Especially for use in the semiconductor industry, a displacement device (701) is disclosed comprising a first part comprising a carrier (714) on which a system of magnets (710) is arranged according to a pattern of row and columns extending parallel to the X-direction and the Y-direction, respectively. The magnets in each row and column are arranged according to a Halbach array, i.e. the magnetic orientation of successive magnets in each row and each column rotates 90° counter-clockwise. The second part comprises an electric coil system (712) with two types of electric coils, one type having an angular offset of +45°, and the other type having an offset of −45° with respect to the X-direction. The first part (714, 710) is movable over a range of centimeters or more with respect to the stationary second part (712). For high precision positioning of the first part, an interferometer system (731, 730) is provided.