The magnitude of magnetic dipole moment of the loop shown in figure is  $M=\frac{N\pi I}{2}\left(inward\right)$. Where $R_2^{ }=2m$ and $R_1^{ }=4m$ . Find value of $N$ ?

The given loop may be considered as the superposition of the two loops, as shown in the figure.

The resultant dipole moment is $M=\frac{\pi R_1^{2}I}{2}-\frac{\pi R_2^{2}I}{2}$  or  $M=\frac{\pi I}{2}(R_1^2-R_2^2)\left(inward\right)$