Discussion
For the vector field \( \mathbf{A} \) to be expressible as the gradient of a scalar in a region, it is necessary that
Answer: C
Correct answer: its curl vanish throughout the region
A field expressible as \( \nabla V \) has zero curl, since the curl of any gradient vanishes identically, and in a simply connected region the converse holds too. The divergence is unconstrained: it equals \( \nabla^2 V \), which may be anything the sources require.
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