\begin{problem*}{23.64} % inductor energy
A novel method of storing energy has been proposed.  A huge,
underground, superconducting coil, $d = 1.00\U{km}$ in diameter, would
be fabricated.  It would carry a maximum current of $I=50.0\U{kA}$
through each winding of an $N = 150$ turn Nb$_3$Sn solenoid.
\Part{a} If the inductance of this huge coil were $L = 50.0\U{H}$,
what would be the total energy stored?
\Part{b} What would be the compressive force per meter length acting
between two adjacent windings $r = 0.250\U{m}$ apart?
\end{problem*}

\begin{solution}
\Part{a}
\begin{equation}
 U_L = \frac{1}{2} L I^2 = \ans{62.5\E{10}\U{J}}
\end{equation}

\Part{b}
Because the radius of the loop is so much larger than the spacing
between windings, we can ignore the curvature of the wires and treat
them as infinitely long and parallel.
Then the magnetic field of one at the location of it's neighbor is
\begin{equation}
 B = \frac{\mu_0 I}{2 \pi r}
\end{equation}
And the force per unit length is
\begin{equation}
 F/l = IB = \frac{\mu_0 I^2}{2 \pi r} = \ans{2000\U{N/m}}
\end{equation}
\end{solution}
