POTENTIAL DISTRIBUTION DUE TO A CYLINDRICAL ELECTRODE MOUNTED ON AN INSULATING PROBE

Abstract

The potentials around a finite cylindrical electrode can be obtained by dividing the electrodes into rings of equal thickness and substituting an infinitely thin current ring for each of the slices. The field of an infinitely thin ring electrode mounted on an insulating cylindrical probe of the same diameter can be found by combining the properties of the delta function with a solution of Laplace’s equation in cylindrical co‐ordinates. Combination of solutions for the infinitely thin rings under the condition that the potential of the electrode surface be constant leads to a system of simultaneous linear equations. By increasing the number of slices, the potential around the finite electrode can be found arbitrarily close. The problem of a cylindrical electrode on a sonde located coaxially in a conducting hole, drilled through a medium of different conductivity, is treated by the same method. This arrangement is of interest in electrical logging of drill holes. Numerical examples have been calculated on an IBM 650 magnetic drum computer. The potential along the surface of the insulating probe, at distances larger than twice the electrode length, can be approximated with good accuracy by assuming that all of the current is emitted from an infinitely thin ring located in the median plane of the electrode.