A single superconducting coaxial cable could carry a power of 1 GW (the output of a large power plant) at 200 kV, DC, over a distance of 1000 km without loss. An inner wire of radius a = 2.40 cm, made from the superconductor Nb3Sn, carries the current (I) in one direction. A surrounding superconducting cylinder of radius b = 4.54 cm would carry the return current (I). a) In such a system, what is the magnetic field at the surface of the inner conductor (in mT)? b) What is the magnetic field at the inner surface of the outer conductor (in mT). c) How much energy would be stored in the magnetic field in the space between the conductors in a 1000 km superconducting line (in MJ)? d) What is the pressure exerted on the outer conductor due to the current in the inner conductor (in Pa)?
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A single superconducting coaxial cable could carry a power of 1 GW (the output of a large power plant) at 200 kV, DC, over a distance of 1000 km without loss. An inner wire of radius a = 2.40 cm, made from the superconductor Nb3Sn, carries the current (I) in one direction. A surrounding superconducting cylinder of radius b = 4.54 cm would carry the return current (I). a) In such a system, what is the magnetic field at the surface of the inner conductor (in mT)? b) What is the magnetic field at the inner surface of the outer conductor (in mT). c) How much energy would be stored in the magnetic field in the space between the conductors in a 1000 km superconducting line (in MJ)? d) What is the pressure exerted on the outer conductor due to the current in the inner conductor (in Pa)? |
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