Two conducting rings P and Q of radius r and 3r move in opposite directions with 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) 2Brv
C) 6Brv
D) 10Brv
Correct Answer:
D
Solution :
\[{{V}_{A}}={{V}_{B}}=(B)(2v)(2r)\] \[=4\,vr\] (1) \[{{V}_{C}}-{{V}_{D}}=(v)(v)(6r)=6\,Bvr\] (2) Further \[{{V}_{A}}={{V}_{D}},\]from (1) and (2) \[{{V}_{C}}-{{V}_{B}}=10\,Bvr\] Hence, the correction option is (d).