Axisymmetric stars with both poloidal and toroidal magnetic fields

Chandrasekhar and Prendergast have established a result which has been assumed to imply that axisymmetric stars with an internal toroidal magnetic field should have zero external poloidal field. By considering mildly singular functions, the range of solutions is increased, and models can then be constructed which have toroidal and poloidal fields in the interior and a non-zero, external, poloidal field. Both the magnetic field and its associated current are continuous everywhere.