The Effect of Fringing Fields on the Resistance of a Conducting Film

We have calculated the effect of fringing fields on the measured resistance of a conducting film between two circular disks, using two complementary approaches, for a wide range of disk separations. The problem is cast as the numerical solution of a dual integral equation and a straightforward relaxation procedure for the isomorphic problem of the fringing effects on the capacitance of a circular disk between two grounded planes. These results also represent the solution for the capacitance in the high dielectric limit for two disks separated by a dielectric medium.