A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s.
The EMF induced in the loop is ____ mV.

We need to find the EMF induced when a circular loop is converted into a square loop in a magnetic field.

By Faraday’s law of electromagnetic induction, the EMF is given by $$\text{EMF} = -\frac{d\Phi}{dt} = -B\frac{dA}{dt} \approx B\frac{|\Delta A|}{\Delta t}$$, where $$\Phi = BA$$ is the magnetic flux (since $$B$$ is uniform and perpendicular to the loop), and $$\Delta A$$ is the change in area.

First, the area of the circular loop is calculated. With radius $$r = 7 \, \text{cm} = 0.07 \, \text{m}$$, we have $$A_{\text{circle}} = \pi r^2 = \pi \times (0.07)^2 = \pi \times 0.0049 = 0.015394 \, \text{m}^2$$.

Next, when the wire is reshaped into a square, its perimeter remains equal to that of the original circle. Since the circumference is $$2\pi r = 2\pi \times 0.07 = 0.4398 \, \text{m}$$, each side of the square measures $$\frac{2\pi r}{4} = \frac{\pi r}{2} = \frac{\pi \times 0.07}{2} = 0.10996 \, \text{m}$$.

Accordingly, the area of the square becomes $$A_{\text{square}} = \left(\frac{\pi r}{2}\right)^2 = \frac{\pi^2 r^2}{4} = \frac{\pi^2 \times 0.0049}{4} = \frac{0.04835}{4} = 0.012088 \, \text{m}^2$$.

Therefore, the change in area is $$|\Delta A| = A_{\text{circle}} - A_{\text{square}} = 0.015394 - 0.012088 = 0.003306 \, \text{m}^2$$.

Finally, substituting this into Faraday’s law yields $$\text{EMF} = B \times \frac{|\Delta A|}{\Delta t} = 0.2 \times \frac{0.003306}{0.5} = 0.2 \times 0.006612 = 0.001322 \, \text{V}$$, or equivalently $$\text{EMF} = 1.32 \, \text{mV}$$.

The correct answer is Option (4): 1.32 mV.