Analysis shows solutions to the 2D inverse problem in magnetostatics, suggesting applications in magnetometry.
We consider 2D magnetostatics inverse problem for uniformly magnetized body and reduce it to a nonlinear 1D integrodifferential equation determining body(cavity) shape based on the measured strength of the external magnetic field. We design an numerical algorithm for solution of this equation based on minimization of a function of several variables and develop a FORTRAN program implementing this algorithm. To test and illustrate our approach we find a solution for the cross-section of a homogeneous infinite cylinder in a non-magnetic and opaque medium based on the known strength of the external field.
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V.V. Dyakin (2025) studied this question.
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