Interaction of a traveling magnetic field with rigid conducting spheres or cylinders

The case of a rigid conducting sphere or cylinder that travels with uniform velocity relative to a two-dimensional primarily transverse magnetic field with sinusoidal variation in space and time is analyzed to determine the electromechanical characteristics of the interaction. Interest is centered on conductors with diameters small relative to the wavelength of the applied field. For the sphere, an exact solution is not tractable by standard techniques, hence, a method is utilized in which the force is approximated by one of its components. The results are verified by: 1) applying the approximation to the analogous case of a cylinder and comparing the result with the exact solution to that case, 2) comparing the limit of the approximate solution for the sphere with the result obtained by assuming the magnetic Reynolds number to be small, and 3) determining the net time-average force of electromagnetic origin experimentally for comparison with the predictions of the theory. The latter were carried out for the cylinder as well as the sphere over a range of magnetic Reynolds numbers (sR m = µ 0 σsωD 2 ) from 0.4 to 20. In the course of the work, a method is also utilized in which the original "skin effect" problem is reduced to a problem involving interacting low sR m components and the force is found via the techniques of lumped parameter electromechanics. The study is concluded with a determination of the condition under which two spheres or cylinders are electromagnetically independent so that the results for a distribution of conductors may he obtained by superposition of the results for a single body. Situations which may be modeled using the results of this study include holdup or separation of a highly conducting liquid phase from a two-phase flow in heat transfer apparatus as a result of the application of a magnetic field gradient or the energy conversion in a liquid metal magnetohydrodynamic induction machine with a two-phase working fluid.