This question reminds me of two problems that I wrote about years ago: "Faraday induction paradox"

and the "Feynman disc paradox". Here are some excerpts which may give some food for thought:

The Faraday induction paradox:

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"So the "flux rule"—that the emf in a circuit is equal to the rate of change of the magnetic flux through the circuit—applies whether the flux changes because the field changes or because the circuit moves (or both). The two possibilities—"circuit moves" or "field changes"—are not distinguished in the statement of the rule. Yet in our explanation of the rule we have used two completely distinct laws for the two cases— v x B for "circuit moves" and del x E = -¶B/¶t for "field changes".

We know of no other place in physics where such a simple and accurate general principle requires for its real understanding an analysis in terms of two different phenomena. Usually such a beautiful generalization is found to stem from a single deep underlying principle. Nevertheless, in the case there does not appear to be any such profound implication. We have to understand the "rule" as the combined effects of two quite separate phenomena."— Richard P. Feynman, The Feynman Lectures on Physics Vol. II, pp. 17-2

Note the asymmetry in the behavior. This seems to imply some sort of absolute motion. We probably are indeed missing a "profound implication". See also

http://en.wikipedia.org/wiki/Faraday%27s_law_of_induction ; http://en.wikipedia.org/wiki/Faraday_Paradox ; http://www.youtube.com/watch?v=1ZeCIejT2NY

More about the implications for absolute motion:

http://en.wikipedia.org/wiki/Faraday_Paradox (concerning a rotating disk, magnets, and currents generated, or not )

The experiment proceeds in three steps:

1. The magnet is held to prevent it from rotating, while the disc is spun on its axis. The result is that the galvanometer registers a direct current. The apparatus therefore acts as a generator, variously called the Faraday generator, the Faraday disc, or the homopolar (or unipolar) generator.

2. The disc is held stationary while the magnet is spun on its axis. The result is that the galvanometer registers no current.

3. The disc and magnet are spun together. The galvanometer registers a current, as it did in step 1.

Compare the behaviors in the Faraday paradox with the one often done in physics classes:

1. A small bar magnet is dropped down a plastic tube. Speed of fall is noted.

2. The same bar magnet is dropped down a copper tube.. Speed of fall is noted.

The magnet falls much more slowly in the copper tube. Is this consistent with result #2 of the Faraday paradox? What is happening to the magnetic flux?

***

Feynman disc paradox:

"Suppose we take the example of a point charge sitting near the center of a bar magnet, as shown in [the figure]. Everything is at rest, so the energy is not changing with time. Also, E and B are quite static. But the Poynting vector says that there is a flow of energy, because there is an E X B that is not zero. If you look at the energy flow, you find that it just circulates around and around. There isn't any change in the energy anywhere—everything which  flows into one volume flows out again. It is like incompressible water flowing around. So there is a circulation of energy in this so-called static condition. . . .

You no doubt begin to get the impression that the Poynting theory at least partially violates your intuition as to where energy is located in an electromagnetic  field. . . . The circulation of energy around a magnet and a charge seem, in most circumstances, to be quite unimportant. It is not a vital detail, but it is clear that our ordinary intuitions are quite wrong." (The Feynman Lectures on Physics, Vol. 2, p. 27-8) With that in mind, consider a little gizmo Feynman describes. It is very similar to our problem, except that it includes some spheres that are charged with static electricity:

(picture of Feynman disc)

"Do you remember the paradox we described in Section 17-4 about a solenoid and some charges mounted on a disc? It seemed that when the current turned off, the whole disc should start to turn. The puzzle was: Where did the angular momentum come from? The answer is that if you have a magnetic field and some charges, there will be some angular momentum in the field. It must have been put there when the field was built up. When the field is turned off, the angular momentum is given back. So the disc in the paradox would start rotating. This mystic circulating flow of energy, which at first seemed so ridiculous, is absolutely necessary. There is really a momentum flow. It is needed to maintain the conservation of angular momentum in the whole world." (p. 27-11)

What accuracy should the sensor have?

Is the experiment to be used in the student lab?

If so have you checked LD didactics? https://www.ld-didactic.de/en.html

Dear Brian,

Thank you very much for the extended information. The Faraday disc paradox is easily explained.

The production of the magnetic field in the magnetic bar is caused by the motion of electrons in a frame of protons. When the bar rotates, every change of motion of the electrons coincides with the motion of an opposite charge as well. Hence, no effect will be registered.

The rotation of the disc in the magnetic field will generate a Lorentz force upon the protons, and an opposite Lorentz force to the electrons, both radially. However, the free electrons can jump from one atom to the other, and produce a current. The protons cannot.

Something similar (but not the same) is happening in the copper tube when a magnetic bar is dropped. The Lorentz force acts on both the protons and the electrons, but in an electrical conductor, only the free electrons can move, and they will form a circular current, which will be more present at the conductor's surface. This is a property of electrical conduction.

A quite complex effect of local, magnetic attraction is created between the inner wall of the copper cylinder and the magnetic bar, which slows down the magnetic bar.

The Pointing vector is a model with an incomplete force of validity, and should not be used.

Dear Jonas,

Thank you for your interesting questions!

Yes, indeed, this can be performed in a lab, with an amber rod, which is made electrostatic.

The measuring device should be well shielded from any electrostatic discharge.

However, this measuring device for the magentic field should be quite sensible since the Lorentz force of the magnetic part will be F ~ v2/c2 compared with the electrical part.

The system can be put on (non-conducting) rails, and the sensor moving either with the rod, or standing still.

It should be a real exiting experiment to do.

P.S. Unfortunately, I didn't find anything that I could use in LD didactics.

I think that it is number 1 which has been never reported because labs in Earth are moving with Earth. Theoretically: the actual values in cases 1 and 2 are different, but the measured values are the same.

Dear Thierry,

If you can calculate the expected magnitude of the magnetic field, it might be easier to find suitable sensors.

When you want to experiment with the relativity, you need two frames which move with velocity comparable to the velocity of light. Therefore, it is difficult to do such an experiment in the lab.

The experiments that you discuss is related to the induced current which normally opposes the inducing magnetic field. In plastic not much current is induced. So less deceleration. In copper stronger current is induced, due to higher conductivity, so more deceleration. This experiment can not be used as the proof of relativity.