WAVEGUIDE TRANSMISSION 329 



Included are the relative directions of E and H both before and aftei 

 reflection. 



In Fig. 6.4-2 there are shown in cross section representative lines of 

 electric force in an advancing plane wave front. They are numbered re- 

 spectively 1, 2, 3, 4, 5, 6, and 7. Each individual figure [(a), (b), (c), etc.] 

 represents a succeeding period of time. We shall assume that the particular 

 wave front singled out for illustration represents the crest of a wave 

 Both ahead and behind this crest there are located alternately at half-wave 

 intervals other crests and hollows, and their respective lines of force alternate 

 in direction. Each line of force m the wave front is assumed to be moving 

 in a direction indicated by the vector v. It is furthermore assumed that 

 there is also present a magnetic component, indicated by the dotted vector 

 // that is perpendicular to E and also to v. The vectors v and H must of 

 course be so directed as to be in keeping with the right-hand or cork-screw 

 rule, both before reflection and after reflection. Also at the point of incidence 

 the tangential electric force must be zero. To account for this, we assume 

 that as each line of electric force moves up to the conducting plane it is 

 reversed in direction, thereby making on the average as many lines of 

 electric force at the surface directed toward the observer as directed away 

 from the observer. Consider, for example, lines of force 3 and 5, 2 and 6, 

 and 1 and 7, in Fig. 6.4-2(c). 



Associated with these two components of electric force which, let us say, 

 are E and E', there are two components of magnetic force // and H'. 

 These may be specified by H = e(v x E), each of which at the interface may 

 be resolved into two components shown in Fig. 6.4-3 sls H = H j_ + -^n 

 at the left and H _i_' = —H\{ at the right. Combining these four vec- 

 tors, assuming reflection to be perfect, we find that at the interface 

 H j_ — H j_' = and H^^ — { — H/) = 2H, giving as an over-all result: 

 (1) the electric force at the interface is everywhere zero; (2) the vertical 

 component of the magnetic force at this point is also zero; and (3) the 

 tangential component of the magnetic force at the interface is 2//. 



The peculiar configuration that resides close to the metal boundary is 

 propagated to the right as a kind of magnetic wave. It has rather inter- 

 esting properties which will become more evident by referring again to 

 Fig. 6.4-2. Two conclusions may be drawn from this figure, depending 

 on the point of view assumed. To a myopic observer located at the inter- 

 face and unable to see far beyond the point p and unable to distinguish one 

 line of force from another, the advancing wave front would look like a con- 

 figuration of amplitude H^^ = 2H and £|| = moving parallel to the inter- 

 face with velocity v^ = I'/sin d. To this observer the apparent velocity 

 would increase as 6 becomes progressively smaller until, at perpendicular 

 incidence, Vz would approach infinity. These results follow from the geo- 



