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To detect an electrical fault in a generator magnetic core with the ELCID method, a circulation of the magnetic field between two teeth is determined. To model this problem with the finite element method, two potential formulations can be used. With the scalar formulation, such circulation can be easily determined; this is not the case with the vector potential formulation. In this paper, we propose to use a supplementary relation to compute a magnetomotive force in the case of vector potential formulation.