The article sets the task of determining the rational value of the displacement of the center of the magnetic system of an electromagnetic bearing relative to the axis of rotation, at which, with equal currents in opposite electromagnets, the weight force falling on one axis of the bearing will be completely compensated. To achieve the set, the equations of motion of the rotor in the field of electromagnets are considered. It is shown that the rational value of the displacement of the center of the magnetic system is determined from a fourth-order algebraic equation. The analytical solution of Descartes-Euler of this equation is applied. Analytical expressions are found that allow to determine the rational value of the displacement of the center of the magnetic system relative to the axis of rotation according to the known parameters of the electromagnetic bearing. A study was made of the stability of a three-circuit control system of an electromagnetic bearing when the center of the magnetic system is shifted by a rational value relative to the axis of rotation. It is proved that the displacement of the center of the magnetic system by the calculated value does not affect the stability of the control system of the electromagnetic bearing with the settings of the regulators selected for the central position of the rotor.