Of the terms appearing in(28.), the first one evidently goes inversely as the luare of the distance, and the second is only a correction for delay, so it is easy to show that both of them vary inversely as the square of the distance. all of the effects we are interested in come from the third term, which is not very complicated after all. What this term says is: look at the charge and note the direction of the it onto the surfac of a unit sphere). As the charge moves around, the unit vector wiggles, and the acceleration of that unit vector is what we are looking for. That is all.Thus is a statement of the laws of radiation, because that is the only important term lough away that the fields are varying inversely as the distance (The parts that go as the square have fallen off so much that we are not interested in them. go a little bit further in studying(28. 5)to nat it 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 light that we are try rying 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 e, is pointed toward the apparent position of the charge. Of course, the end of e, 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 wiggling of er' 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 'e 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 Thus Eq.(28.5)is the complete and correct formula for radiation; even relativity effects are all contained in it. However, we often want to apply it to a still simpler circumstance in which the charges are moving only a small distance at a relatively slow rate. Since they are moving slowly, they do not move an ap- preciable distance from where they start, so that the delay time is practically constant. Then the law is still simpler, because the delay time is fixed. Thus we imagine that the charge is executing a very tiny motion at an effectively constant distance. The delay at the distance r is r/ c. Then our rule becomes the following If the charged object is moving in a very small motion and it is laterally displaced by the distance x(o), then the angle that the unit vector e,is displaced sInce r is practically constant, the x-component of der/dr 2 is simply the accelera tion of x itself at an earlier time, and so finally we get the law we want, which Only the component of ax perpendicular to the line of sight is important. Let us see why that is. Evidently, if the charge is moving in and out straight at us nit vector in that direction does not wiggle at all, and it has no acceleration it is only the sidewise motion which is important, only the acceleration that see projected on the screen