Solution to 2008 Problem 90

From Gauss's Law, the electric field between the two spherical shells will be the same electric field as that from a point charge +Q at the origin and the electric field outside of both shells will be 0.
So, the potential in region I will be
\begin{align*}\frac{Q}{4 \pi \epsilon_0 r} + V_0\end{align*}
and the potential in region II will be
\begin{align*}\frac{Q}{4 \pi \epsilon_0 b} + V_0\end{align*}
We are told that the potential is 0 at r=a, so
\begin{align*}V_0 = \frac{-Q}{4 \pi \epsilon_0 a}\end{align*}
and answer (D) is correct.

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