# Spinning a Magnet About its Axis

Q:
Magnets rotating about their axis and Faraday's Law Suppose you have a stationary cylindrical permanent magnet ,which is magnetized axially, and a electrically conductive rod pointed directly at the center of the magnet and revolving around it within a plane perpendicular to the magnet's axis. An electrical potential will develop between the two ends of the rod due to electromagnetic induction (Faraday's Law). My first question: What will happen if the magnet is rotating at the same rate and in the same direction that the conductor is revolving around it? If the magnetic field is “bound” to the spinning (at the quantum level) electrons that are responsible for it and it rotates with them, then I would expect that the conductor would no longer be “cutting through” the field lines and producing a electrical potential. Otherwise, I would not expect rotation of the magnet to make a difference. Second question: What if the permanent magnet was replaced by a current loop? The moving electrons will clearly have a average direction around the loop. Polarity aside, does the magnitude of the charge developed by the conductor depend on whether the its movement is co-rotational or anti-rotational with the flow of electrons? If there is any deference, then it would open up an intriguing possibility of using satellite based instruments to probe, and even map, the Earth's internal mechanisms that create its magnetic field. [For context, this question was spurred by an article about the use of electrodynamic tethers to deorbit defunct satellites, thoughts about the effects of the Earth's rotation, and their effectiveness for geostationary satellites.]
- Alec (age 30)
Lewiston, Maine, USA
A:

This is a thought-provoking set of questions.

Let me answer the 2nd one first. All the local electromagnetic effects are fully described by the local electromagnetic field. So unfortunately there's no clever way of moving around local conductors etc. to find out something more about the sources of that field.

That means that your first question boils down to whether spinning that magnet about its axis changes its field in some way. In particular, we're interested in whether it makes a radial electric field and thus changes the electrical effects on the rotating conductor. The spinning doesn't break the cylindrical symmetry of the problem. So any radial field would be outwards everywhere or inwards everywhere. That would require that the magnet not be electrically neutral- but it is.

So it looks like spinning that magnet about its axis won't affect the potential on the conductor. (We're ignoring general relativistic effects such as frame-dragging, which would all be very weak.)

Mike W.

(published on 03/24/2014)

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