There is a the system of two concentric loops of radii r and R `(R gt gt r)` . Find the mutual inductance of the system . If the loops have currents of same magnitude `i_(0)` lgnore the effect of self inductance .

Explanation

Let current I is setup in the loop 1. It develops magnetic field of induction `B_(1) = (mu_(0)i)/(2R) ` at its center. The flux linked by the ( smaller) loop 2
`phi_(12)= B_(1)(pir^(2))= piB_(1)r^(2)`
Putting the value of `B_(1)= (mu_(0)i)/(2R)` we obtain mutual inductance
`M= (phi_(12))/(i)=(pimu_(0)r^(2))/(2R) `