A Discussion on Efficient Methods for Computing Magnetic Flux Density of Circular Coils

In this article, polynomial approximation methods are used to compute the elliptical integrals involved in the magnetic flux density formulation of the coil composed by circular loops. A superconducting magnet coil for the magnetic resonance imaging is analyzed with the methods. Numerical results showed that the piecewise polynomial approximation method proposed by Toshio is the most efficient method. With this method, the efficiency for computing the magnetic flux density of circular coils can be greatly improved.