Some simple inductance formulas are given for a circular or square coil of any shape ratio. Each one represents a continuous transition between the extremes of a long coil and a short coil. A unique case is a cubic coil whose inductance is 2/3 the reference value based on area/length. For any shape, the relative error is very small and is stated. The theoretical formulas are given for comparison.
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H.A. Wheeler (1982) studied this question.
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