This question is motivated by the model used in The Feynman Lectures on Physics Vol II Section 18-4. In the model there are two plane sheets extending infinitely in both their dimensions. Each has a uniform electric charge equal in magnitude and opposite in sign to the other. They are place in immediate mutual proximity. One is accelerated abruptly to a constant velocity parallel to itself.
The purpose of the model is to illustrate some basic features of electromagnetic waves. But my question regards the actual consequences of that models, taking to its logical conclusions. In particular, it is evident to me that the Liénard-Wiechert potential of such a construct would overwhelm any other effect such as the electric and magnetic fields produced by the relative motion.
NB:This is a non-relativistic result.
The Liénard-Wiechert potential is discussed in The Feynman Lectures on Physics Vol II 21-5 The potentials of a moving charge; the general solution of Liénard and Wiechert As well as in this PDF document of lecture notes UIUC Physics 436 EM Fields & Sources II
The gist of the Liénard-Wiechert potential theory is that a charge distribution moving toward a filed point will have an apparent volume greater than the actual volume. In the case of a receding charge distribution, it will appear to have less volume than it actually has. Thus an approaching charge will appear greater than it would were it stationary or receding. A receding charge will appear to be less than if it were stationary or approaching.
I didn't set out to destroy Feynman's example, but this appears to the the final nail in the coffin.
Is it not the case that the moving charged sheet of infinite extent would produce an electric field approaching an infinite magnitude due to its Liénard-Wiechert potential?