Question

Two conducting rings of radii r and 2r move in opposite directions with 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. $zero$
• B. $2rvB$
• C. $4rvB$
• D. $8rvB$

Answer 1

Answer: (D)

$8rvB$

Replace the induced emf in the rings by cells.
${\epsilon }_1=B2r\left(2v\right)=4Brv.$
${\epsilon }_2=B\left(4r\right)v=4Brv$.
$V_2-V_1={\epsilon }_2+{\epsilon }_1=8Brv$.