JEE Advanced 2023 Physics question on Electromagnetic Induction and AC

A rectangular conducting loop of length 4 cm and width 2 cm is in the $xy$-plane, as shown in the figure. It is being moved away from a thin and long conducting wire along the direction $\dfrac{\sqrt{3}}{2}\,\hat{x} + \dfrac{1}{2}\,\hat{y}$ with a constant speed v. The wire is carrying a steady current $I = 10$ A in the positive $x$-direction. A current of 10 $\mu$A flows through the loop when it is at a distance $d = 4$ cm from the wire. If the resistance of the loop is 0.1 $\Omega$, then the value of v is ________ m s$^{-1}$.

[Given: The permeability of free space $\mu_0 = 4\pi \times 10^{-7}$ N A$^{-2}$]