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

Answer

`7.`

Explanation

`B = (mu_(0)iR^(2))/(2(R^(2) xx X^(2))^(3//2))`
`B = (mu_(0)iR^(2))/(2(R^(2) xx 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 = 2 (mu_(0)i)/(16R) a^(2) (1)/(sqrt(2)) = (mu_(0)ia^(2))/(8sqrt(2)R)`
`M = (phi)/(i)`
`M = (mu_(0)a^(2))/(2^(7//2)R) = (mu_(0)a^(2))/(2^(p//2)R)`
`p = 7`