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The divergence of \( \mathbf{D} \) at a point tells us

  • A.the surface charge density on the nearest conductor
  • B.the potential at that point relative to infinity
  • C.the volume charge density at that point
  • D.the total charge enclosed by any surface round that point

Answer: C

Correct answer: the volume charge density at that point

Divergence is a local operation, so it reports the source strength at the point itself and nothing about what lies elsewhere. The total charge enclosed by a surface is what the integral form gives, and the two are connected by the divergence theorem rather than being the same statement.

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