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During semiconductor crystal growth with an externally applied magnetic field, thermoelectric currents may drive a melt circulation which affects the properties of the crystal. This paper treats a model problem for a floating zone process with a uniform axial magnetic field, with planar solid-liquid interfaces, with a cylindrical free surface, with a parabolic temperature variation along the crystal-melt interface, and with an isothermal feed rod-melt interface. The ratio of the electrical conductivities of the liquid and solid is a key parameter. The azimuthal velocity is much larger than the radial or axial velocity. There is radially outward flow near the crystal-melt interface which should be beneficial for the mass transport of dopants and species.