Two identical conducting rings `A` and `B` of radius `R` are rolling over a horizontal conducting plane with same speed `v` but in opposite direction. A constant magnetic field `B` is present pointing into the plane of paper. Then the potential difference between the highest points of the two rings is

Options

A. Zero
B. 2 Bvr
C. 4 Bvr
D. none of these

Answer

C

Explanation

Considering a projected length 3R on the ring in vertical plane
This length will move at a speed b 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 rotating of diameter about lowest point :
`e=(B omega(2r)^(2))/(2)=2Bvr A` (since pure rotation).