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.

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

“…The problem in the case of a strong magnetic field has been studied in some detail by Stewartson (1956). For the case of a weak magnetic field, calculations of the induction drag for a sphere have been made by Chopra (1956Chopra ( , 1957 and by Chopra & Singer (1958), but the expressions they obtain are incorrect as is evident from the fact that their drag force does not vanish when the conductivity of the fluid goes to zero, a result in conflict with the Special Theory of Relativity. Their error appears to arise, among other things, from a failure to observe that a concomitant of such motion is the induction of charges on the surface of a sphere (and in the case of a spinning sphere, induced volume charge density in the sphere itself) producing electric fields of comparable magnitude to those produced by induction (dynamo effect).…”