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This paper presents a closed form solution for the electrical potential perturbation of a perfectly insulating flat circular disc embedded in a homogeneous half-space in a uniform primary electric field. This has applications to the detection of insulating underground targets such as hydrocarbon reservoirs or plastic mines, as well as to the electrical properties of composite materials. The solution method is an adaptation of Weber’s method for the potential around a charged conducting disk. It yields closed form analytic solutions for the electric and magnetic fields and by straightforward numerical integration, an easily evaluated numerical solution for the electric potential and an explicit solution for the electrical resistivity of a composite material consisting of a dilute concentration of such embedded disks in an otherwise uniform conductor.

THE ELECTRICAL RESPONSE OF AN INSULATING CIRCULAR DISK TO UNIFORM FIELDS