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The vertical levitation force between a superconductor disk (SC) and a permanent magnet disk (PM) has been calculated from first principles using different Jc(B) relationships of the magnetic field. Based upon the first principles, the current distribution inside the SC induced by the applied inhomogeneous magnetic field generated by the PM and the field profiles have been calculated with a power law E ∼ J relationship: E(J) = Ec(J/Jc(B))n. The levitation force is highly hysteretic for the approaching and the retreating branches. The saturated current value, magnetization, and levitation force are found to depend strongly on the Jc(B) relations. Features of the supercurrent distribution, the force loop, and the levitation force density are discussed.