If you have a length (l) of wire coiled to make an inductor and you stretch the wire (ie. space the coils further) but do not change the diameter (see
inductor question
Where does your formula come from? The closest reference I could find was this page:
A common formula for an air core cylinder coil is Wheeler's formula,
L (microhenries) =(0.8 * N^2 * R^2)/(6*R + 9*L + 10*B). N = total number of turns R = average radius = (inner radius + outer radius)/2 L = coil length (along the axis) B = thickness of the winding = outer radius - inner radius (all dimensions in inches, coil immersed in air) The L in that equation does not refer to the length of the wire, but to the length of the cylinder of the coil's form. So stretching the coil out into a longer cylinder certainly changes L and thus the inductance.
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