The influence of inhomogeneities of the Earth's magnetic field is studied as it affects the stability of the relative equilibrium positions of an Earth satellite which has a cylindrical screen for electrostatic protection and moves on a circular equatorial orbit. The necessary and sufficient stability conditions are derived. The regions of admissible values of satellite parameters are constructed. The type and degree of influence are described for each of the components of the principal moment of Lorentz forces, introduced by the inclusion of the geomagnetic field inhomogeneity in the screen volume as it influences the dimensions of the regions and the vibration frequencies of the satellite.