Solenoid vs transformer inductance

Discussion in 'General Electronics Chat' started by eigenvictor, Jan 23, 2015.

  1. eigenvictor

    Thread Starter New Member

    Jul 16, 2014
    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.