308 BELL SYSTEM TECHNICAL JOURNAL 



first, and having centers on a line at right angles to the first as shown in 

 Fig. 6.2-2(b). The total flow of power through any plane set up perpen- 

 dicular to the wires is found by adding up the various component products 

 of E and H from the boundaries of the wires to infinity. The method by which 

 this is carried out is outside of the scope of this chapter, but, as already 

 pointed out, it leads to the same result as obtained by multiplying together 

 the total voltage and the total current. There are two results of this integra- 

 tion that are of special interest. (1) In the case of two parallel cylinders, one- 

 half of the total power flows through the space enclosed by a circle drawn 

 about the wire spacing as a diameter [see Fig. 6.2-2(b)]. The remaining half 

 extends from this circle on out to infinity. (2) Since both the electric and 

 magnetic intensities are greatest in the neighborhood of the wire, most of 

 the total power flow takes place in the immediate vicinity of the wire. 



Transmission of A-c Power 



If the simple d-c source mentioned previously is replaced by an alternat- 

 ing electromotive force, a variety of phenomena may take place, the more 

 important of which will depend on the frequency of alternation. If this fre- 

 quency is low (very long wavelength), the line may be relatively short com- 

 pared with the wavelength, with the result that changes occurring at the 

 source may appear very soon at the remote end. For this case, the observed 

 phenomena will vary sinusoidally with time everywhere along the line, in 

 substantially the same phase. This is the typical alternating-current power 

 line problem* and, except for minor details, which we shall not discuss at 

 this time, it does not differ materially from the simple d-c case already 

 covered. 



If, on the other hand, the frequency is high (short wavelength), the line 

 may be regarded as being electrically long, with the result that sinusoidal 

 changes occurring at the source may not have traveled very far before the 

 direction of flow at the source has changed. The over-all result in extreme 

 cases may become very complicated indeed; for, wavepower may not only 

 be reflected from the remote end of the line but, if there are sharp bends in 

 the line or abrupt changes in spacing, it may be reflected from these points 

 also. The phenomenon observed is usually referred to as wave inlerference 

 and it often leads to standing waves. Though described above as complicated, 

 there are many cases where the results of wave interference may be suffi- 

 ciently simple to be readily visualized. Practical difliculties of various kinds 

 may arise from these effects, but they may also serve very useful purposes. 

 In fad, a substantial i)orti()n of our microwave technique is based on wave 



■' The wavclcnglh corresponding to a frequency of 60 cycles per second is five million 

 meters. A commercial |)ower line having a length as great as 100 miles is therefore but 

 0.03 wavelength long. It is said to he electrically sliorl. 



