Four-point direct-current potential drop techniques are well-suited for accurate, nondestructive
measurement of material conductivity (or resistivity). From measurements of potential
drop on a large metal plate, the electrical conductivity of the plate can be inferred if the
thickness of the plate and the dimensions of the probe are known. In this work, an
expression for the voltage measured by a four-point probe in contact with a large metal
plate of arbitrary thickness is derived from an analytic series representation of the electric
field in the plate. The position of the voltage pickup points is permitted to be offset with
respect to the current injection points, allowing analysis of colinear, rectangular, and
square-head probes. Analytical asymptotic expressions are derived in the limiting cases
of plates that are thin or thick with respect to the dimensions of the probe. The range of plate
thicknesses for which the asymptotic expressions are valid is determined as a function of
relevant probe dimensions. The results of this study provide a useful guide in selecting
the most appropriate arrangement of probe points for measurement of the electrical conductivity
of large metal plates, depending on the level of accuracy required. Theory is compared
with experimental data for measurements made with colinear probes on a variety
of metal plates and very good agreement is obtained.
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