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A Monte Carlo simulation of the ballistic motion of electrons in a mesoscopic Hall bar containing a local inhomogeneous magnetic field profile is presented. We find that in the regime of low magnetic fields, the Hall resistance is determined by the average magnetic field in the cross junction and is independent of the shape and position of this profile in the junction. Information on the size of the local magnetic field profile can also be obtained from the Hall measurement. The bend resistance, on the other hand, is much more precise on the exact details of the local magnetic field in the cross junction.
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Peeters et al. (1998) studied this question.
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