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`(altltR)` having two turns is placed with its centre at `=sqrt(3)R` along the axis of hte 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 bu `(mu_(0)a^(2))/(2^(p//2)R)`, then the value of p is

Explanation

The magnetic field due to current carrying wire at the location of square loop is
`B=(mu_0)/(4 pi)(2 pi iR^2)/((R(2)+3R^(2))^(3//2)=(mu_(0)i)/(16R)`
`M=(N phi)/(i) =2/i [(mu_(0)i)/16 R)xx(a^2) cos 45^(@)]`
`:. M=(mu_(0)a^(2))/((7)/(2^(2)R))`.