Inter-spacecraft electromagnetic proximity operation has many potential advantages, such as no propellant consumption and plume contamination, while providing high-precision, continuous, reversible, synchronous, and noncontacting control capability. In addition, with constant magnetic moment actuation, the inter-spacecraft electromagnetic force is, in essence, a kind of conservative force and has dynamics conservation. This yields specific and targeted evolvement laws of relative motion among these actuated magnetic dipoles. Exploiting these properties, spacecraft self-and soft-docking could be achieved with proper piece-wise constant magnetic moments design, which not only improves control precision, but also reduces the demand of relative motion measurement and simplifies docking controller design. Aiming at electromagnetic spacecraft self-and soft-docking controller design, this paper uses dynamic modeling and dynamics conservation analysis to derive the specific evolvement laws of relative motion between the actuated magnetic dipoles first, and then utilize these laws and corresponding dynamics conservation to design the piece-wise constant electromagnetic moments.