An image method to compute the static magnetic field due to currents injected into a homogeneous, conducting, and magnetically polarizable half-space

An image method for computing the static magnetic field due to an arbitrary current injected into a conducting and polarizable half-space is derived. The advantage of this approach is that the magnetic field is given in terms of a Biot-Savart integral over only the impressed current sources and their finitely many images. Integration over the conducting currents, which are distributed in the entire conductive half-space, is avoided. The magnetic field is evaluated in closed form when the conductors that feed current to the electrodes are laid out in a rectilinear path.