A circular wire loop of radius R is placed in the x-y plane centered at the origin O. A square loop of side a (a << R) having two turns is placed with its centre at $\mathrm{z}=\sqrt{3}\mathrm{R}$  along the axis of the circular wire loop, as shown in figure. The plane of the square loop makes an angle of 45° with respect to the z-axis. If the mutual inductance between the loops is given by $\frac{{\mathrm{\mu }}_0{\mathrm{a}}^2}{2^{\mathrm{p}/2}\mathrm{R}}$ , then the value of p is