In electric machines, core losses limit, at high fundamental frequency, the permissible full-load power. The aim of the invention is to develop a design which enables a high power density at high magnetic reversal frequencies and which is easy to produce. To this end, the primary part comprises coils which, for the majority of their length, run in the direction of movement and which are surrounded in this area on three sides by soft magnetic material. In the direction of movement, at least two coils are arranged one behind the other. Coils of different phase are arranged perpendicular to the direction of movement inside different running tracks. In the secondary part, at least two oppositely magnetized hard magnets with three collector segments, which are flatly adjacent in a manner that is perpendicular to the direction of movement, form magnet poles having a high flux concentration. The primary and secondary parts can be shifted with regard to one another in a manner that is perpendicular to the direction of movement by means of a mechanism. The machine is characterized by having an easily producible modular design which has low core losses also at high frequencies. A high power density and, at the same time, a large low-loss field control area is realized in compact dimensions.