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Magnetic force calculation methods such as Maxwell stress, virtual work principle, equivalent magnetic charge, and equivalent magnetizing current are widely used until now. The force density is still controversial issue even though it is common sense that all of these methods have legitimate results. The surface force densities of each method are quite different with each other in the point of numerical result and final expression. In this paper, it is shown that a unified expression of body force density is derived using virtual air-gap scheme for an analytic model in which cylindrical magnetic material with a vertical current runs through its center.