\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} a) Create a two-dimensional force
field ${\bf F} = M {\bf i} + N {\bf j}$ defined on all of ${\bf R}^2$ {\it
except}\/ $(0,0)$ with the following properties:

\medskip

{\parindent = 40pt

\item{i)} $\bf F$ is {\it always} perpendicular to the level curves of the
function $g(x,y)= x^2 + 4 y^2$.

\smallskip

\item{ii)} The magnitude of $\bf F$ at $(x,y)$ is inversely
proportional to the distance of $(x,y)$ to the origin.

\smallskip 

\item{iii)} $\bf F$ at $(1,0)$ is $\bf i$ .
}

\medskip 

\noindent b) Compute ${\displaystyle\int_{C} M\, dx + N\, dy}$
where $C$ is the curve given 
${\cases{x=2 \cos \left(t^{78}\right)\cr y= \sin
\left(t^{78}\right)\cr}, \ .34 \le t \le .56}$. (Think physically!)










\vfil\eject\end

