Apparatus and method are provided for damping the induced fluid flow, particularly in the region of the base plate, in an electrically conductive material that is heated and melted in a cold crucible induction furnace. Damping is accomplished by establishing a dc magnetic field such that flow of the electrically conductive liquid metal in that dc magnetic field would induce eddy currents in the liquid metal which would generate forces that tend to oppose the flow. The dc magnetic field may be established by dc current flow in the ac induction coil that induces current in the material, dc current flow in a separate dc coil, or coils, constructed to prevent excessive induced losses, by discrete magnets, or a combination of any of the three prior methods. The dc magnetic field may also be established by dc current flow in one or more dc coils disposed around a magnetic pole piece located below the base of the furnace. One end of the magnetic pole piece is located adjacent to the bottom of the crucible base, so that the pole piece concentrates the dc field into the lower portion of the molten electrically conductive material.