The invention relates to a ground power supply device for electric vehicles (5), the device including power supply segments (52) insulated from each other and each having a length less than half the length of the footprint of the vehicle (5), and being adapted to apply a supply voltage to a segment (52) only when said segment (52) is within the footprint of the vehicle (5), the vehicle (5) having a power supply rubbing member (80), and the device being adapted to apply the supply voltage to two adjacent segments (52) when the rubbing member (80) is in simultaneous contact with the two segments (52) and to earth one of the two segments (52) a short time after said rubbing member (80) has left that segment (52).