Chapter 17.4, Problem 49E

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.

a.    The work required to move an object around a closed curve C in the presence of a vector force field is the circulation of the force field on the curve.

b.    If a vector field has zero divergence throughout a region (on which the conditions of Green’s Theorem are met), then the circulation on the boundary of that region is zero.

c.    If the two-dimensional curl of a vector field is positive throughout a region (on which the conditions of Green’s Theorem are met), then the circulation on the boundary of that region is positive (assuming counterclockwise orientation).