Define the term 'mutual inductance' between the two coils.
Obtain the expression for mutual inductance of a pair of long coaxial solenoids each of I and radii `r_(1) and `r_(2)(r_(2)gt gt r_(1))`. Total number of solenoids are `N_(1) and N_(2)` respectively.

Explanation

(i) The ratio of magnetic flux passing through one coil to the current passing through the other is known as mutual inductance between the two coils.
Suppose a current is passed through the inner solenoid `S_(1)`. A magnetic field `B=mu_(0)n` is produced inside `S_(1)`, whereas, the field outside it is zero.
The flux through each turn `S_(2)" is "bet pir_(1)""^(2)=mu)n,ipir_(1)""^(2)` the total flux through all the turns in a length l of `s_(2)` is
`phi=(,mu_(0)n_(1)ipir_(1)""^(2))n_(2)l`
`=(mu_(0)n_(1) n_(2)r_(1)""^(2)e)i`
`M=mu_(0
)n_(1)n_(2)pir_(1)""^(2)l`.