Question

A vertical conducting ring of radius $R$ falls vertically with a speed $V$ in a horizontal uniform magnetic field $B$ which is perpendicular to the plane of the ring. Which of the following statements is correct?

• A. $A$ and $B$ are at the same potential
• B. $C$ and $D$ are at the same potential
• C. current flows in clockwise direction
• D. current flows in anticlockwise direction

Answer 1

Answer: (B)

When the ring falls vertically, there will be an induced emf across $A$ and $B(e=Bv(2r))$.
Note that there will be a potential difference across any two points on the ring, and the line joining these has a projected length in the horizontal plane. For example, between points $P$ and $\bar{Q}$ there is a projected length $x$ in the horizontal plane.
$\therefore$ P.D. across $P$ and $Q$ is
$\cdot V=Bvx$
But for points $C$ and $D,x=0$
Therefore, P.D. $=0$