The use of superconductors has been proposed for power transmission lines. A single coaxial cable (as shown) could carry a power of 1.00 × 103 MW (the output of a large power plant) at 200 kV, DC, over a distance of 1.00 × 103 km without loss. An inner wire of radius a = 2.00 cm, made from the superconductor Nb3Sn, carries the current Iin one direction. A surrounding superconducting cylinder of radius b = 5.00 cm would carry the return current I. In such a system, what is the magnetic field (a) at the surface of the inner conductor and (b) at the inner surface of the outer conductor? (c) How much energy would be stored in the magnetic field in the space between the conductors in a 1.00 × 103 km superconducting line? (d) What is the pressure exerted on the outer conductor due to the current in the inner conductor?
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