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The generation of uniform magnetic fields over extended regions of space by means of circular coils of large cross-sectional area is analyzed. It is shown by an extension of Garrett's theory of axially symmetric magnetic fields that the optimum shape of the coil cross section can be found analytically without numerical integration over the winding area. The theory is illustrated by application to Helmholtz coils and double Helmholtz coils of rectangular cross section. Choice of the optimum dimensions makes it possible to generate very uniform fields of great intensity.
W. Franzen (1962) studied this question.