A displacement device comprise a stator having a plurality of electrically conductive coils shaped to provide: a first plurality of coil traces generally elongated in a stator-x direction and distributed over at least a first portion of a first layer; a second plurality of coil traces generally elongated in a stator-y direction and distributed over at least a second portion of a second layer. The first and second portions of the first and second layers overlapping one another in a stator-z direction. The displacement device also comprises a moveable stage having one or more magnet arrays. The moveable stage is moveable relative to the stator within a two-dimensional working region. The one or more magnet arrays include a first magnet array comprising a plurality of first magnetization segments, each having a corresponding first magnetization direction. The displacement device comprises one or more amplifiers connected to drive a plurality of currents in the plurality of electrically conductive coils; and a controller configured to control the currents driven by the one or more amplifiers and to thereby cause the moveable stage to track a desired position, (xr,yr), within the working region.