The door actuator generally has a receiving structure having a door carriage path; a first coil assembly and a second coil assembly both being mounted to the receiving structure along a common coil assembly plane and being longitudinally spaced from one another along the door carriage path by a spacing distance; and a door carriage being slidingly received by the receiving structure, the door carriage having a plurality of alternate-pole magnets provided along a magnet plane being parallel and spaced apart from the coil assembly plane, the first and second coil assemblies being operable to move the door carriage back and forth between the two ends of the rail.