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Question

Two conducting rings P and Q of radii r and 2r rotate uniformly in opposite directions with centre of mass velocities 2v and v respectively on a conducting surface S. There is a uniform magnetic field of magnitude B perpendicular to the plane of the rings. The potential difference between the highest points of the two rings is

A
Zero
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B
4 Bvr
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C
8 Bvr
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D
16 Bvr
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Solution

The correct option is C 8 Bvr
Let A be topmost point of smaller ring and
B be topmost point of larger ring

Due to motional emf generated in the rings, the circuit can be redrawn as

VP+4 Bvr=VA
VQ4 Bvr=VB
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯VAVB=8 Bvr as VP=VQ

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