Two identical conducting rings A & B of radius R are in pure rolling over a horizontal conducting pl

Question

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

Accepted Answer

Considering a projected length 2R 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.
e = Bv(2R) in the ring.
In Ring ″A″ : eA =B(-v)(2R)
In Ring ″B″ : eB = B(v)(2R)
Therefore, potential difference between A & B = B(v)(2R) - B(-v)(2R) = 4 BvR.
Note : there wil be no p.d. across a diameter due to rotation.
Alternate – Considering rotation of diameter about lowest point :
e = = 2Bvr in A (since pure rotation).
and e = − 2Bvr in B.

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