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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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COM - Center Of Mass. Also, what if the imparted energy is rotational? It's very odd to refer to the "kinetic energy of the COM" if we are talking some or all of this being rotational, and that doesn't require some magic "change in the configuration" of the electrons either. –  AlanSE Jun 6 '11 at 22:37
@zassounnotsukushi I've changed the COM reference since it didn't make sense. –  Larry Harson Jun 6 '11 at 23:25
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2 Answers

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

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The Stern Gerlach experiment shows that the electron has in intrinsic magnetic dipole; I don't see what this has to do with determining its kinetic energy experimentally. –  Larry Harson Jun 7 '11 at 11:35
Nice answer Hans, I'd have written it up myself. I'm amazed that I'm the first to vote it up. People are getting very stingy with votes lately. –  Carl Brannen Jun 8 '11 at 22:31
@Carl the Stern Gerlach experiment operates on atoms, so what has this got to do with showing the kinetic energy of an isolated electon in a non-uniform magnetic field can change? –  John McVirgo Jun 9 '11 at 1:36
@John Suppose that, initially, the electron is stationary. It has no kinetic energy. When we release it, if it is attracted or repelled by the static magnetic field then its kinetic energy has changed. If this isn't enough of a hint, add another comment and I'll spell it out further. –  Carl Brannen Jun 9 '11 at 2:43
Alternatively, one could model the attraction by computing the total energy of the combined magnetic fields $\int |B+B_m|^2\;d^3x$. In this case one could avoid thinking about the dipole as an approximation given by two magnetic monopoles. One notes that when the dipole is aligned one way there is an attraction, the other way a repulsion. –  Carl Brannen Jun 9 '11 at 16:37
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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.

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