. Electric traction and transmission engineering . ig. 98. From Fig. 98, which is drawn in accordance with equa-tion (2), it appears that triangles ACP and BCP with the CA rcommon angle at C are similar, since from (2) — = —-• r CB Therefore AP^B£ n rz CA CP °^ CA r and — = -; r H 232 ■TRACTION AND TRANSMISSION. which shows that — is constant whatever the position of P on the circle. Consequently the equipotential surfaces re-sulting from the charges on the two wires A and B arecyUndrical in shape and are not coaxial with those wires;furthermore,-the axes of such cylinders of different radii a
. Electric traction and transmission engineering . ig. 98. From Fig. 98, which is drawn in accordance with equa-tion (2), it appears that triangles ACP and BCP with the CA rcommon angle at C are similar, since from (2) — = —-• r CB Therefore AP^B£ n rz CA CP °^ CA r and — = -; r H 232 ■TRACTION AND TRANSMISSION. which shows that — is constant whatever the position of P on the circle. Consequently the equipotential surfaces re-sulting from the charges on the two wires A and B arecyUndrical in shape and are not coaxial with those wires;furthermore,-the axes of such cylinders of different radii arenot coincident. The radius of the zero potential surfacewhich passes through the mid-point 0 must be infinitely large (for — = i|, and therefore this surface is a neutral plane which bisects the line AB at right angles. All theequipotential surfaces to the left of this plane surround Aand those to the right surround B. Consider two equipotential surfaces surrounding thewires A and B to be replaced by solid cylindrical conductors. Fig. 99- of radii at and az respectively, Fig. 99, and carrying chargesrespectively oi -\- q and — q units per centimeter length ofconductor. Such substitution does not alter the potentialor electric flux distribution beyond these surfaces. Thepotentials of the wires are respectively Fx = ^ log. BMAM TRANSMISSION LINES 233 J Tr 2g, AN and 7,= _^ Therefore their potential difference is £ = 7i-F2 = ^log, BM-AN k =AM-BN But from the figure BM BM BCi and AM AM ai^iV AN AC2 BN BN 02 also AC2 X -BC2 = Oi , ^ 2q, BCi a<i consequently £=-Iog,—.-^ (3) Furthermore, 5Ci(5Ci-d)=Vand 5C2 (^Ca + d) = 02^ whence 5Ci = —V\ a^ -\ 2 V 4 and 5C2 = - - + \la2^+—- 2 V 4 Therefore the capacity per centimeter length of line havingtwo cylinders of radii ai and ch as conductors is, from (3), If both wires have the same diameter, r = Ci = a^, andthe capacity is TRACTION AND c = 2 log. v/-(0 2r V \2r) 2r (4) spresenting the dis
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