Analytical calculations of flux induction and forces of thick coils with finite length

The analytical modeling of toric coils is considered. The mathematical relations involve elliptic integrals which are rapidly and easily calculated using the arithmetic geometric mean (AGM) method. Two applications are studied, numerical results are analyzed and compared, when possible, with those obtained directly. The analytical method presented provides all the characteristics (such as inductances, flux densities, forces, etc.) of toric coils with any section. Thanks to the AGM method, which is used for intermediate calculations, the final results are obtained rapidly with a very good precision