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A field is conservative if and only if

  • A.its line integral between two points is independent of the path
  • B.its line integral round every closed path is non-zero
  • C.its divergence vanishes throughout the region
  • D.its magnitude is the same at every point of the region

Answer: A

Path independence, a vanishing circulation round every closed loop, the existence of a scalar potential, and an identically zero curl on a simply connected region are four equivalent statements. A vanishing divergence is a different condition altogether, describing a solenoidal rather than a conservative field

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