Question

The element niobium, which is a metal, is a superconductor (i.e., no electrical resistance) at temperatures below $9\mathrm{K}$. However, the superconductivity is destroyed if the magnetic field at the surface of the metal reaches or exceeds $0.10\mathrm{T}$. What is the maximum current in a straight,$3\mathrm{mm}$ diameter superconducting niobium wire?

Short answer

The maximum current will be$750\mathrm{A}.$

Step-by-step solution

Given information

We have given,

Magnetic field = $0.1\mathrm{T}$

Diameter of wire = $3\mathrm{mm}$

We have to find the maximum current in the straight niobium wire.

Simplify

The magnetic field due to wire will be

$$\begin{gathered} \mathrm{B}=\frac{{\mathrm{\mu }}_0\mathrm{I}}{2\mathrm{\pi R}} \\ \mathrm{I}=\frac{\mathrm{B\pi D}}{{\mathrm{\mu }}_0}=\frac{0.1\times \mathrm{\pi }\times 3\times {10}^{-3}}{4\times \mathrm{\pi }\times {10}^{-7}} \\ \mathrm{I}=750\mathrm{A} \end{gathered}$$