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Two geometrically identical bicycle wheels differ only in their number of spokes: one has 20 spokes, the other 10. The rims and spokes have zero resistance. A resistor R is connected between the centre (axle) and the rim of each. When the wheels rotate in a magnetic field, the current through R is:

1. twice as large in the first wheel as in the second
2. four times as large in the first wheel as in the second
3. twice as large in the second wheel as in the first
4. the same in both wheels

Correct answer: the same in both wheels

Solution

Every spoke develops the same motional emf and all spokes are connected between the same two nodes (the axle and the rim), so they are all in parallel and have identical emf. Parallel identical emf sources of zero internal resistance behave like a single source of that same emf. Since the spokes are resistanceless, the emf across R is the same regardless of how many spokes there are. Hence the current through R is identical for both wheels.

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