Question

A conducting ring of radius $r$ and resistance $R$ is placed in a region of uniform time varying magnetic field $B$ which is perpendicular to the plane of the ring. If the magnetic field is changing at a rate $\alpha $ , then the current induced in the ring is

• A. $\frac{\pi r^{2} \alpha }{2 R}$
• B. $\frac{2 \pi r \alpha }{R}$
• C. $\frac{ \pi r \alpha }{R}$
• D. $\frac{\pi r^{2} \alpha }{R}$

Answer 1

Answer: (D)

The magnitude of the induced emf in the ring is
$\left|\epsilon \right|=\frac{d \phi}{d t}=\frac{d}{d t}\left(B A\right)=A\frac{d B}{d t}=\pi r^{2}\alpha $
The induced current in the ring, $I=\frac{\left|\epsilon \right|}{R}=\frac{\pi r^{2} \alpha }{R}$