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\centerline{\bf Electric Potentials from Two Charges}
\bigskip


Your group will be assigned one of the following problems.  Work out your
problem together with your group at the whiteboard.  Then the recorder
should write your solution (with a reasonable number of intermediate steps)
on the board.  If your group gets done early, go on to another problem.  The
last 2 problems are the most challenging, and the most interesting.

\begin{itemize}
\item
Two charges $+Q$ and $+Q$ are placed on a line at $x=-D$ and $x=+D$
respectively.  What is a fourth order approximation to the electric potential
$V(x)$ for $|x| \ll D$?  For what values of $x$ does your series converge?
For what values of $x$ is your approximation a good one?  Which direction
would a test charge move under the influence of this electric potential?

\item
Two charges $-Q$ and $+Q$ are placed on a line at $x=-D$ and $x=+D$
respectively.  What is a fourth order approximation to the electric potential
$V(x)$ for $|x| \ll D$?  For what values of $x$ does your series converge?
For what values of $x$ is your approximation a good one?  Which direction
would a test charge move under the influence of this electric potential?

\item
Two charges $+Q$ and $+Q$ are placed on a line at $x=-D$ and $x=+D$
respectively.  What is a fourth order approximation to the electric potential
$V(x)$ for $|x| \gg D$?  For what values of $x$ does your series converge?
For what values of $x$ is your approximation a good one?  Which direction
would a test charge move under the influence of this electric potential?

\item
Two charges $-Q$ and $+Q$ are placed on a line at $x=-D$ and $x=+D$
respectively.  What is a fourth order approximation to the electric potential
$V(x)$ for $|x| \gg D$?  For what values of $x$ does your series converge?
For what values of $x$ is your approximation a good one?  Which direction
would a test charge move under the influence of this electric potential?

\item
Two charges $+Q$ and $+Q$ are placed on a line at $x=-D$ and $x=+D$
respectively.  What is a fourth order approximation to the electric potential
$V(x,y)$ for $x=0$ and $|y| \ll D$?  For what values of $y$ does your
series converge?  For what values of $y$ is your approximation a good one?
Which direction would a test charge move under the influence of this electric
potential?

\item
Two charges $-Q$ and $+Q$ are placed on a line at $x=-D$ and $x=+D$
respectively.  What is a fourth order approximation to the electric potential
$V(x,y)$ for $x=0$ and $|y| \ll D$?  For what values of $y$ does your series
converge?  For what values of $y$ is your approximation a good one?  Which
direction would a test charge move under the influence of this electric
potential?

\item
Two charges $+Q$ and $+Q$ are placed on a line at $x=-D$ and $x=+D$
respectively.  What is a fourth order approximation to the electric potential
$V(x,y)$ for $x=0$ and $|y| \gg D$?  For what values of $y$ does your series
converge?  For what values of $y$ is your approximation a good one?  Which
direction would a test charge move under the influence of this electric
potential?

\item
Two charges $-Q$ and $+Q$ are placed on a line at $x=-D$ and $x=+D$
respectively.  What is a fourth order approximation to the electric potential
$V(x,y)$ for $x=0$ and $|y| \gg D$?  For what values of $y$ does your
series converge?  For what values of $y$ is your approximation a good one?
Which direction would a test charge move under the influence of this electric
potential?
\end{itemize}

\vfill
\leftline{\it by Corinne Manogue}
\leftline{\copyright DATE Corinne A. Manogue}
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