A conducting circular loop is placed in a uniform magnetic field of 10 T with its plane normal to the field. Now, the radius of the loop starts shrinking at the rate 5 mm/s. When the radius is 5 cm then the induced emf is

15.7 mV

The correct answer is Option (2) → 15.7 mV

Magnetic flux through the loop:

$\Phi = B \cdot A = B \cdot \pi r^2$

Induced emf:

$\mathcal{E} = -\frac{d\Phi}{dt} = -B \cdot \frac{d}{dt}(\pi r^2)$

$\mathcal{E} = -B \cdot (2\pi r \cdot \frac{dr}{dt})$

Taking magnitude:

$\mathcal{E} = 2\pi B r \cdot \frac{dr}{dt}$

Substitute values: $B = 10 \,T,\; r = 5 \,cm = 0.05 \,m,\; \frac{dr}{dt} = 5 \,mm/s = 0.005 \,m/s$

$\mathcal{E} = 2 \pi (10)(0.05)(0.005)$

$\mathcal{E} = 2 \pi (0.0025)$

$\mathcal{E} = 0.0157 \, V \approx 1.57 \times 10^{-2} \, V$

Answer: $1.57 \times 10^{-2} \, V$