We show that the interaction between a surface and a charge packet moving parallel to it can become repulsive above a critical relativistic energy. We find that this is true for a lossless dielectric surface and also for a Drude metallic surface-in apparent contrast with such common notions as image charge. This counterintuitive phenomenon occurs for packets larger in the transverse than in the longitudinal ( parallel to the motion) direction. The repulsion does not occur for a point charge that is instead attracted at all energies. In addition to the above attractive or repulsive transverse force, there is a longitudinal decelerating force, which for a dielectric corresponds to the Cerenkov effect. Once again, the behavior of a line packet differs from that of a point charge: for a packet with infinite transverse size, the decelerating field decreases to zero as the relativistic factor gamma -> infinity, whereas, for a point charge, the asymptotic value is finite. These findings have a potential impact not only on fundamental electrodynamics but also on accelerator physics and electron spectroscopy.