Solid Conductor in a Magnetic Field That Moves at a Uniform Velocity along a Channel

A two dimensional magnetic field is suddenly moved at a uniform velocity along a channel of infinite length containing an electrically conducting solid metal with magnetic permeability and magnetic diffusitivity under the assumption of finite Reynolds number. An analytical solution is obtained for the case of one Fourier-component magnetic field. The numerical scheme is developed with the implementation of the boundary conditions. It is shown that in the steady state the numerical and the analytical results agree well for magnetic Reynolds number in the range of! to 1200. It is found that as magnetic Reynolds number increases the solid metal behaves more and more like a perfect conductor where the field lines are frozen in the moving solid metal Pictures of evolution of field-lines with time are plotted for various times.

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