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

`B=(mu_(0)iR^(2))/(2(R^(2)+X^(2))^(3//2))`
`B=(mu_(0)iR^(2))/(2(R^(2)+3R^(2))^(3//2))=(mu_(0)iR^(2))/(2(4R^(2))^(3//2))=(mu_(0)iR^(2))/(2.2^(3).R)=(mu_(0)i)/(16R)`
`phi=NBA cos45^(@)`
`=2(mu_(0)i)/(16R)a^(2)1/sqrt2`
`phi=(mu_(0)ia^(2))/(8sqrt2R)`
`M=phi/i`
`M=(mu_(0)a^(2))/(2^(7//2)R)=(mu_(0)a^(2))/(2^(P//2)R)`
`P=7`