SOME EQUIVALENCE THEOREMS OF ELECTROMAGNETICS 109 



Let us now calculate the more general expression for the power 

 radiated from an open end of a coaxial pair. The cylindrical con- 

 ductors whose cross-sections are shown in Fig. 9 are supposed to extend 



Fig. 9 — The end view of a coaxial pair of cylindrical conductors. 



below the surface of the paper and the s-axis of the coordinate system 

 is directed toward the reader. The primed letters will refer to points 

 situated in the opening, the unprimed letters being reserved for typical 

 points in space. 



The electric intensity in the coaxial pair varies inversely as the 

 distance from the axis 



£.' = 



£^' - 0. 



(21) 



In accordance with the Equivalence Principle we assume that the field 

 below the .rj-plane is wiped out and the discontinuity in E arising as 

 the result of the separation is replaced by a magnetic current sheet. 

 This magnetic current is perpendicular to E; by (14) its density is 



M^' =-£„,= 



P 



M.. = 0. 



(22^ 



The constant E is related to the voltage V between the ends of the 

 coaxial conductors; in fact, we have 



V 



C^ b 



P = 



V 



1 ^ 



(23) 



