# A long solenoid with 1.5 turns per cm has a small loop of area 2.0 cm^2 placed inside the solenoid normal to its axis…

Q: A long solenoid with 1.5 turns per cm has a small loop of area 2.0 cm^2 placed inside the solenoid normal to its axis. If the current in the solenoid changes steadily from 2.0 A to 4.0 A in 1.0 s. The emf induced in the loop is

Sol: The magnetic field along with the axis of solenoid is B = μ_0ni where n is no. of turns per units length
Flux through the smaller loop placed in solenoid is φ = B × A  ; since current in solenoid is changing, emf induced in loop is

$\large e = \frac{d \phi}{dt}$

$\large e = \frac{d}{dt}(\mu_0 n i A)$

$\large e = (\mu_0 n A)\frac{d i}{dt}$

$\large e = 4\pi \times 10^{-7} \times 1.5 \times 10^2 \times 2 \times 10^{-4}( \frac{4-2}{1-0})$

= 0.75 × 10-6 V