Relativistic Causality and Conservation of Energy in Classical Electromagnetic Theory

The change of the electromagnetic field in a particular place due to the event of a change in the motion of a charged particle can occur only after the light signal from the event can reach this place. Naive calculations of the electromagnetic energy and the work performed by the electromagnetic fields might lead to paradoxes of apparent non-conservation of energy. A few paradoxes of this type for a simple motion of two charges are presented and resolved in a quantitative way providing deeper insight into various relativistic effects in the classical electromagnetic theory.