Solution to 1986 Problem 80

The electric field must obey Gauss's Law
\begin{align*}\nabla \cdot \mathbf{E} = \rho/\epsilon_0\end{align*}
\begin{align*}\nabla \cdot \mathbf{E} = 0\end{align*}
since there are no charges in the region. Only answer (B) is divergenceless, hence answer (B) is the correct one.

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