Question

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?

Answer 1

Let,

n1  = Number of turns per unit length of S1

n2 = Number of turns per unit length of S2

I1 = Current passing through solenoid S1

= Flux linked with S2  due to current flowing in S1

 

 is the coefficient of mutual inductance of two solenoids.

When current is passed through S1, emf is induced in S2 .

Magnetic field inside solenoid S1 is given by, 

Magnetic flux linked with each turn of the solenoid  =  

Total magnetic flux liked with S2 is given by,

 

Similarly, mutual inductance between two solenoids, when current is passed through S2 and emf induced in solenoid S1 is given by, 

 

Hence, coefficient of mutual induction between the two long solenoids is given by,