Most textbook authors assume that the force on a magnetic moment sent into a Stern–Gerlach apparatus, is exclusively in the direction of the magnetic field. Hence they conclude that classically one should expect a continuous distribution of particles along a line in the field direction, on a screen placed behind the apparatus. However, it is easily shown that, because the divergence of the field is zero, there is in fact an equally large force transverse to the field direction. This would lead to an isotropic distribution of particles on the screen, in contradiction to the above conclusion. The paradox is resolved by taking into account the torque on the magnetic moment. This produces a rapid precession about the field direction, causing the transverse force to average out and thus giving the usual textbook result.
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Papers| August 01 1982
Paradox in the classical treatment of the Stern–Gerlach experiment
Am. J. Phys. 50, 697–698 (1982)
Preben Alstro/m, Poul Hjorth, Richard Mattuck; Paradox in the classical treatment of the Stern–Gerlach experiment. Am. J. Phys. 1 August 1982; 50 (8): 697–698. https://doi.org/10.1119/1.12732
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