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 $P Q$ is

• A. $B \omega r^{2}$
• B. $\frac{B \omega r^{2}}{2}$
• C. $4 B \omega r^{2}$
• D. $\frac{\pi^{2} r^{2} B \omega}{8}$

Answer 1

Answer: (A)

$|E|=$ Magnitude of induced emf
$=\frac{B \ell^{2}}{2} \omega, \ell=\sqrt{2} r$
$E=\frac{B\left(2 r^{2}\right) \omega}{2}=B \omega r^{2}$