Forces Due to a Magnetic Dipole Near a Sliding Conductor: Applications to Magnetic Levitation and Bearings

A conducting body moving with respect to a magnet experiences lift and drag forces from the eddy currents induced in the conductor. The force on the conductor is dependent on the relative velocity between the conductor and the magnet. In this study, we investigate the force dependence on magnetic Reynolds number, a dimensionless indicator of velocity. The Lorentz equation is used to predict the force on the conductor, given the spatial dependence of the eddy currents and magnetic induction vector inside the conductor. Maxwell’s equations, which govern the electromagnetic quantities, are reduced to a single convection-diffusion equation for the magnetic induction vector inside the conducting body. An integral solution which satisfies the governing equation and boundary conditions is used to obtain the eddy currents and magnetic field. For our model, both lift and drag forces increase sharply with Reynolds number, reach a maximum, and decrease with increasing Reynolds number to an asymptotic limit. We also find that skin depth, the depth to which the eddy currents decay inside the conductor, decreases with increasing Reynolds number. The relevance to magnetically supported high-speed vehicles and magnetic bearings is discussed.