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Find the mutual inductance of two long c...

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)`.

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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 exists uniformly across the area A. The flux linked with outer solenoid is
`phi= (n_(2) xx l) xx B xx A` (`n_(2) xx i= "numbers of turns in lenght l"`)
`phi= (n_(2) xx l) xx mu_(0)n_(1)i`
`phi= mu_(0)n_(1) n_(2)Ali`
as `M= phi li`
`implies M= mu_(0)n_(1) n_(2)Al`
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