Track support of a ground-based electricity supply system for a land vehicle, rail comprising such a support and installation method

This support (36), in the form of a profile made of an electrically insulating material, comprises: an upper surface (50) substantially planar, provided with a longitudinal groove (60) intended to receive a track segment, and a longitudinal channel (70) intended to receive a low-voltage electrical power cable; and a lower surface (52) intended to rest on a base for holding the support in the roadway. It is characterized in that the lower surface (52) is curved, preferably V-shaped, so that the support is arched in such a way as to be held, at least transversely, in a recess of complementary shape made in the base.