The present invention is based on a novel electric induction furnace design that enables the removal of zinc-containing filter dust (FD) originating from the production of steel (alloy or non-alloy) and the production of cast iron with galvanized steel scrap, using a novel process based on the carbothermal reduction of the metal oxides present in the FD, performed at the temperature at which the materials are melted inside the electric induction furnace. The electric induction furnace of the invention incorporates an electric arc or plasma beam generator to melt all the inorganic non-metallic material. The incorporation of this generator also enables the use of large volumes of molten slag.