A long solenoid with 15 turns per cm has a small loop of area 2.0 cm² placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what is the induced emf in the loop while the current is changing?

Number of turns on the solenoid = 15 turns/cm = 1500 turns/m

Number of turns per unit length, n = 1500 turns

The solenoid has a small loop of area, A = 2.0 cm² = 2 x 10⁻⁴ m²

Current carried by the solenoid changes from 2 A to 4 A.

Therefore, change in current in the solenoid, di = 4- 2 = 2A

Change in time, dt = 0.1 s

Induced emf in the solenoid is given by Faraday’s law as: e =dφ/dt   ————Eq-1

Where, φ= Induced flux through the small loop =BA————–Eq -2                                                B = Magnetic field =μ0ni————–Eq -3

μ0 = Permeability of free space = 4π x10^-7 H/m

Hence,  equation (i) reduces to:

e =d/dt    (BA)

= Aμ0n (di/dt)

= 2 x 10⁻⁴ x 4π x10^-7 x 1500 x 2/ 0.1

= 7.54 x 10⁻⁶ V

Hence, the induced voltage in the loop is 7.54 x 10^-6V