Abstract
The study of force-free and other equilibrium configurations of magnetic fields in a conducting fluid sphere with volume currents flowing in the interior of the sphere forms the subject matter of this note. In Part I, assuming the electrical conductivity of the sphere to be infinite, the general conditions governing the force-free and other equilibrium fields are derived, and their solutions obtained. It is found that a force-free field must be a suitable combination of a poloidal and a toroidal part. The magnetic energy is equally divided in its poloidal and toroidal components. The Part II of this note deals with the case of finite electrical conductivity. Here, the possibility of a current distribution is explored such that the corresponding magnetic field does not decay with time. It is concluded that it is difficult to imagine a poloidal configuration of the magnetic field, whereas a purely toroidal non-decaying magnetic field is certainly possible.
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