max L with given length of wire

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Jim Lux by way of Terry Fritz <twftesla-at-qwest-dot-net>" <jimlux-at-earthlink-dot-net>

This came up recently in some posts...

Turns out Maxwell (of equation fame) solved this problem and found that the 
optimum coil has a square cross section with mean diameter 3.7 times the 
dimension of the square... 2a = 3.7c.  Brooks and others refined the 
estimate and recommended 2a = 3c as the optmimum shape.  L = 1.353* mu0*a * N^2

  a is the mean radius, b is the thickness of the coil (along the center 
axis), c is the width of the windings.