A circular wire loop of radius R is placed in the $\mathrm{x}-\mathrm{y}$ plane centered at the origin O . A square loop os side a (a $\ll \mathrm{R}$ ) having two turns is placed with its center at $\mathrm{a}=\sqrt{3} \mathrm{R}$ along the axis of the circular wire loop, as shown in figure. The plane of the square loop makes an angle of $45^{\circ}$ with respect to the z-axis. If the mutual inductance between the loops is given by $\frac{\mu_0 a^2}{2^{p / 2} R}$, then the value of $p$ is