Formulation of a computational model for determining the magnetic field produced by an in-service underground pipe-type cable

A computational model for determining the magnetic field produced by a practical in-service underground pipe-type cable is formulated. In the formulation, the contribution from the circulating current in the steel pipe is taken into account. The first step of the formulation is to derive a set of integro-differential equations for the magnetic vector potentials and the source current densities, from which the electric and magnetic fields can be determined. Then, in the second step, the equivalence principle is employed to construct a model equivalent to the region outside the steel pipe. Using the equivalent model, the magnetic field can be obtained.