A current source emitting in the presence of an insulating and a conducting disk over stratified media

The mixed boundary value problem of two different disks, one conducting, and one insulating involving a point current source is sovolved. We generalize the approach of Tranter, and apply his method to a set of vector dual integral equations. The unknown charges on the conducting disk, and the unknown dipole layer on the insulating disk are expanded in terms of basis functions. The basis functions are Jacobi polynomials. The integral equations are then converted to a matrix equation where the unknown charges and dipole layers can be solved for. The method is variational, and converges very rapidly. With the solution, we can plot the current flow patterns around the disks. Such current flow patterns provide insight into the problem.