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A metal disc spins freely between the poles of a magnet in the direction shown. Brush P touches the rim of the disc and brush Q touches the metal axle, and they are connected through a resistor R. What current, if any, flows through R?

1. a current from P to Q
2. a current from Q to P
3. no current, because the emf in the disc is opposed by a back emf
4. no current, because the emf induced in one side of the disc is opposed by the emf induced in the other side
5. a current flows (Faraday disc / homopolar generator), its direction set by v x B from axle to rim

Correct answer: a current from P to Q

Solution

Each element of the rotating conducting disc moves with velocity v in the field B, so free charges feel a force q(v x B) directed radially. This produces a steady (radial) motional emf between the axle and the rim - the principle of the homopolar generator. A current therefore flows through R; with the indicated rotation and field, the rim is at higher potential, driving conventional current from the rim brush P through R to the axle brush Q (P to Q). The 'no current' options are wrong because a net radial emf does exist.

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