Flow past spheres and spheroids in the presence of a toroidal magnetic field

Summary

Stewartson [1]²) has considered the inviscid flow past a sphere in the presence of a uniform magnetic field andMurray andLudford [2] have investigated a similar problem in which the magnetic field originates from an axially symmetric dipole field situated at the centre of the sphere. In connection with the study of earth's magnetic field, the toroidal part of this field plays a dominant part. This gives rise to the importance of studying the effect of a toroidal magnetic field on flows past different bodies of revolution; specially past spheres and spheroids. In the present note inviscid flows past a sphere, and a spheroid, are considered, for the case of a toroidal magnetic field originating in the fluid. In the case of the sphere the field inside the sphere consists of an electric dipole directed along the axis of symmetry together with a uniform electric field which produces a uniform current along the axis. In the case of the spheroid, the field inside it is due to an electric dipole and quadrupole directed along the axis of symmetry, together with a uniform electric field which produces a uniform current along this axis.