Solution to 2001 Problem 60

We apply Gauss's Law. The charge contained within the sphere is
\begin{align*}\sigma \pi \left(R^2 + x^2\right)\end{align*}
Therefore, by Gauss's Law, the electric flux \phi through the Gaussian surface is

\begin{align*}\boxed{\frac{\sigma \pi \left(R^2 + x^2\right)}{\epsilon_0}}\end{align*}
Therefore, answer (D) is correct.

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