Magnitude and location of a dipole in a circular ring with non-insulating boundaries

It was shown that the resultant dipole moment of a system of sources and sinks within a region can be found from integrations of potential and potential gradient or normal current over the surfaces bounding the region. The method was applied in two dimensions to the case of a dipole in an infinite medium of one resistivity outside a circle having a different resistivity. The results agree with the Brody theory in that potentials at remote points due to a radial dipole were increased and potentials due to tangential components were decreased. Potentials on and within the circle are more complicated, however. For a radial or oblique dipole, potentials on the "endocardium" are increased in some areas but reduced at others. In addition, the effects are non-linear, depending on the distance of the dipole from the circle. Neglecting the effects of the low resistance circle leads to false values of dipole moment. When the integrations of potential and potential gradient are used, however, accurate values of dipole moment are obtained. The low-resistivity disk makes a radial dipole appear more centric but a tangential dipole appear further away.