Electrodynamics of Hyperbolically Accelerated Charges: IV. Energy-Momentum Conservation of Radiating Charged Particles

The relativistic equation of motion of a radiating charge is discussed with special emphasis upon a clarification of the significance of the Schott energy for the energy-momentum conservation of the charge and the field it produces. In particular hyperbolic motion is studied. The case that a charge with constant velocity enters and leaves a region with hyperbolic motion is analysed. We find that the Schott energy is increased as the particle enters the region and that the energy it radiates while the charge moves hyperbolically comes from the Schott energy. A result of our analysis is that this energy is localized in the field close to the charge.