Compute the mutual inductance:

A long single layer solenoid has an effective diameter of 10 cm and it is wound with 1000 turns/m. There is a small concentrated coil with its plane lying in the centre cross-sectional plane of the solenoid. Compute the mutual inductance among two coils if the concentrated coil has 100 turns and an effective diameter of 4 cm.

Solution

Figure  is illustrated as follows :

Figure

Let current I₁ is flowing through the solenoid. Then the flux density B is given by  

= μ 1000 I₁  (wb/ m²)

So the flux linked with concentrated coil:

φ₂  = BA₂

The cross-sectional area of concentrated coil is following:

A₂ = π r ²   =π (4 × 10^-2 /2)²

= 12.568 × 10^{- 4} m²

∴          Flux φ₂ = μ₀ 1.256 I₁ wb

Mutual inductance between coil and solenoid

M = N₂ φ₂ / I₁

= 100 × μ₀ × 1.256 I₁  / I₁= 125.6 μ_o  Henry