Question

Two identical conducting rings $A$ and $B$ of radius $R$ are rolling over a horizontal conducting plane with same speed $v$ but in opposite direction. A constant magnetic field $B$ is present pointing into the plane of the paper. Then the potential difference between the highest points of the two rings is

• A. $0$
• B. $2BvR$
• C. $4BvR$
• D. none of these
• E. answer required

Answer 1

Answer: (C)

$4BvR$

Let us consider one ring, travelling in one direction. Each ring has two components of velocity, the linear component and the angular component.

The potential difference induced between the top and bottom points of each ring due to the angular component is zero.

The potential difference induced between the same points due to linear component $={\int }_{0-\pi /2}^{\pi /2}B\left(vcos\theta \right)Rd\theta$

$=2BvR$

This is the potential difference between top and bottom points of one ring.

Similarly the potential difference between top and bottom of other ring is $2BvR$, however the polarity is opposite since the rings travel in opposite directions. The potential of the bottom of both ring is equal(connected).

Hence potential difference between top of both the rings $=2BvR-(-2BvR)=4BvR$