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We have measured the magnetic field and the levitation force of a bulk Y-Ba-Cu-O superconductor in varying the external field with a Bi-Sr-Ca-Cu-O superconducting magnet. The height dependence of the levitation force could well be explained in terms of the field gradient in the sample and the radial component of the external magnetic field. The field gradient also induces the trapped field and decreases the levitation force. The experimental data showed a deviation from the theoretical value when the levitation process was repeated.