One problem with some of the newer high-temperature superconductors is getting a

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 861 A without losing its superconductivity? mm x 10^5 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 1.0

Explanation / Answer

apply the formula for current density J   = Current/area = i/A

where A is area = pi r^2

so

current i = J A

i = (1e5/1e-4) * 3.14 * 0.51 e-3*0.51e-3

i = 816.714 Nano Amps

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now use Area A = i/J

A = pi r^2 = 861/(1e10)

r^2 = 8.61 e-8/3.14

r^2 = 2.74 e-8

r = 0.165 mm

diameter D = 2r = 0.3311 mm

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