Question

Two conducting rings $P$ and $Q$ of radii $r$ and $2r$ rotate uniformly in opposite directions with centre of mass 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. Zero
• B. $4Bvr$
• C. $8Bvr$
• D. $16Bvr$

Answer 1

The correct option is C $8Bvr$

Let $A$ be topmost point of smaller ring and
$B$ be topmost point of larger ring

Due to motional emf generated in the rings, the circuit can be redrawn as

$V_P+4Bvr=V_A$
$V_Q-4Bvr=V_B$
$\overline{V_A-V_B=8Bvr\text{as}{V}_P=V_Q}$