30 BELL SYSTEM TECHNICAL JOURNAL 



the wave-length) we have 



//^+ = 7. — ^cos if, H+ = - - — r,sin <p. (11) 



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

 / 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 



E^^ = cos (f, ZJ' = ioijxp. (12) 



l-Kp 



The exact field of the line doublet and the corresponding radial 

 impedance are : 



•qa 



am 



Ez^ = ;: Ki(ap) cos (f, H^+ = - -^r—Ki{ap) COS ^p, 



l-K ZTT 



, all j^ / X • 7 , K\{ap) 



Hp^ = - 75 — Ai(o-p) sin if, Z+ = - r]^^—r, — r. 



ZTrp Ai \ap) 



The internal cylindrical wave with the same relative amplitude 

 distribution over equiphase surfaces as in the wave originated by the 

 line doublet is^ 



EzT — icon A I\{<Tp) cos ip, II^~ = a A Ii(ap) cos (p, 



Hp = — 1 i{(Tp) sm ip, Zp = r}-j-ri — r. 



p 1 1 {(jp) 



Close to the doublet we have approximately 



Ef — iwjjiPp cos (p, II^~ = P cos ip, 



lip" — P sin ip, Zp~ = iwp.p. 



Another familiar field is that produced by two parallel line charges 

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



_ ql sin ip 77 + _ g^ cos "P 



Iirep- Zirep- 



(13) 

 TT + _ ^cog/ sin y 7 +— 1 



Zirp icoep 



^ The symbols In(x) and Kn{x) designate the modified Bessei functions as defined 

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



