A rectangular conducting loop of length $4 \mathrm{cm}$ and width $2 \mathrm{cm}$ 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 $\frac{\sqrt{3}}{2}\stackrel{\wedge }{x}+\frac{{\displaystyle 1}}{{\displaystyle 2}}\stackrel{\wedge }{y}$ with a constant speed $v$. The wire is carrying a steady current $I=10 \mathrm{A}$ in the positive $x$-direction. A current of $10 \mu \mathrm{A}$ flows through the loop when it is at a distance $d=4 \mathrm{cm}$ from the wire. If the resistance of the loop is $0.1 \Omega$, then the value of $v$ is _____ $\mathrm{m} {\mathrm{s}}^{-1}$.

[Given: The permeability of free space ${\mu }_0=4\pi \times {10}^{-7} \mathrm{N} {\mathrm{A}}^{-2}$]

Hence, the correct answer is 4.