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Due to path-length variation and strain, the current distribution in the wire of a solenoid inductor is not uniform at low frequencies. This causes the effective solenoid radius to differ from the physical average, leading to a systematic error in inductance calculations. Formulae and program routines for the effective radius, for coils wound with solid rectangular and round wire, are given.
"Practical Model and Calculation of AC resistance of Long Solenoids". E. Fraga, C Prados, and D.-X Chen. IEEE Transactions on Magnetics, Vol 34, No. 1. Jan 1998.
Formula for the inductance of a helix made with wire of any section. C. Snow. BS Sci. 537, 1926 (5.74MB PDF).