1. Maxwell's equations do not hold in NON INTERTIAL reference frames, right?? 2. Lets say you have a charge which was briefly accelerated. You surround it by a closed surface CLOSE to the charge and integrate the Poynting vector over this surface and with respect to time to get the TOTAL energy radiated (the energy which passed through this surface). Now you surround the charge by a closed surface INFINITELY FAR from the charge and find the total energy which went through this surface. Will the second integration yield LESS TOTAL energy than the first??? I'm thinking that some of the energy which passes through the closed surface near the charge does not make it to infinity, rather it is "used" to increase the magnetic field of the charge. Remember, the magnetic field will have to increase since the speed of the charge increased, and this energy has to come from somewhere. Now what if the acceleration was negative (i.e. the speed of our charged decreased), will the radiation at infinity be greater than radiation close to the charge? If not, where does the energy which was in the magnetic field end up? Could someone who really knows this stuff tell me which, if any, errors I've made.