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This paper presents two new theories and a new current representation to explain the magnetic force between two filamentary current elements as a result of electric force interactions between current charges. The first theory states that a current has an electric charge relative to its moving observer. The second theory states that the magnetic force is an electric force in origin. The new current representation characterizes a current as equal amounts of positive and negative point charges moving in opposite directions at the speed of light. Previous work regarded electricity and magnetism as different aspects of the same subject. One effort was made by Johnson to unify the origin of electricity and magnetism, but this effort yielded a formula that is unequal to the well-known magnetic force law. The explanation provided for the magnetic force depends on three factors: representing the electric current as charges moving at the speed of light; considering the relative velocity between moving charges; and analyzing the electric field spreading in the space due to the movement of charges inside current elements. The electric origin of the magnetic force is proved by deriving the magnetic force law and Biot-Savart law using the electric force law. This paper is helpful for unifying the concepts of magnetism and electricity.

Two New Theories for the Current Charge Relativity and the Electric Origin of the Magnetic Force Between Two Filamentary Current Elements