question_answer

Two identical conducting ring A and B of radius R are in pure rolling over a horizontal conducting plane with same speed (of center of mass) v 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:

A) Zero                   

B)        2BvR

C) 4BvR          

D)        None of these

Correct Answer: C

Solution :

[c] 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 In Ring \[''A'':eA=BV\left( 2R \right)\] In Ring  \[''B'':cb=B\left( V \right)\left( 2R \right)\] \[\therefore \] potential difference between upper points \[=BV\left( 2R \right)+BV\left( 2R \right)=4BVR\]