3d BELL SYSTEM TECHNICAL JOURNAL 



the wave-length) we have 



In this equation // is the moment of the doublet per unit length, 

 I being the current and I the distance between the filaments. These 

 equations are well known in the elementary theory of electromag- 

 netism. The electric field is obtainable from (11) with the aid of 

 Faraday's law of electromagnetic induction. This field and the corre- 

 sponding radial impedance are 



Ej+ = ^ cos (p, Zp+ = ioofip. (12) 



Zirp 



The exact field of the line doublet and the corresponding radial 

 impedance are : 



£/ = — ^ — Ki{ap) cos if, II^+ = - %— Kx{ap) cos ip, 



LTV /TT 



TT + ^^^ z^ r \ • V 4- Ki(ap) 



Hp+ = -- — Ai(o-p) sm ip, Zp+ = - v-^-T? — X- 



The internal cylindrical wave with the same relative amplitude 

 distribution over equiphase surfaces as in the wave originated by the 

 line doublet is" 



Ez~ — ioj/uA I\{<Tp) cos <p, 11 ^~ = crA Ti(ap) cos (p, 



Hp = — li{(Tp) sm cp, Zp = ■n-j-r, — r- 



p li {ap) 



Close to the doublet we have approximately 



Ef = iufxPp cos (p, II^~ = P cos (p, 



Hp~ = P sin (f, Zp~ = icofip. 



Another familiar field is that produced by two parallel line charges 

 in a perfect dielectric. Close to the doublet this field is 



_ 9/_sin_j^ _ £/_cos_^ 



Zirep- Zirep 



(13) 

 TT + _ ^'^g^ sin (p 7 +— _A_ 



Zirp iwep 



* The symbols 7„(x) and Kn{x) designate the modified Bessel functions as defined 

 in G. N. Watson's "Bessel Functions." 



