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Inductance of a short coil

I have the inductance of the long coil which is
L=( Meu (not)* N^2 * A ) / (D)
A = Area , D = Length , N = number of turns in the coil

I need to prove that for a short coil the inductance (L) is the following:
L =[( Meu (not)* N^2 * A ) / (D)] * [ [{(D^2 - a^2)^(1/2)} - a ] / (D)] ]
a = radius of the coil
A = 3.14 a^2

Solution Summary

This solution is provided in a 2 page .pdf file and a .jpg image is attached as well to further understanding. It uses step-by-step equations for magnetic field and self induction to find the answer to the problem.