Question

Niobium metal becomes a superconductor when cooled below 9 K. Its superconductivity is destroyed when the surface magnetic field exceeds 0.100 T. In the absence of any external magnetic field, determine the maximum current a 4.50-mm-diameter niobium wire can carry and remain superconducting.

Answer 1

To develop the problem it is necessary to apply the concepts related to Magnetic Field.

The magnetic field is defined as

`B = (\mu_0 I)/(2\pi r)`

Where,

`\mu_0 =` Permeability constant in free space

r = Radius

I = Current

Our values are given as,

B = 0.1T

d = 4.5mm

r = 2.25mm

If the maximum current that the wire can carry is I, then

`B = (\mu_0 2I)/(4\pi r)`

`I = (Br)/(2(\mu_0)/(4\pi))`

`I = ((0.1T)(2.25*10^(-3)m))/(2(1*10^(-7)N/A^2))}`

`I = 1125A`

Therefore the maximum current is 1125A