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The line integral of a conservative field round any closed path is

  • A.proportional to the length of the closed path
  • B.zero
  • C.equal to the flux of the field through the enclosed surface
  • D.equal to the divergence of the field within the enclosed area

Answer: B

Correct answer: zero

A conservative field is the gradient of a scalar, so the line integral between two points is just the difference of that scalar at the ends. Round a closed path the ends coincide and the difference is zero. This is why moving a charge round any closed path in an electrostatic field requires no net work.

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