\begin{problem*}{22.43}
Niobium metal becomes superconducting when cooled below 9K.  Its
superconductivity is destroyed when the surface $B$ field exceeds
$B_{max} = 0.100\U{T}$.  Determine the maximum current in a
$d=2.00\U{mm}$ diameter niobium wire can carry and remain
superconducting, in the absence of any external $B$ field.
\end{problem*} % problem 22.43

\begin{solution}
For long, cylindrical wires, the magnetic field a distance $r$ from
the center of the wire is
\begin{equation}
 B = \frac{\mu_0 I}{2 \pi r}
\end{equation}
As long as you are outside the wire.

Therefore, the magnetic field at the surface is maximized when
\begin{align}
 B_{max} &= \frac{\mu_0 I_{max}}{2 \pi r} \\
 I_{max} &= (2 \pi r B_{max})/\mu_0 = \ans{500\U{A}}
\end{align}
\end{solution}
