Solenoid vs transformer inductance

Thread Starter

eigenvictor

Joined Jul 16, 2014
28
Why is the same formula used for both a long solenoid and a transformer coil inductance: L = μ * N^2 * A / ℓ

In case of an air core solenoid, it only gives a reasonable result for a single layer solenoid with the coil length ℓ >> D. However for multilayer coils with an arbitrary length to D ratio, mutual inductance between layers need to be accounted for, and basically different formulas are used, such as elliptic integrals and other numeric methods. For example, a more compact coil with shorter length but more layers will have higher inductance according to those formulas. Isn't this also the case for transformers? I just find this odd that the standard formula is so elegantly derived from the Ampere's law and the Faraday's law, and it contains the all important N^2, A, and ℓ that are all used in many other formulas. Yet it may not give an accurate result in a general case.
 
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