\begin{problem*}{23.2} % induction
An $N = 25$ turn circular coil of wire has diameter $d = 1.00\U{m}$.
It is placed with it's axis along the direction of the Earth's
magnetic field of $B = 50.0\U{$\mu$T}$, and then in $t = 0.200\U{s}$
it is flipped 180\dg.  An average emf of what magnitude is generated
in the coil?
\end{problem*}

\begin{solution}
The flux before the flip is
\begin{equation}
 \Phi_{Bi} = AB = N \pi r^2 B \;,
\end{equation}
and the flux after the flip is
\begin{equation}
 \Phi_{Bf} = -AB = -N \pi r^2 B \;.
\end{equation}

From Ampere's law
\begin{equation}
 \varepsilon = - \frac{d\Phi_B}{dt} = 2 N \pi r^2 B/dt = \ans{9.82\U{mV}} \;.
\end{equation}
\end{solution}
