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 I_{1} is flowing through the solenoid. Then the flux density B is given by
= μ 1000 I_{1 }(wb/ m^{2})
So the flux linked with concentrated coil:
φ_{2 } = BA_{2}
The cross-sectional area of concentrated coil is following:
A_{2} = π r ^{2 } =π (4 × 10^{-2} /2)^{2}
= 12.568 × 10^{- 4} m^{2}
∴ Flux φ_{2} = μ_{0} 1.256 I_{1} wb
Mutual inductance between coil and solenoid
M = N_{2} φ_{2} / I_{1}
= 100 × μ_{0 }× 1.256 I_{1 }/ I_{1}= 125.6 μ_{o} Henry