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  $Z=\sqrt{3}R$  along the axis of the circular wire loop, as shown in figure. The plane of the square loop makes an angle of  ${45}^0$  with respect to  the z-axis. If the mutual inductance between the loop is given by  $\frac{{\mu }_0{a}^2}{2^{p/2}R}$ , then the value of p is