Question

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. $\text{zero}$
• B. $2Brv$
• C. $6Brv$
• D. $10Brv$

Answer 1

The correct option is D $10Brv$

Let say, magnetic field is inwards.

$V_A-V_B=\left(B\right)\left(2v\right)\left(2r\right)=4Bvr...\left(1\right)$
$V_D-V_C=\left(B\right)\left(v\right)\left(6r\right)=6Bvr...\left(2\right)$
Further $V_A=V_C$, therefore, from Eq. $\left(1\right)$ and Eq. $\left(2\right)$
$V_D-V_B=10Bvr$