Series expansions for the vector potential and field components produced by a toroidal conductor

Alternative solutions for the vector potential and the magnetic-field components produced by a toroidal conductor of rectangular cross section are considered. Series expansions are obtained and found to agree with those obtained independently by M. W. Garrett [J. Appl. Phys. 22, 1091 (1951)]. Results are obtained for a particular coil geometry by using only a few terms from the series expansions and, by comparing with the exact results, are found to be highly accurate at points close to the coil axis.