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

$B = \frac{\mu_0 I}{2\pi r}$

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

$B = \frac{\mu_0 2I}{4\pi r}$

$I = \frac{Br}{2\frac{\mu_0}{4\pi}}$

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

$I = 1125A$

Therefore the maximum current is 1125A