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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 μo Henry
derive transfer function of S= 2.25+j4.5
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