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\begin{figure}\centerline{ \psfig{file=problems/prob_3_10.eps,height=2.5in} }\end{figure}

A sphere of uniform charge density $\rho_0$ has a hole of radius $b = R/2$ centered on $x = b$ cut out of it as shown in the figure.

a) Find the electric field vector inside the hole.

b) Find the electric potential at an arbitrary point $x > R$.

c) What is the limiting form of the electric potential as $x \to +\infty$? What kind of field does this correspond to?

Robert G. Brown 2003-02-09