Question

The use of superconductors has been proposed for power transmission lines. A single coaxial cable (see figure below) could carry a power of 1.00 x 103 MW (the output of a large power plant) at 200 kV, DC, over a distance of 1.00 x 103 km without loss. An ?nner wre o radius a 1.00 cm made rom the superconductor Nb3Sn, carries he currentl n ne direction. A surrounding superconducting C linder of radi uso 0 8cm ould a mite return current I. (a) In such a system, what is the magnetic field at the surface of the inner conductor? mT (b) What is the magnetic field at the inner surface of the outer conductor? mT (c) How much energy would be stored in the magnetic field in the space between the conductors in a 1.00 x 103 km superconducting line? MJ (d) What is the pressure exerted on the outer conductor due to the current in the inner conductor? Pa

Answer 1

Given p = 1.0 times 10^3 Mw (power) P = 1.0 times 10^3 times 10^7 w = 1.0 times 10^9 w Delta v = 200 kv = 200 times 10^3 v we know that, P = I times Delta v I = P/Delta v = 1.0 times 10^9/200 times 10^3 I = 5.00 times 10^3 A Current enclosed I = 5.00 times 10^3 A from amphere law, we have B (2 pi r) = mu_0 I (a) At surface of inner conduction i.e., = a = 1.60 cm = 0.016 m B (2 pi r) = mu_0 I B = mu_0 I/2 pi r we know that, mu_0 = 4 pi times 10^- 7. T. m/A B = 4 pi times 10^- 7 times 5 times 10^3/2 pi times (0.016) B = 0.0625 Tesla B = 62.5 milli Tesla rightarrow 62.5 MT \r\n (b) At inner surface of outer conduction, i.e., r = b = 5.50 cm. = 0.055 m B = mu_0 I/2 pi r B = 4 pi times 10^- 7 times 5 times 1063/2 pi times (0.055)