where ao is the maximum acceleration, -wxo. Putting this formula into(29. 1), E=-q sin 8 Now, ignoring the angle 0 and the constant factors let us see what that looks like as a function of position or as a function of time 29-2 Energy of radiation First of all, at any particular moment or in any particular place, the strength of the field varies inversely as the distance r, as we mentioned previously.Now we must point out that the energy content of a wave, or the energy effects that such an electric field can have, are proportional to the square of the field, because if. for instance, we have some kind of a charge or an oscillator in the electric field then if we let the field act on the oscillator, it makes it move. If this is a linear oscillator, the acceleration, velocity, and displacement produced by the electric field acting on the charge are all proportional to the field. So the kinetic energy which is developed in the charge is proportional to the square of the field. So we shall take it that the energy that a field can deliver to a system is proportional somehow to the square of the field fare. his means that the energy that the source can deliver decreases as we get farther away; in fact, it varies inversely as the square of the distance. But that has a very simple interpretation: if we wanted to pick up all the energy we could from the wave in a certain cone at a distance r1(Fig. 29-4), and we do the same at an other distance r2, we find that the amount of energy per unit area at any one place goes inversely as the square of r, but the area of the surface intercepted by the cone goes directly as the square of r. So the energy that we can take out of the gave within a given conical angle is the same, no matter how far away we are ig. 29-4. The energy flowing within In particular, the total energy that we could take out of the whole wave by putting the cone OABCD is independent of the absorbing oscillators all around is a certain fixed amount. So the fact that the distance r at which it is measured amplitude of E varies as l/r is the same as saying that there is an energy flux hich is never lost, an energy which goes on and on, spreading over a greater and greater effective area. Thus we see that after a charge has oscillated, it has lost some energy which it can never recover; the energy keeps going farther and farther ay without diminution So if far enough away that our basic tion is good enough, the charge cannot recover the energy which has been, as we say, radiated away. Of course the energy still exists somewhere, and is available to be picked up by other systems. We shall study this energy"loss"further in apter Let us now consider more carefully how the wave(29.3)varies as a function f time at a given place, and as a function of position at a given time. again we ignore the 1/r variation and the constants 29-3 Sinusoidal waves First let us fix the position r, and watch the field as a function of time. It is oscillatory at the angular frequency a. The angular frequency w can be defined as the rate of change of phase with time(radians per second ). We have already studied such a thing, so it should be quite familiar to us by now. The period is the time needed for one oscillation, one complete cycle, and we have worked that out too; it is 2T/, because w times the period is one cycle of the cosine Now we introduce a new quantity which is used a great deal in physics.This has to do with the opposite situation, in which we fix t and look at the wave as a function of distance r. Of course we notice that, as a function of r, the wave(29.3) also oscillatory. That is, aside from 1/r, which we are ignoring, we see that e oscillates as we change the position. So, in analogy with n define symbolized as k. This is defined as the rate of of phase with distance (radians per meter). That is, as we move in space at a fixed