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Imagine a charged particle suspended between 2 horizontal magnetic plates, which create a uniform magnetic field. Now instantaneously, the particle is accelerated to velocity $v$. By my understanding, the particle will now start doing uniform circular motion, due to the Lorentz force.

However, what if the magnetic field is moving, instead of the charged particle? Instead of the particle being accelerated, now the magnetic plates are instantly accelerated to velocity $v$.

What happens to the charged particle?

  1. Does it now undergo that same uniform circular motion (in the magnetic plates' reference frame), and in doing so, does it "keep up" with the magnetic plates?

Or

  1. Does it get accelerated by the Lorentz force, but eventually falls out of the magnetic field?

If 1 is what happens, how did the particle gain kinetic energy? It went from stationary to moving, but I was taught that magnetic field cannot do work on charged particles. So then what did the work on the particle?

If 2 is what happens, then why is this scenario any different than accelerating the particle instead of the plates? Shouldn't those two scenarios be the same in the magnetic plates' reference frame?

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What is a "moving magnetic field"? If you have a moving magnet, then the magnetic field at every point in space is changing in time... which by Maxwell's laws generates an electric field. This electric field can do work.

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Focus on a short time interval in which the particle moves with constant velocity. In the magnet frame there is a current component parallel to its velocity. In the rest frame of the particle a charge density appears due to this current component. A net electric field appears perpendicular to the velocity and the particle is deflected. It will move in an orbit that can be derived from its orbit in the magnet frame by directly transforming it. To answer the unrelated question in the title: no work is performed.

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  • $\begingroup$ Is it that no work is done at all, or that no work is done by the magnetic field, but some work is done by the generated electric field? $\endgroup$ – a.deshpande012 May 31 '20 at 7:27

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