Headlamp device comprising a system for determining a position or a variation of position

The system has a Hall effect sensor (6) to determine values of position of a headlight on an entire position range (13). The sensor has a higher sensitivity range (14) determining the positioning of the headlight and lower sensitivity ranges (15,16) determining the position of rotation of the headlight around an axis. The higher range corresponds to vicinity of an axial position (10) of the headlight. An independent claim is also included for a motor vehicle.