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A region in which the divergence of \( \mathbf{D} \) is zero contains

  • A.charge only on its bounding surface, by definition
  • B.no net charge density
  • C.no field of any kind
  • D.a uniform charge density of small magnitude

Answer: B

Correct answer: no net charge density

Zero divergence means no source or sink at that point, so the charge density vanishes there. It says nothing at all about the field, which may be strong and varying - the field of charges lying outside the region has zero divergence throughout it.

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