'624 Mr. J. R. Carson on 



To apply the law cnrlE= — yui/>H to this surface, it is 

 only necessary to calculate the magnetic flux through the 

 surface and the line integral of the electric force around 

 the contour. The contribution to the line integral from the 

 elements dz is, by (15) and (17), 



a,** 3 



lt>v { ) /oT n / -< 7 '1 1 , 7 J 2 \ 



which m;iy be written as 



21Zdz = 2Z Idz(l-h 1 J 1 ± + 7i 2 ^-..A . . (55) 



where Z = 2/nip J /f J ' and the argument of the Bessel 

 functions is f = ia V ^irkjiip. Z is the " internal " or 

 "self-impedance" of the wire when the return wire is 

 either concentric or at such a distance as to make the 

 proximity effect negligible. 



To calculate the contribution to the contour integral of 

 the lines in the dielectric joining the corresponding ends 

 of the segments dz, it will be recalled that the electric 

 force in the dielectric in the plane XY is derivable as the 

 gradient of a scalar or electrostatic potential, as given in 

 equation (14). Consequently the contributions of these 

 lines are simply 



(v +^V,-T )<fa = -yVodz, 



where V is the electrostatic potential betiveen the two wires. 

 If K denote the electrostatic capacity between the two 

 wires, then 



v^W 1 (56; 



and 7 2 



-yV dz =--r^Idz, 



and the total line integral of electric force around the 

 contour is 



( 8Z -&) IA (57 > 



The calculation of the electrostatic capacity K involves 

 merely the solution of the two-dimensional potential problem 

 in which the surfaces of the wires are equipotential. 



