Theory of four-point alternating current potential drop measurements on conductive plates

Measurements of alternating current potential drop (ACPD) made at the surface of a conductive plate can be used to determine, non-destructively, the parameters of the plate such as its thickness, electrical conductivity and linear effective magnetic permeability. In order to invert the measured potential drop to yield values for these parameters, a theoretical model is needed. In this work, closed form analytical expressions are derived for the ACPD measured between the two voltage electrodes of a four-point probe. Alternating current is injected and extracted by two current electrodes. The problem is formulated in terms of a single, transverse magnetic, potential. The exact solution for the electromagnetic field is expressed in terms of a Green's function for a plate via the method of images. The ACPD is also expressed as a sum of contributions from multiple images. Two series representations are given: one converges more rapidly for plates which are somewhat thicker than the probe dimensions and the other for plates which are somewhat thinner. Theoretical expressions for the ACPD in special cases of thick (half space) and thin conductors are shown to agree with the results presented previously. In this paper, calculated ACPD values are compared with the experimental data taken on a titanium plate, in the regime in which the plate thickness is similar to the probe length and excellent agreement is obtained.