How to optimise wire gauge selection for electromagnetic applications?
Number of turns and current are variables that depend upon design goals. However, there is an optimization to be had in terms of geometry. A &quot;Brooks coil&quot; is a coil with a square cross section and an inside radius of the same dimension as a side of the square cross section.

(from www.circuits.dk)
The Brooks coil has the property of maximizing the magnetic flux for a given length of wire.