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A single-valued magnetic scalar potential is introduced for arbitrary distributions of electric current in free space. It is defined as a Laplacian potential within a specified region outside the current distribution and is determined from the free-space values of the normal component of the field intensity over the region boundary. Once this scalar potential is obtained, the resultant magnetic field in the presence of magnetic material bodies located in the region considered can be expressed in terms of only a scalar potential. This yields a field analysis method substantially more efficient than existing methods, where the field due to the given current distributions is usually computed by employing the Biot-Savart formulas and, thus, the resultant field outside the magnetic bodies remains expressed in terms of vector quantities.