SOME EQUIVALENCE THEOREMS OF ELECTROMAGNETICS 105 



There are times, however, when the current distribution in the 

 "screen" can be determined with a fair accuracy without elaborate 

 mathematics. It is so, for instance, in the case of a pair of perfectly 

 conducting coaxial cylinders (Fig. la and Fig. lb) in which the radii 



Fig. la — An axial cross-section of a coaxial pair. 



15 



Fig. Ih — An axial cross-section of a coaxial pair. 



are small by comparison with the wave-length. We shall assume that 

 the coaxial pair is semi-infinite. Trusting his common sense, the 

 engineer assumes that inside this structure the magnetic lines are 

 circles coaxial with the cylinders. The electric lines are the radii and 

 the electric current in the cylinders as well as the transverse voltage 

 between the cylinders vary along the length in the same way as in a 

 transmission line with uniformly distributed series inductance and 

 shunt capacity. A careful analysis by John R. Carson indicates that 

 this simple picture is justifiable if the cross-section of the coaxial pair 

 is small by comparison with the wave-length.^" While a whole series 

 of electric waves can exist in such a structure, all of these waves except 

 the one recognized by the engineer, the principal wave, are attenuated 

 very rapidly and are significant only very close to the generator and 



'"John R. Carson, "The Guided and Radiated Energy in Wire Transmission," 

 A. I.E. E. Journal, pp. 908-913, October, 1924. 



