Uniformity condition for a rectangular field coil with a split winding

A generalized Helmholtz condition for field uniformity is derived from the closed form solution of the magnetic field in a multilayer rectangular coil pair as a function of coil dimensions and pair separation. The relation among the dimensions satisfying this condition is found and plotted in parametric form for single layer coils and for a multilayer coil with a specific winding thickness. For square coils of cross section small compared to their mean radius, the gap separation approaches half the coil radius, analogous to the classical condition for circular coils. Comparison between theoretical and measured values for tolerances within +/-5% of the field at the system center agree within a 6% maximum deviation. For the experimental coil, the area enclosed by the +/-5% contour was 58% of the area of the full coil.