The Calculation of the Electric Potential and Flux Distributions in Thin Sheets of Isotropic and Anisotropic Conducting Materials with Application to the Measurement of Conductivity Tensors

A brief account is given of some of the tensor properties of anisotropic materials with particular reference to the electrical conductivity and resistivity tensors. This is followed by a survey of methods for measuring electrical conductivity and resistivity, and an outline of mathematical methods, both analytical and numerical, for the solution of electric potential problems is given.
The problem of the potential and flux distribution in flat rectangular sheets with point electrodes attached to adjacent corners has been solved analytically for both isotropic and anisotropic materials. The results, which are in the form of infinite series, have been evaluated with the aid of a computer and used to draw equipotential and flux diagrams. The equipotentials have been determined experimentally and are in good agreement with the theory. The analagous problem for isotropic circular sheets with electrodes at two points on the circumference has been solved, and similar work has been done on equipotential and flux diagrams.
From the theoretical results obtained a method by van der Pauw for measuring electrical resistivity in isotropic flat samples has been modified to give the principal resistivities in anisotropic samples of rectangular shape. This was used to investigate the dependence of the principal resistivities on applied stress in rectangular sheets of conducting rubber and the results appear to be satisfactory.
The analytical solution of the problem for an anisotropic circular sheet appears to be too complicated to be conveniently applied in practice.