Question

Obtain the expression for mutual inductance of a pair of long coaxial solenoids each of length l and radii r₁ and r₂ (r₂ >> r₁). Total number of turns in the two solenoids are N₁ and N_2, respectively.

Answer 1

Suppose a current i is passed through the inner solenoid S₁.

A magnetic field B=μ₀n₁i is produced inside S₁ , whereas the field outside it is zero.

The flux through each turn S₂ is Bπr₁²=μ₀n₁iπr₁²

The total flux through all the turns in a length l of S₂ is

ϕ=(μ₀n₁iπr₁²)n₂l=(μ₀n₁n₂πr₁²l)i

⇒M=μ₀n₁n₂πr₁²l