In this paper, a spacecraft formation consisting of an uncharged spacecraft-target and an electrically charged pursuer spacecraft is under consideration. The paper focuses on the dynamics of the formation flying in the magnetic and gravitational fields of the Earth. The geomagnetic field is modeled using the quadrupole approximation. An analytical study of the differential system is carried out that describes the relative orbital dynamics of the pursuer spacecraft with a variable electrical charge. Novel dynamic effects are revealed due to the use of the quadrupole model of the geomagnetic field. Employing the Lorentz force, a control strategy is suggested to counteract initial disturbances and prevent the pursuing spacecraft relative drift in order to ensure its motion in a closed relative orbit. The control gains are chosen using the Monte Carlo method. The operability and effectiveness of the proposed control algorithm are demonstrated based on the statistical analysis of a series of numerical experiments.