Faraday's paradox: homopolar generator on a train

[Drakkith]

Yes, blue horseshoe thing is the magnet. That's the original design Faraday used, that's what he was talking about when he was puzzled with the paradox himself, so I don't think it produces different results than disk magnets, but we can analyze both and see how it fits.

Well, for one thing, the magnet is no longer simply rotating, but moving around the edge of the disk so that a varying magnetic field is felt by the charges in the disk. This should result in an induced electric field that exerts a radial force on the charges and causes current to flow. The effects should be exactly the same as when the disk is spinning and the magnet is stationary.

 

[carrz]

Ad #44: Finally you provided a clear picture. The upper one is the classical Faraday Disk setup. Of course, an EMF is induced. The calculation is precisely the same as the one I've given yesterday. It doesn't matter here, whether the magnet is rotating with the disk or not. The EMF is due to the drift of the electrons in the conductor which builds up an electric field.

The EMF is due to the drift of the electrons. And drift of electrons is due to Lorentz force. So then what is Lorentz force due in the 1st scenario, why there is no Lorenz force in the 2nd scenario, and what is Lorentz force due in the 3rd scenario?

The 2nd setup is not as clear to me, because it's not properly written what represents what. I guess the horse-shoe shaped thing is the magnet and you consider two cases: (a) only the disk is rotating and the magnet stays fixed and (b) the magnet is fixed at the disk and rotating with it. In both cases you measure an EMF. In case (a) it's qualitatively the same as with the first case: The magnetic field is time-independent and the electrons in the conductor drift due to the Lorentz force \vec{v}\times \vec{B}/c building up an electric field.

What is that velocity of and what is it relative to?

In case (b) the magnet is rotating and thus you have both a magnetic and an electric field. In principle you can calculate both by using Maxwell's equations, noting that the magnetization of the permanent magnet is equivalent to a current \vec{j}_{\text{mag}}=c \vec{\nabla} \times \vec{M}. In any case the electrons in the conducting disk are drifting again due to the Lorentz force due to the electromagnetic field of the rotating magnet.

What is the difference between the magnet and the disk spinning together and them being stationary on a train that circles around the world?

 

[Dale]

This thread is hopelessly confused. There are at least three different sets of scenarios, some with three sub scenarios being discussed, and the OP throws in a train to make it more confusing.

Carrz, please start a new thread picking at most two scenarios (or one scenario in two reference frames), as simple as possible, clearly described, and stick to those alone. Everyone else, please stick with the requested scenario in your comments.

Carrz, please realize that a paper may not exactly duplicate your scenario, but still provide value, if you think that it is substantively inapplicable please explain in detail why. Simple dismissal of referenced material is irritating to people who did the research and thought it would help.