Energy conservation of a uniformly accelerated point charge

Abstract

Direct numerical calculation shows that the total electromagnetic-field energy of a one-dimensional uniformly accelerated classical point charge at one instant is the same as that at another instant when the charge is moving at the same speed but in the opposite direction of the first instant. This seems contradictory to the fact that the radiation power calculated by the Larmor formula is constant, but is required by the fact that the radiation reaction vanishes. It is also shown numerically that the electromagetic-field energy changes a finite amount when a charge begins or ends its uniformly accelerated motion. This change of energy is equal to the work done against a \ensuremath{\delta}-function radiation reaction. The implications of these results on the question of whether a uniformly accelerated charge radiates are discussed.