Magnetic fields of current monopoles in special volume conductors

A theory for deriving the magnetic fields generated by monopoles of current (i.e. point sources of current) located in two volume conductor shapes is presented. The solution is derived for the magnetic field exterior to a semi-infinite conducting volume and exterior to a conducting spherical volume. In both volumes, the magnetic field of the dipole volume current is shown to be a spatial derivative of the magnetic field due to a current monopole. The magnetic field exterior to the semi-infinite volume conductor is equivalent to that of a semi-infinite line current, starting at the position of the monopole, oriented perpendicular to the surface of the conducting volume, and flowing toward infinity. The field exterior to a conducting sphere is equivalent to that generated by a finite-length line current flowing from the position of the monopole to the center of the sphere. Current monopoles can be used in lieu of dipole current sources to reduce source modeling errors and to better understand the effects of volume currents.