. Electric traction and transmission engineering . alone is pB = ZLAll = 7rr2 r2 Representing the potential at the point P due to thecharge on A by VA, and that due to the charge on B by VB,it follows from the definition of potential that dVA = 2_q dri kri , dVB 2 q and — = - -* dr2 kr2 where k is the permittivity or specific inductive capacityof the dielectric. If the potentials at the point O midwaybetween the two very small wires due to their charges berespectively VA and VBf, then the potential differencebetween P and 0 is the sum of -fa *-¥><* <L kn ± k DC 2 r\ TRANSMISSION
. Electric traction and transmission engineering . alone is pB = ZLAll = 7rr2 r2 Representing the potential at the point P due to thecharge on A by VA, and that due to the charge on B by VB,it follows from the definition of potential that dVA = 2_q dri kri , dVB 2 q and — = - -* dr2 kr2 where k is the permittivity or specific inductive capacityof the dielectric. If the potentials at the point O midwaybetween the two very small wires due to their charges berespectively VA and VBf, then the potential differencebetween P and 0 is the sum of -fa *-¥><* <L kn ± k DC 2 r\ TRANSMISSION LINES. 231 and VB- Vb = f*- ^dr2 ^loge —• Or, since for the point 0, Va + VBf = o, the potential atP due to the charges on both wires is VA+VB=V=^log^. (1) For any point to be on the equipotential surface whichpasses through the point P, the ratio of its distances fromB and A respectively must be constant. The locus of a point P which moves so that — is constant is a circle, and if C be its center and r its radius, then CAXCB = r\ (2). Fig. 98. From Fig. 98, which is drawn in accordance with equa-tion (2), it appears that triangles ACP and BCP with the CA r common angle at C are similar, since from (2) — = —— • r CB Therefore AP BPCA CP or CA =-2r and CAr r2 232 TRACTION AND TRANSMISSION. which shows that -1- 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 arecylindrical 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 J, and therefore this surface is a neutralV r2 J plane which bisects the line AB at right angles. All the equipotential surfaces to the left of this plane surround A and those to the right surround B. Consider two equipotential surfaces surrounding the wires A
Size: 2304px × 1084px
Photo credit: © Reading Room 2020 / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., boo, bookauthorsheldonsamuel1862, bookcentury1900, bookdecade1910
