Planar coil system consisting of three coil pairs for producing a uniform magnetic field

A planar coil system that produces a uniform field and consists of three coil pairs has been designed and constructed. The design process involves the numerical solution of an equation based on the filamentary coil current and the truncation of the ratio of coil currents. This process makes it possible to realize the ratio by the coils' number of turns and then modifying the geometrical parameters to make allowances for the practical cross sections of coil conductors. Although design parameters obtained using this process may not be optimum, the uniformity of the calculated magnetic field is satisfactory for most practical situations. The uniformity of the magnetic field was confirmed by constructing a coil system with an outer diameter equal to 1 m. The predicted area of uniformity (less than 0.01% error), for the proposed design, was six times larger than that obtained using a conventional Helmholtz coil of the same diameter.