question_answer

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).