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

Explanation

The magnetic field along the axis of solenoid is `B = mu_(0) n i` where `n` is no. of turns per unit length.
flux through the smaller loop placed in solenoid is `phi = B xx A` Since current in solenoid is changing, emf induced in loop is `e = (d phi)/(dt) = (d)/(dt)[mu_(0)niA]`,
`e = mu_(0)nA((di)/(dt))`
`= 4pi xx 10^(-7) xx 1.5 xx 10^(2) xx 2 xx 10^(-4) xx ((4-2)/(1-0))`
`= 0.75 xx 10^(-6) V`