Question

A conducting circular loop is placed in a uniform magnetic field, B = 0.025 T with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of 1 mm s-1. The induced emf when the radius is 2 cm, is

• A. $2\pi\mu V$
• B. $\pi\mu V$
• C. $\frac{\pi}{2}\mu V$
• D. $2\mu V$

Answer 1

Answer: (B)

$\pi\mu V$

Answer 2

Here,

Magnetic field, $B = 0.025T$

Radius of the loop, $r = 2cm = 2 \times 10^{- 2}m$

Constant rate at which radius of the loop shrinks

$\frac{dr}{dt} = 1 \times 10^{- 3}ms^{- 1}$

Magnetic flux linked with the loop is

$\varphi = BA\cos\theta = B(\pi r^{2})\cos 0º = B\pi r^{2}$

The magnitude of the induced emf is

$|\varepsilon| = \frac{d\varphi}{dt} = \frac{d}{dt}(B\pi r^{2}) = B\pi 2r\frac{dr}{dt}$

$= 0.025 \times \pi \times 2 \times 2 \times 10^{- 2} \times 1 \times 10^{- 3}$

$\pi \times 10^{- 6}V = \pi\mu V$