Find the mutual inductance of two long concentric solenoids for a length l. The area of cross-section of inner solenoid is A and number of turns per unit length are `n_(1)` and `n_(2)`.

Explanation

A current `i` is passed through inner solenoid having `n_(1)` number of turns/length. The magnetic field is `B=mu_(0)n_(1)i`. This magnetic field axists uniformly across the area A. The flux linked with outer solenoid is
`phi=(n_(2)xxl)xxBxxA" "(because n_(2)xxl=" number of turns in length l")`
`phi=(n_(2)xxl)xxmu_(0)n_(1)iA`
`phi=mu_(0)n_(1)n_(2)Ali`
`"as "M=phili`
`rArr" "M=mu_(0)n_(1)n_(2)Al`.