A square loop of side 2.0 cm is placed inside a long solenoid that has 50 turns per centimetre and carries a sinusoidally varying current of amplitude 2.5 A and angular frequency 700 rad s$$^{-1}$$. The central axes of the loop and solenoid coincide. The amplitude of the emf induced in the loop is $$x \times 10^{-4}$$ V. The value of x is _______ (Take, $$\pi = \frac{22}{7}$$)

$$n = 50/\text{cm} = 5000/\text{m}$$, area of loop = $$(0.02)^2 = 4 \times 10^{-4}$$ m².

Flux: $$\Phi = \mu_0 n I A = 4\pi \times 10^{-7} \times 5000 \times 2.5\sin(700t) \times 4 \times 10^{-4}$$

EMF amplitude = $$\mu_0 n I_0 A \omega = 4\pi \times 10^{-7} \times 5000 \times 2.5 \times 4 \times 10^{-4} \times 700$$

$$= 4 \times 22/7 \times 10^{-7} \times 5000 \times 2.5 \times 4 \times 10^{-4} \times 700$$

$$= 88/7 \times 10^{-7} \times 5000 \times 700 \times 10^{-3}$$

$$= 88/7 \times 3500 \times 10^{-7} = 44000 \times 10^{-7} = 44 \times 10^{-4}$$ V.

The answer is 44.