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Alternating magnetic fields induce eddy currents within electrically conducting liquid metal that can be used to levitate and shape the liquid. If the frequency of the applied field is high enough, the electromechanical coupling can be reduced to the self-consistent relationship between the shape of the liquid metal and the distribution of the magnetic fields. This article describes a method of modeling this coupling for general three-dimensional geometries. The method is an extension of the free movement method previously used to describe two-dimensional magnetic levitation.

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