A conducting circular loop is placed in a uniform magnetic field of 0.5 T, with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at the rate of 4 mm/s. When the radius of the loop is 4 cm, the induced emf in the loop is

$1.6π\, μV$

The correct answer is Option (2) → $1.6π\, μV$ **

Given:

Magnetic field, $B = 0.5\ \text{T}$

Rate of change of radius, $\frac{dr}{dt} = -4\ \text{mm/s} = -0.004\ \text{m/s}$

Radius of loop, $r = 4\ \text{cm} = 0.04\ \text{m}$

Magnetic flux through the loop, $\Phi = B \cdot A = B \cdot \pi r^2$

Induced emf, $\mathcal{E} = \left| \frac{d\Phi}{dt} \right| = B \cdot \frac{d(\pi r^2)}{dt} = B \cdot 2\pi r \frac{dr}{dt}$

Substitute values:

$\mathcal{E} = 0.5 \cdot 2 \pi (0.04)(0.004)$

$\mathcal{E} = \pi \cdot 0.04 \cdot 0.004 = \pi \cdot 0.00016 $

∴ Induced emf in the loop = $1.6π\, μV$