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In a previous question, Does a magnetic field do work on an intrinsic magnetic dipole?, one highly rated answer suggested that static magnetic fields do work on intrinsic magnetic dipoles in a non-uniform magnetic field. I can visualise the change in kinetic energy of the nucleus of an atom coming from a change in the configuration of the electrons around the nucleus. But for an electron, since it's truly fundamental, I'm scratching my head over where the energy comes from to change its kinetic energy. If it does, then it really must come from the static magnetic field.

So what is the experimental evidence that shows the kinetic energy of an electron changes in a static non-uniform magnetic field?

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Larry Harson
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The Stern Gerlach experiment is such an example (although we have an extra complication because the wave function splits)

1) There is a change in the EM Field energy $\tfrac12 B$ because the total magnetic field (static field + electron's own magnetic field) becomes less. A static field in isolation doesn't change per definition and its energy contents doesn't change either. To do work it needs to provide energy. The energy is provided by the total magnetic field and not the static field in isolation.

2) The equivalent view is that the work is provided by the internal energy -$\mu\cdot B^2$. This is also true, both views are equivalent, even if the energies actually come from different parts of the Lagrangian since ultimately -$\mu\cdot B$ comes from the interaction term $j_\mu A^\mu$.

This equivalence also hold classically even though the math for dipoles is somewhat involved.

Regards, Hans

Hans de Vries
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There is no evidence that the kinetic energy of an electron changes in a static magnetic field. You'd end up with a perpetual motion machine otherwise.

Jason Armitagee
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