Question

Niobium metal becomes a superconductor when cooled below 9K. Itssuperconductivity is destroyed when the surface magnetic fieldexceeds 0.100 T. Determine the maximum current a 2.00-mm-diameterniobium wire can carry and remain superconducting, in the absenceof any external magnetic field.

Answer 1

the maximum current is 500 A

Step-by-step explanation:

Given the data in the question;

the B field magnitude on the surface of the wire is;

B = μ₀i / 2πr

we are to determine the maximum current so we rearrange to find i

B2πr = μ₀i

i = B2πr / μ₀

given that;

diameter d = 2 mm = 0.002 m

radius = 0.002 / 2 = 0.001 m

B = 0.100 T

we know that permeability; μ₀ = 4π × 10⁻⁷ Tm/A

so we substitute

i = (0.100)(2π×0.001 ) / 4π × 10⁻⁷

i = 500 A

Therefore, the maximum current is 500 A