Im sure everyone has hit this wall at some point, when the thoretical equation does not give the exact result in the real world. These last few weeks i have been battling this problem in the form of Coil Inductance's. I have a need for a ver specific and relitively low inductance with my latest pience of work and figuring out the kinks in the real world vs thoretical has been a right problem.
This equation will only hold up if a lot of real world factors are controlled. In addition to the obvious factors given in the equation ( Coil Diameter, Number of turns, Length of winding) the uniformity of pitch (essenialy the length & number of turns) can have a dramatic effect of low inductance coils.
My theory is that variation in the coil winding has an effect of the quality of the flux field and therefore the inductance of the overall coil. When i have more information i shall report further . . . . .