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single layer inductor
Factoring b from the denominator gives:
L = 10-6 a² N² / [ b (10 + 9a/b)] [Henrys]
The quantity a/b is dimensionless, and so we can immediately substitute in the denominator:
L = 10^-6 a² N² / [ b (10 + 9r/l)] = 10^-6 a² N² / [ b (10 + 4.5 (D/l)))]
Factoring 10 from the denominator gives:
L = 10^-7 N² ( a² / b ) / (1 + 0.45 (D/l)) [Henrys]
where..
L is the inductance in Henry
D is the coil diameter in meters
r is the radius in meters (or D/2)
l is the lenght of the coil in meters
N is the number of turns