The Feynman Lectures on Physics Vol. I Ch. 28: Electromagnetic Radiation by Unknown

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Now we can go a little bit further in studying (28.5) to see what it means. Suppose a charge is moving in any manner whatsoever, and we are observing it from a distance. We imagine for a moment that in a sense it is “lit up” (although it is light that we are trying to explain); we imagine it as a little white dot. Then we would see this white dot running around. But we don’t see exactly how it is running around right now, because of the delay that we have been talking about. What counts is how it was moving earlier. The unit vector $\FLPe_{r'}$ is pointed toward the apparent position of the charge. Of course, the end of $\FLPe_{r'}$ goes on a slight curve, so that its acceleration has two components. One is the transverse piece, because the end of it goes up and down, and the other is a radial piece because it stays on a sphere. It is easy to demonstrate that the latter is much smaller and varies as the inverse square of $r$ when $r$ is very great. This is easy to see, for when we imagine that we move a given source farther and farther away, then the wigglings of $\FLPe_{r'}$ look smaller and smaller, inversely as the distance, but the radial component of acceleration is varying much more rapidly than inversely as the distance. So for practical purposes all we have to do is project the motion on a plane at unit distance. Therefore we find the following rule: Imagine that we look at the moving charge and that everything we see is delayed—like a painter trying to paint a scene on a screen at a unit distance. A real painter, of course, does not take into account the fact that light is going at a certain speed, but paints the world as he sees it. We want to see what his picture would look like. So we see a dot, representing the charge, moving about in the picture. The acceleration of that dot is proportional to the electric field. That is all—all we need.

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