A Lorentz actuator includes: a magnet arrangement; a coil arrangement; and a current controller for supplying a current to the coil arrangement; wherein the magnet and coil arrangement are moveable relative to each other in a main direction, wherein the coil arrangement has a first and second coil portion that are separately operable by the current controller, such that when the same current is supplied to the first coil portion as is supplied to the second coil portion, Lorentz forces generated in the main direction by the first and second coil portions are also the same, and wherein the current controller is configured to supply a current to the first and second coil portions with a phase difference in order to compensate for parasitic reluctance and/or Lorentz forces in an auxiliary direction perpendicular to the main direction.