Magnetism

A rectangular conducting loop of length $4 \mathrm{~cm}$ and width $2 \mathrm{~cm}$ is in the $x y$-plane, as shown in the figure. It is being moved away from a thin and long conducting wire along the direction $\frac{\sqrt{3}}{2} \hat{x}+\frac{1}{2} \hat{y}$ with a constant speed $\mathrm{v}$. 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 $\mathrm{v}$ is ________ $\mathrm{m} \mathrm{s}^{-1}$.


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