Two identical conducting rings P & Q of radius R are in pure rolling over a horizontal conducting plane with same speed (of center of mass) ‘v’ but in opposite direction . A constant magnetic field B is present pointing into the plane of paper. Then the potential between the highest points of two rings, is :

zero

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2 Bvr

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4 Bvr

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8 Bvr-

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Solution

The correct option is C
4 Bvr

Considering a projected length 2 R on the ring in vertical plane.
This length will move at a speed v perpendicular to the field. This results in an induced emf : e = Bv(2R) in the ring
In Ring P : e = A = B (–v)(2R) ; In Ring Q : e = A = B(v) (2R)
Therefore, potential difference between P & Q = B(v) (2R) – B(–v)(2R) = 4 BvR

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