The force on a sphere moving through a conducting fluid in the presence of a magnetic field

The force on a sphere moving through an inviscid, conducting fluid in the presence of a uniform magnetic field B0 is calculated for the low-conductivity case where the hydrodynamic motion deviates only slightly from potential flow. The magnetic Reynolds number is assumed small. The force on the sphere is found to consist of both a drag and a deflective component which tends to orient its motion parallel to a magnetic field line; if the sphere's velocity is V, the force may be written R = -AB²₀V + C(V.B₀)B₀ where the coefficients A and C depend on the conductivities of both sphere and fluid. The coefficients are evaluated by calculating the Joule dissipation for particular orientations of V relative to B0. In one case the force is also calculated directly from the perturbed pressure distribution in the fluid. In an analogous way, a spinning sphere in a conducting fluid experiences both resistive and gyroscopic torques.