736 BELL SYSTEM TECHNICAL JOURNAL 



If po is the d-c linear charge density and p the a-c Hnear charge density 



Po = --. (30) 



If g, is the z component of convention current, we have 



qz = PqZ -\- Uqp ■ 



(31) 





(32) 



(33) 



?' = 4(i/3-r)- (^^) 



3. Combined Equation 

 Combining (34), (28) and (25) with (IS), we obtain 



_ ^0 To r iff aKr* - (iff - r)) 1 



^ - «5 ^o(r^ - Tl) L(iff - r)5 [(iff - D + ffS] J • ^ ^ 



We now introduce new parameters 



K = ^ = ^1^ (36) 



C^ = ('^«V (37) 



Here Po is the power transmitted by the circuit for a field strength £2 . K 

 has the dimensions of impedance. Vo is the voltage specifying the electron 

 velocity Uq 



ul = 2riVo . (38) 



From (36)-(38) and (35) we see 



_ 2ff'C'r, [- jt. ::_^ w^ -'' I (3y) 



2ff'C'r, r iff _ «Kr* - (iff - r)) ' 

 (r' - rS) L(iff - r)^ [(iff - r)^ + ffSl 



