problem of a two-wire line with different radii is that of two equipotential circles of unequal radii, one on each side

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Problem Of A Two Wire Line With Different Radii Is That Of Two Equipotential Circles Of Unequal Radii One On Each Side 1 (69.09 KiB) Viewed 85 times

problem of a two-wire line with different radii is that of two equipotential circles of unequal radii, one on each side of the y-axis in Fig. 4-8; it can be solved by deter- mining the locations of the equivalent line charges. Assume that the radii of the wires are a, and a2 and that their axes are separated by a distance D, as shown in Fig. 4-9. The distance b of the line charges to the origin is to be determined. This can be done by first expressing c, and c₂ in terms of a₁, a2, and D. From Eq. (4-54) we have 2 [0²-2²-3²279²=4 (4-55) and 6²=c²-a² (4-56) But C₁ + C₂ = D (4-57) Solution of Eqs. (4-55), (4-56), and (4-57) gives C1 = 1 - 2/0 (D² + a²-a3) 2D (4-58) and 1 -20 (D² + a²-a). (4-59) The distance b can then be found from Eq. (4-55) or Eq. (4-56). An interesting variation of the two-wire problem is that of an off-center con- oting gulindrigal tunnel shown in