\begin{problem*}{22.33}
In studies of the possibility of migrating birds using the Earth's
magnetic field for navigation, birds have been fitted with coils as
``caps'' and ``collars'' as shown in Figure P22.33.
\Part{a} If the identical coils have radii of $r=1.20\U{cm}$ and are
$d=2.20\U{cm}$ apart, with $N=50$ turns of wire apiece, what current
should they both carry to produce a magnetic field of
$B=4.50\E{-5}\U{T}$ halfway between them?
\Part{b} If the resistance of each coild is $R=210\Omega$, what
voltage should the battery supplying each coil have?
\Part{c} What power is delivered to each coil?
\end{problem*} % problem 22.33

\begin{solution}
\Part{a}
From page 745 we have the magnetic field along the axis of symmetry of
a loop of wire as
\begin{equation}
 \vect{B} = \frac{\mu_0 I r^2}{2(x^2 + r^2)^{3/2}}\ihat
\end{equation}
All of our $2N$ loops are equidistant from the center, with $x = d/2$ so
\begin{align}
 B &= \frac{\mu_0 I r^2}{2(x^2 + r^2)^{3/2}}\cdot(2N) \\
 I &= \frac{(x^2+r^2)^{3/2} B}{\mu_0 N r^2}
    = \ans{21.4\U{mA}}
\end{align}

\Part{b}
Using Ohm's law
\begin{equation}
 V = IR = \ans{4.51\U{V}}
\end{equation}

\Part{c}
\begin{equation}
 P = IV = \ans{96.7\U{mW}}
\end{equation}
\end{solution}
