Optimum Spacing of Square and Circular Coil Pairs

Abstract

In a previous note Crownfield pointed out that the magnetic field along the axis of a coil pair is within a prescribed uniformity over a substantially longer region than that given by the Helmholtz spacing if a somewhat larger spacing is used. In the note, values of coil spacing and length of uniform field region are given for a few desired uniformities, but only for a particular "thick" coil pair, i.e., one with cross-sectional dimensions comparable to the spacing. Many coil pairs, such as those used to annul the earth's field over the region occupied by some apparatus, have cross-sectional dimensions which are small compared to the spacing. This note presents calculations for such "thin" coils, both circular and square. Square coils have some advantages, as recently pointed out by Firester, who calculated field deviations both off axis and on axis for square coil pairs but only for coils at the Helmholtz spacing.