A square loop of side 2 . 0cm is placed inside a long solenoid that...

It is given that the current is varying sinusoidally. The current can be written as $I = {I}_{0}sin\omegat$.

The magnetic field through the solenoid $B = {\mu}_{0}nI$

The flux through the square is $ϕ = {\mu}_{0}nIA$

The emf is

$ε = {\mu}_{0}nA \times \dfrac{d ( {I}_{0}sin\omegat )}{dt} ⇒ ε = {\mu}_{0}nA{I}_{0}\omega cos\omegat$

The amplitude of the emf is,

$ε = {\mu}_{0}nA{I}_{0}\omega = 4\pi \times {10}^{- 7} \times \dfrac{50}{{10}^{- 2}} \times 4 \times {10}^{- 4} \times 2 . 5 \times 700 ⇒ ε = 44 \times {10}^{- 4}V$