Note on induction drag

Abstract

An attempt to describe some aspects of induction drag is made in this short paper. The quoted expressions for translational and rotational induction drags of a sphere of infinite electrical conductivity moving in an incompressible fluid of finite electrical conductivity in the presence of a magnetic field may be derived following an earlier paper by the author. An analogy with the viscous drag is drawn, and it is shown that, unlike ordinary viscosity, the hydromagnetic or inductive viscosity is anisotropic in nature. A condition for this second viscosity to play an important role is also obtained. The rest of the paper is devoted to a discussion of the limitations of the results obtained. It is shown that the results hold good for small bodies or weak induction currents. When applied to large bodies or strong currents, the appropriate corrections for the electromagnetic and for electrostatic shielding effects must be applied. An order of magnitude calculation shows that, for bodies of cosmical dimensions, the correction is precisely of the same order as the induction effect itself.