968 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1954 



Once the appropriate H^ is determined, Hr and E^ are given by 



(28) 



/3- — uryLii \ dr 





(f - -^-0 



^2 - coV^i 

 The tangential impedance for TE-fields is thus 



^^- "'^ ^^log//. -pH/3). (29) 



H, ji0-' - co'uLe,) \dr 



The reader will recall that for isotropic media (pn = 0) the numerator 

 of the right hand side of equation (29) can always be expressed as the 

 ratio of first order to zero order Bessel functions by virtue of relations 

 Hke Ko (x) = —Kiix), V(x) = h(x) and so on. Analogous results 

 hold true in the present case. Suppose, for example, that we are dealing 

 with a geometry such that the correct H, is 



Hz = — AC — = Rxo{2a2r), say 



Then 



and 



Hz or 



2a2C0n RxO + xR 



xo 



i((S2 — co-fiei) R^o 



It is shown in Appendix I that 



^xo' + X^xo = (x - ^) Rxi ■ 

 Therefore 



^ _ a^M«o(2x - 1) Rxii2a.r) 

 j{l3~ - o}-fxei) Rxo{2a2r) ' 



^ co/ia2(2x — 1) W^,i(2a2r) 

 i(^2 _ ^2^,^) Wx.oi2a.yr) " 



A similar difference relation shows that if the region is such that 



Hz = Mx,o{2a2r)/V2a2r, 



(30) 



