One problem with some of the newer high-temperature superconductors is getting a
ID: 1282222 • Letter: O
Question
One problem with some of the newer high-temperature superconductors is getting a large enough current density for practical use without causing the resistance to reappear. The maximum current density for which the material will remain a superconductor is called the critical current density of the material. In 1987, IBM research labs had produced thin films with critical current densities of 1.0 x 10^6 A/cm^2. What diameter cylindrical wire of such a material would be needed to carry 956 A without losing its superconductivity? mm x 0^5 A/cm^2. (a) How much current could an 18-gauge wire of this material carry and still remain superconducting? (18-gauge has a nominal diameter of 1.02 mm.) A (b) Researchers are trying to develop superconductors with critical current densities of 1.0Explanation / Answer
a)
i = J A
=> i = J (pi d^2/4)
d = 1.02 mm = 0.102 cm
=> i = (1.0e5)*(3.1416*(0.102)^2/4)
=> i = 817 A
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b)
i = J A
=> i = J (pi d^2/4)
=> d = sqrt(4 i/(J pi))
=> d = sqrt(4*956/(3.1416*1e6))
=> d = 0.0349 cm
=> d = 0.349 mm
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