Wave Propagation over Parallel Wires. 625> 



We have now to calculate the magnetic flux through the 

 surface ; it is 



which by reference to equation (13) becomes 

 -Uz \ C " i dy(B 1 ly--B 2 /f + B i lf- . . . ) 



»y a 



= -2 ( L-rB 1 log(^)-B 2 ( 1 --i-) 

 L °\ a / \a c — a/ 



+ iB 3 (i-^p)-.. 



From (27) and (33) this reduces to 



MHM 



j 



. . (58) 



The law curlE= — fiipB. now gives at once 





r 7 ^=2Z + ^L, . . . 

 where 



. . (59) 



Z = Z (l-/* 1 J 1 /J o +7i 2 J 2 /J 



-...), ... 



. . (60) 



L = Ul-lj,-p , +ji 



-(AT 



L 



..) 



and 



Z = 2/tipJ /f J ', 



L = 41oo( 1 ^'j 



(61). 



(62) 

 (63) 



Z may therefore lie regarded as the impedance of the 

 wire, and L the inductance corresponding to the magnetic 

 flux between the wires ; Z and L are their limiting values 

 when the parameter k is vanishingly small — that is, when the 

 proximity effect is negligibly small. While it is convenient 

 from this standpoint to regard L as the inductance per 

 unit length of the circuit, it must be carefully borne in 

 mind that both Z and L are complex. Consequently the 



