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BELL SYSTEM TECHNICAL JOURNAL 



E„ = + f — COS I [- u(fiiu) + gi(u)) 



+ oi\{p\{u) — qi{ti))']Jx{ni)du. 



Or since cos 



Ji(ru)dn = - ^ I 

 '^•^" Jo 



Jo(ru) 



E.= 



(00 

 (/i(«) + gi(n))Jo{ru)du 

 - „ 



>.j'^[-(Mu)+g,(u)) 



H — ipiiii) — gi(u)) Jo(ru)du, (26a) 



ai 



+ T7(/'i(") -ei(«)) 



Jo(ru)du. 



Inserting the values of /i(m), gi(M), pi(w). and gi(zO for h = and 

 neglecting all displacement currents (eo = ci = C2 = 0), the following 

 expression is obtained: 



-C-Xj -*— '2/ C/ O 



\vh( 



icoP(r) 



d^Q(r) d^Q(r) 



dx' 



' dxdy J ' 



(27) 



^(^) = 2 r|[«i + «o + («, - a2)e-2''«.]Jo(nO^«, 

 Jo 



+ [ai + a2 + (ai - a2)e-^^''^2A2] Jo{ru)du, 

 where as before 



and 



A = (ao + ai){ai + 02) + (ao — «i)(«i — a2)e~-^i 



A] — (aoXi + aiXo)(aiX2 + a2Xi) + (aoXi — a:]Xo)(aiX2 — Q!2Xi)e~-^i, 

 A2 = (ao + ai) (0:1X2 + a2Xi) + (ao — ai)(ai\2 — a2\i)e~'^'^i. 



The mutual impedance of wire elements dS and ds lying in the plane 

 2=0, and including the angle e between their directions, is: 



