﻿56 Effect of a Long Straight Wire on Electric Waves. 



have to do with waves propagated outwards from the wire. 

 Thus we get 



h (ter) =Be- iKr /y / Kr, V(*r) = —iBe- iKr /^/Kr~, 



h '(Ka)=l/Ka, h "(Ka) = -l/(Ka) 2 . 



Substituting these we obtain for the magnetic force in 

 the scattered wave the approximate formula 



y 1 =BB o K 2 a 2 ({-cos0)e i <P t -' er >/ \Zk^, . . (26) 



valid for values of r which are great compared with the 

 wave-length. 



6. When the electric intensity in the incident wave is 

 parallel to the axis of the wire, we denote it by 



that is 



Z o = E^-Zg s Ccr)cosB0 (27) 



By reasoning similar to that of the previous Article, it is 

 seen that the electric intensity Z 2 of the scattered wave will 

 be of the form 



Z^^BAMcos^. .... (28) 



The boundary condition at the surface of the wire is 



z +z 1= o, 



whence 



B s = -E g s (Ka)h s (Ka) 

 and 



Z^-E/^Mfgcos^. . . . (29) 



When Ka is very small the successive terms decrease 

 rapidly in importance, and we may use the approximate 

 formula 



Z^-E^^Mlg+^MlgJcos^], (30> 



= -%-[(l-W!g-^^cos*]. (3D 



Introducing the approximations for the // functions for 

 Ka small and for Kr large, we get finally 



log {Ka) J ^/ Kr 



for values of r great compared with the wave-length. 



7, Results (26) and (32) should be compared with the 



