Question

A uniform magnetic field B points vertically up and is slowly changed in magnitude, but not in direction. The rate of change of the magnetic field is $\alpha$. A conducting ring of radius r and resistance R is held perpendicular to the magnetic field and is totally inside it. The induced current in the ring is then

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

Answer 1

Answer: (D)

$\frac{\pi r^2\alpha }{R}$

given:

Rate of change of magnetic field $\frac{dB}{dt}=\alpha$

The magnitude of induced emf is:$|ϵ|$

$=\frac{d\varphi }{dt}=\frac{d}{dt}BA=A\frac{dB}{dt}=\pi r^2\alpha$

The induced current in the ring, $I=\frac{|ϵ|}{R}=\frac{\pi r^2\alpha }{R}$