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In the Feynman Lectures the modified Stern-Gerlach thought experiment uses high-gradient magnets. I'm confused as to what a high-gradient magnet would be. From what I understand about the Stern-Gerlach apparatus magnets are oriented in a certain direction (such as the z direction). This means that the magnetic field produced by the two magnets is in the z direction and the gradient of the magnetic field is also in the z direction? If this is the case then how are the magnetic fields inhomogeneous? From this Stack Exchange post it seems like if a magnetic field is only in one direction then it would be homogeneous.

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A homogeneous magnetic field is one which is spatially uniform, that is one with zero gradient. You may recall from magnetostatics that the force on a magnetic dipole in a magnetic field is proportional to the dot product of the dipole moment with the gradient of the magnetic field. If the magnets in the Stern-Gerlach experiment generated homogeneous fields the atoms would not be deflected at all. Only in the presence of a magnetic field with a gradient in the z-direction will you see splitting due to the z-component of the angular momentum of the atoms.

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    $\begingroup$ The asker is rather asking how you make such magnets. $\endgroup$ – FGSUZ Aug 16 '18 at 22:35
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    $\begingroup$ This is a much more difficult question. In principle, one could just use an ordinary bar magnet, allowing the particles to run between the north and south poles. This is certainly an inhomogeneous magnetic field with a gradient in a particular direction, but for the purposes of the Stern-Gerlach experiment we would like to maximize the magnitude of the gradient. For a sketch of how this is typically done, see any diagram of the experiment. It usually involves a single long magnet with a wedge-shaped cut along its length. Computing the magnetic field of this setup is a highly nontrivial task. $\endgroup$ – Alex Buser Aug 16 '18 at 23:34

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