeter to measure surface charge is addressed. By design a noncontacting voltmeter enforces a zero-field condition at its probe by adjusting its own probe potential. When an isolated charge distribution is measured, the field around the probe is shown to consist of two superimposed components, one equal to the field caused by the measured charge distribution and a grounded probe, and the other equal to the field of the energized probe with the charge distribution absent. The resulting probe potential is shown to depend on the magnitude of the measured charge, its physical geometry, the geometry of the probe, and the position of the probe relative to the charge distribution. A method for interpreting the reading of a noncontacting voltmeter based on these factors is presented and experimentally verified