Question

Two conducting rings P and Q of radii and r and 2r rotate uniformly in opposite directions with centre of mass velocities 2 v 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. (a) zero
• B. (b) 4 Bvr
• C. (c) 8 Bvr
• D. (d)16 Bvr

Answer 1

The correct option is C (c) 8 Bvr

Effective length moving in magnetic field is $2r$ and $4r$ respectively.

$\therefore E_1=B\left(2r\right)\left(2v\right)=4Bvr$

$E_r=B\left(4r\right)\left(v\right)=4Bvr$

To find the potential difference, we replace the induced emfs in the rings by cells.

$\therefore$ Potential Difference $=E_1+E_2=8Bvr$