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

$($ Take, $\left.\pi =\frac{22}{7}\right)$