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\centerline{\bf AMPERE'S LAW}
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A steady current is flowing parallel to the axis through an infinitely long
cylindrical shell of inner radius $a$ and outer radius $b$.  Each group is assigned one of the current densities given below: (In each case, $\alpha$ and $k$ are
constants with appropriate units.)

\begin{enumerate}
\item $\vert \vec J\vert=\alpha\, r^3$.

\item $\vert \vec J\vert=\alpha\, {\sin{kr}\over r}$.

\item $\vert \vec J\vert=\alpha\, e^{kr^2}$.

\item $\vert \vec J\vert=\alpha\, {e^{kr}\over r}$.

\end{enumerate}

For your group's case, answer each of the following questions:
\begin{enumerate}

\item Find the total current flowing through the wire.

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\item  Use Ampere's Law and symmetry arguments to find the magnetic field at
each of the three radii below:

\begin{enumerate}[(i)]
\item $r_1>b$

\item  $a<r_2<b$

\item  $r_3<a$

\end{enumerate}

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\item  What dimensions do $\alpha$ and $k$ have?

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\item For $\alpha=1$, $k=1$, sketch the magnitude of the magnetic field as a
function of $r$.
\end{enumerate}

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%\leftline{copyright David McIntyre}
\hfill\textit{ by David McIntyre}

%\hfill \today
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