The dipole radiator
As our fundamental “law” of electromagnetic radiation, we are going                         to assume that (28.6) is true, i.e., that the electric                         field produced by an accelerating charge which is moving                         nonrelativistically at a very large distance $r$ approaches that                         form. The electric field varies inversely as $r$ and is proportional                         to the acceleration of the charge, projected onto the “plane of                         sight,” and this acceleration is not today’s acceleration, but the                         acceleration that it had at an earlier time, the amount of delay being                         a time, $r/c$. In the remainder of this chapter we shall discuss this                         law so that we can understand it better physically, because we are                         going to use it to understand all of the phenomena of light and radio                         propagation, such as reflection, refraction, interference,                         diffraction, and scattering. It is the central law, and is all we                         need. All the rest of Eq. (28.3) was written down only to                         set the stage, so that we could appreciate where (28.6)                         fits and how it comes about. We shall discuss (28.3) further next year. In the meantime,                         we shall accept it as true, but not just on a theoretical basis. We                         may devise a number of experiments which illustrate the character of                         the law. In order to do so, we need an accelerating charge. It should                         be a single charge, but if we can make a great many charges move                         together, all the same way, we know that the field will be the sum of                         the effects of each of the individual charges; we just add them                         together. As an example, consider two pieces of wire connected to a                         generator, as shown in Fig. 28–1. The idea is that the                         generator makes a potential difference, or a field, which pulls                         electrons away from piece $A$ and pushes them into $B$ at one moment,                         and then, an infinitesimal time later, it reverses the effect and                         pulls the electrons out of $B$ and pumps them back into $A$!                         So in these two wires charges, let us say, are accelerating upward in                         wire $A$ and upward in wire $B$ for one moment, and a moment later                         they are accelerating downward in wire $A$ and downward in wire $B$.                         The fact that we need two wires and a generator is merely that                         this is a way of doing it. The net result is that we merely have a                         charge accelerating up and down as though $A$ and $B$ were one single                         wire. A wire that is very short compared with the distance light                         travels in one oscillation period is called an electric dipole                             oscillator. Thus we have the circumstance that we need to apply our                         law, which tells us that this charge makes an electric field, and so                         we need an instrument to detect an electric field, and the instrument                         we use is the same thing—a pair of wires like $A$ and $B$!                         If an electric field is applied to such a device, it will produce a                         force which will pull the electrons up on both wires or down on both                         wires. This signal is detected by means of a rectifier mounted between                         $A$ and $B$, and a tiny, fine wire carries the information into an                         amplifier, where it is amplified so we can hear the audiofrequency                         tone with which the radiofrequency is modulated. When this probe feels                         an electric field, there will be a loud noise coming out of the                         loudspeaker, and when there is no electric field driving it, there                         will be no noise. Because the room in which the waves we are measuring has other objects                         in it, our electric field will shake electrons in these other objects;                         the electric field makes these other charges go up and down, and in                         going up and down, these also produce an effect on our probe. Thus for                         a successful experiment we must hold things fairly close together, so                         that the influences from the walls and from ourselves—the reflected                         waves—are relatively small. So the phenomena will not turn out to                         appear to be precisely and perfectly in accord with                         Eq. (28.6), but will be close enough that we shall be able to                         appreciate the law. Now we turn the generator on and hear the audio signal. We find a                         strong field when the detector $D$ is parallel to the generator $G$ at                         point $1$ (Fig. 28–2). We find the same amount of field                         also at any other azimuth angle about the axis of $G$, because it has                         no directional effects. On the other hand, when the detector is at $3$                         the field is zero. That is all right, because our formula said that                         the field should be the acceleration of the charge projected                             perpendicular to the line of sight. Therefore when we look down                         on $G$, the charge is moving toward and away from $D$, and there is no                         effect. So that checks the first rule, that there is no effect when                         the charge is moving directly toward us. Secondly, the formula says                         that the electric field should be perpendicular to $r$ and in the                         plane of $G$ and $r$; so if we put $D$ at $1$ but rotate it                         $90^\circ$, we should get no signal. And this is just what we find,                         the electric field is indeed vertical, and not horizontal. When we                         move $D$ to some intermediate angle, we see that the strongest signal                         occurs when it is oriented as shown, because although $G$ is vertical,                         it does not produce a field that is simply parallel to itself—it is                         the projection of the acceleration perpendicular to the line of                             sight that counts. The signal is weaker at $2$ than it is at $1$,                         because of the projection effect.