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Linear Quadrupole   [12 marks]

The arrangement of charges shown is referred to as a linear quadrupole.


\begin{figure}
\begin{center}
\epsfysize 1.5in
\epsfbox{PS/linquad.ps}
\end{center}\end{figure}

1.
[4 marks] Draw either the equipotentials or the electric field lines around the quadrupole.
    I have drawn \fbox{\rule[-.05cm]{0cm}{.35cm}\hspace{.35cm}} equipotentials \fbox{\rule[-.05cm]{0cm}{.35cm}\hspace{.35cm}} electric field lines.
2.
[4 marks] Find the total electrostatic energy of this system of charges.
3.
[4 marks] Show that the electrostatic potential at a point (x,0) on the x axis drops off approximately as x-3 for $x \gg d$.