Although all textbook references say that a current is not induced in a traditional Faraday wheel when just the magnet rotates and the wheel doesn't, this must be a false assumption. Otherwise, one of the basic laws of induction would be violated. There must be a current induced, but it's just too small to register. Possibly due to the resistance of the entire body of the conducting wheel between the two electrical contacts of the external circuit. Although it's worth noting that experimental tests of the Faraday paradox show only low level noise measured, the noise appears to have a polarity. Ie it is negative when the magnet is rotated in one direction. Unfortunately to date only one direction of magnet rotation is performed. It would be interesting to have further tests to be made to see if the noise does indeed show polarity. By measuring the noise from both clockwise and counterclockwise rotation of the magnet and see if the noise shows polarity.
To show that a current must be being induced in the conducting disc the following experiment should be performed. Take for example the traditional Faraday wheel shown at the top of the page of this link....
https://en.m.wikipedia.org/wiki/Homopolar_generator
(In particular note the external N-S magnetic field is only located at one point on the edge of the disc.)
Remove the conducting wheel from the lab setup. Replace that with a single conducting wire bridging the gap between the contacts at the axle and rim of the setup. This single conducting wire now connects to and completes the external circuit. Now perform the experiment again by rotating just the magnet. According to the laws of induction, every time the magnet passes over the outer end of the conducting wire, there should be a brief electrical current induced. Belying the assumption that no current is induced in the Faraday wheel when just the magnet rotates. Or if as in modern day experiments the magnet is a single disc magnet, then rotating it will give a constant induced current in the conducting wire.
Additionally if one were to position as many possible seperate conducting wires as possible, like spokes on a wheel, radiating out from the central axis to contacts at the periphery of the wheel, and each insulated from the other at the centre. One should then get multiple spikes of direct current in succession from each spoke as the magnet rotates around the stationary wheel, in the traditional faraday setup. Or constant direct currents where the magnet is a circular disc magnet.
