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. $0$
• B. $8Bvr$
• C. $4Bvr$
• D. $16Bvr$

Answer 1

The correct option is B $8Bvr$

EMF between the top and bottom ends of the small ring is $B\times 2v\times 2r=4Bvr$

EMF between the top and the bottom ends of the larger ring is $B\times v\times 4r=4Bvr$
So the potential difference between the two top ends is $4Bvr+4Bvr=8Bvr$ (due to opposite polarity)