. The Bell System technical journal . ikiRi pikiRi „ , „ IIx* is the wave potential of a • dipole placed parallel to a perfectly conducting plane, k^ infinite. So, writing. Fig. 1Y^h = n^« + n^ and correspondingly E^ = E^ + E^ £/ = -iJ n/ + ^r^-f (I- n/ + A n/ +1- n/ ) L OS \ 5x dy dz I = — io)2 cos v? ri I /i(tp) , , _ ( ■ ^ ;, ,—j^j^— / ) T-dr I -{- m\ k^H + k{-m f Jo = — iccil cos ^ I /i(rp)g~ , .,. , , „ ^r,Jo ^2-/ + ^i-w ki dxj^ \k2~l + ki-m I — to: where 1 d^ki dxdw V - 2 rT Jo k-d + ki-m (2)(3) 664 BELL SYSTEM TECHNICAL JOURNAL When ^2= °o, V= IR^^ exp ikiR2 and £/ is zero. When^2 = ki,
. The Bell System technical journal . ikiRi pikiRi „ , „ IIx* is the wave potential of a • dipole placed parallel to a perfectly conducting plane, k^ infinite. So, writing. Fig. 1Y^h = n^« + n^ and correspondingly E^ = E^ + E^ £/ = -iJ n/ + ^r^-f (I- n/ + A n/ +1- n/ ) L OS \ 5x dy dz I = — io)2 cos v? ri I /i(tp) , , _ ( ■ ^ ;, ,—j^j^— / ) T-dr I -{- m\ k^H + k{-m f Jo = — iccil cos ^ I /i(rp)g~ , .,. , , „ ^r,Jo ^2-/ + ^i-w ki dxj^ \k2~l + ki-m I — to: where 1 d^ki dxdw V - 2 rT Jo k-d + ki-m (2)(3) 664 BELL SYSTEM TECHNICAL JOURNAL When ^2= °o, V= IR^^ exp ikiR2 and £/ is zero. When^2 = ki, V = li?2~^ exp ikiR2 and E^^ just cancels the field of theimage dipole in £°°. The wave potential of a vertical dipole is ^^ ^ n/ = ^-^+F. (4) V is the function ITo analysed by Sommerfeld in Riemann-WebersDifferentialgleichungen der Physik. Sommerfeld transforms the inte-gration from 0 to 00 into an integration from — oo to + =» by re-placing the Bessel function by its equivalent Hankel functions andthen wraps the real axis path of integration around the zero of kiH-f ki^m and the two branch cuts from ki and ^2 to -f- * 00. He thusgets V = P
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Keywords: ., bookcentury1900, bookdecade1920, booksubjecttechnology, bookyear1
