The inverse source problems of magnetostatics and electrostatics

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Abstract
The problem of retrieving a static current density from knowledge of the magnetic field it produces at a plane is solved. This problem does not have a unique solution. However, there is a unique solution of the least L2 norm. The Fourier transform of the minimum norm current distribution is given in closed form. The minimum norm current distribution is a filtered version of any other current distribution that produces the same magnetic field data. The kernel of the filter is given in closed form. The electrostatic counterpart of this problem is also similarly solved.