System for charging a battery of a motor vehicle

The system has a stationary charging station (14) and a coupling unit (12) fixed to a motor vehicle (10) i.e. electric vehicle. The coupling unit comprises a coupling element arranged at front, rear and sides of the vehicle. The coupling element is electrically coupled to a charging element (30) of the charging station in a charging position. The coupling element is integrated at rear of the vehicle or on one of the sides of the vehicle. The coupling element is inductively coupled to the charging element of the charging station in the charging position.