Angular dependence of the levitation force on a small magnet above a superconducting cylinder in the Meissner state

The dipole-dipole interaction model was used to calculate the levitation force on a small permanent magnet above a superconducting cylinder in the Meissner state lying on the cylinder's axis. We obtained analytical expressions for the levitation force and energy in terms of the physical dimensions of the cylindrical superconductor as well as the height and the angle between the magnetic moment and the surface of the sample. Results show that the levitation force and energy are maxima when the magnetic moment is perpendicular to the surface and minima when it is parallel. Special cases of infinite radius and infinite thickness were discussed