Find the mutual inductance between two coaxial loops of radii R and r (R gtgt r) with separation between the centre x.

Explanation

Let a current `i` flows through coil of radius R. The field proeduced at the centre of the other coil is
`B=(mu_(0)ixx2xxpiR^(2))/(4pi(R^(2)+x^(2))^(3//2))`
As R gtgt r. this field can be assumed to be acting
on the entire area of the smaller loop.
Thus `phi=BxxA`
i.e., `phi=(mu_(0)ixx2xxpiR^(2))/(4pi(R^(2)+x^(2))^(3//3))xxpir^(2)`
as `M=(phi)/(i)`
`rArr" "M=(mu_(0)piR^(2)r^(2))/(2(R^(2)+x^(2))^(3//2))`