Theoretical study of magnetic field of current monopoles in special volume conductor using symmetry analysis

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Abstract
We derive a formula for the magnetic field outside volume conductors having axial symmetry with radial and axial symmetrically distributed source currents. The magnetic field is shown to have components only along the cylindrical polar angle direction and its magnitude to depend only on the topological structure of the volume conductor and the location of the source current. With this formula, the magnetic field generated by the volume current of a current monopole within and on the symmetrical axis of several volume conductors (such as semi-infinite volume, infinite slab, sphere, infinite cylinder, semi-infinite cylinder, finite cylinder, prolate spheroid, and oblate spheroid) is shown to be equivalent to the magnetic field generated by a line current calculated using the Biot-Savart's law. In the first three volume conductors, the monopole solution of the magnetic field allows the calculation of magnetic fields generated by arbitrarily distributed (and balanced for finite volume conductors) current monopoles.