Question

A conducting ring of radius $r$ is rolling without slipping with a constant angular velocity $\omega$ (figure). If the magnetic field strength is $B$ and is directed into the page then the emf induced across $PQ$ is

• A. $B\omega r^2$
• B. $\frac{B\omega r^2}{2}$
• C. $4B\omega r^2$
• D. $\frac{B\omega r^2}{4}$

Answer 1

The correct option is A $B\omega r^2$

Let the velocity of each point due to rotation form an angle $\theta$ with the vertical.

EMF induced across PQ $={\int }_0^{\pi /2}B\left(r\omega \cos \theta \right)\left(rd\theta \right)$

$={\int }_0^{\pi /2}B{r}^2\omega \cos \theta d\theta =B\omega r^2$