The single-phase power line of Prob. 4.6 is replaced by α three-phase line on a horizontal crossarm in the same position as that of the original single-phase line. Spacing of the conductors of the power line is D13 = 2D12 = 2D23, and equivalent equilateral spacing is 3 m. The telephone line remains in the position described in Prob. 4.6. If the current in the power line is 1 50 A, find the voltage per kilometer induced in the telephone line. Discuss the phase relation of the induced voltage with respect to the power-line current.

Prob. 4.6

The energy density (that is, the energy per unit volume) at a point in a magnetic field can be shown to be B2/2μ, where B is the flux density and μ is the permeability. Using this result and Eq. (4 .10), show that the total magnetic field energy stored within a unit length of sol id circular conductor carrying current I is given by μl2/16π. Neglect skin effect, and thus verify Eq. (4.1 5)