Approximate Theory of Four-Point Alternating Current Potential Drop on a Flat Metal Surface

An analytical expression for the voltage measured by a four-point alternating current potential drop (ACPD) method on a flat metal surface is derived. Far-field expressions for the electric field in a metal plate and in the region of the probe (air) are used to obtain contributions to the ACPD voltage from the metal plate and due to inductance in the pick-up circuit. The far-field approximation is accurate for a plate whose edges are several tens of skin depths from the probe, and for a probe whose pick-up points are several skin depths away from the current drive points. Comparison of the theory with experiment on a brass plate shows excellent agreement.