336 BELL SYSTEM TECHNICAL JOURNAL 



any instant again varies sinusoidally with distance. However, at the 

 boundary of the guide the resultant electric vector is everywhere zero. 

 Since there was no component of the electric force lying along the axis s 

 of the guide in the component waves that gave rise to this configura- 

 tion, there can be no such component in the resultant. Waves in which 

 the electric vector is exclusively transverse are known as transverse electric, 

 or TE, waves. 



A complete account of transmission of this kind should include, of course, 

 a consideration of the lines of magnetic force. From Fig. 6.4-3 it is evi- 

 dent that, at the point of reflection of the component plane wave on the 

 guide wall, there are two components of magnetic force Hj_ and ^n in 

 both the incident and reflected waves. When these are added, the re- 

 sultant of the transverse magnetic force, like that of the electric force, 

 differs at different points in the guides. Following alone the line .v', it 

 is found that for the particular condition here assumed, the magnetic 

 force is zero at each wall increasing sinusoidally to a maximum midway 

 between. At this point the magnetic component is entirely transverse. 

 Following along the line x, it will be found that the magnetic vector is a 

 maximum near each wall decreasing cosinusoidally to zero in the middle. 

 It is of particular interest that, at the wall of the guide, the magnetic 

 component lies parallel to the axis. Magnetic lines of force are, in this type 

 of wave, closed loops, whereas lines of electric force merely extend from 

 the upper to the lower walls of the guide. The arrangement of lines of 

 electric and magnetic force in this type of wave is shown in Fig. 5.2-1. 

 The quantitative relationships between the various components of E and 

 H are specified more definitely by Equation 5.2-1. The significance of the 

 wavelength X^ of this new configuration will be obvious from Fig. 6.5-1 (f). 



There are certain useful results that follow from Fig. 6.5-1 (f). It may 

 be seen from the triangle there shown that 



^ = ^ cot e (6.5-6) 



From Equations 6.5-1 and 6.5-3, it will also be seen that 



7^ 



cos 6 A _ ^ 



cot d = - — = / , ■ • (6.:»-/) 



sm d T 

 2a 



Therefore 



K = — ^T^ = ;yf=, (6.5-8) 



/-ej 



