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The divergence of a vector field at a point measures

  • A.the circulation of the field round a vanishing loop at that point
  • B.the rate at which the field increases along its own direction
  • C.the maximum rate of change of the magnitude of the field
  • D.the net outward flux per unit volume from a vanishing volume there

Answer: D

Correct answer: the net outward flux per unit volume from a vanishing volume there

Divergence is a source density: it reports how much of the field originates at the point, as the flux out of a small volume divided by that volume in the limit. That is exactly what makes \( \nabla\cdot\mathbf{D} = \rho_v \) the local form of Gauss’s law.

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