derive the expression for the mutual inductance of two long coaxial solenoids of same length l having radii r1 and r2 (r2>r1 and l>>r2). is it the derivation for mutual inductance due to two solenoids?

Ans- 

 

Suppose a current i is passed through the inner solenoid . A magnetic field  is produce inside  whereas field outside it is zero.

 is permeability of vaccum.

 

Let  and  be the no of turns it each solenoid of equal length l.

Therefore, flux through each turn of solenoid  is

 

The total flux through all the turns in a length l of  is

 

And we know that  where M is the mutual inductance.

Therefore mutual inductance of two long coaxial solenoids of same lenth is