Mathematical model of the mean electromagnetic force induced by a rotating magnetic field a liquid column of a finite length

J. Priede - Yu. M. Gelfgat

Institute of Physics, Latvian Academy of Sciences, Salaspils-1, LV_2169, Latvia

Abstract
The mathematical model is deduced for the mean electromagnetic force due to the rotating magnetic field driving a flow of a conducting liquid in a cylindrical cavity of finite length. The model takes into account the presence of insulating end-walls causing induced electric currents to close within the liquid volume. For cavities of realistic aspect ratio this effect can result in both the distribution and net value of the torque deviating considerably from a convectional case of an infinite cylinder. We deal with an approximation of an ideal inductor generating a uniform rotating magnetic field along the height of the container. The frequency of the rotating magnetic field is supposed to be sufficiently low for the skin-effect to be negligible. Besides, it is assumed that the contribution of the oscillating part of the electromagnetic force to a liquid flow is negligible comparing to that of the time-averaged part. Validity range of the underlaying approximations is estimated due to the order of magnitude considerations. Eventually, the mean electromagnetic force is defined by means of a single axisymmetric amplitude of the electrostatic potential. This amplitude actually is shown to be independent on the liquid flow, and therefore, determined solely by the boundary conditions for an electric current. Figs 2, refs 6.