Square cross section coils for the production of uniform magnetic fields

A complete presentation for a system of four square coils for the production of uniform fields is offered. The method of calculation is without restriction on geometry or turns- or current-ratio. A number of cases are worked out in detail. For these, the uniformity is calculated and contours of constant homogeneity are drawn. Square loops are only slightly less uniform than circular systems and, when large coils are needed, they are easier to construct. Some effects of errors in construction and that due to winding thickness are calculated and it is shown that the square loop system is very tolerent in these respects.