Solve the Problem $F$ Is Zero Can One Automatically Conclude That the Circulation

question 158

Essay

Solve the problem.
-Assume the curl of a vector field $F$ is zero. Can one automatically conclude that the circulation $\int _ { C } \mathbf { F } \cdot \mathrm { d } \mathbf { r } = 0$ for all closed paths C? Explain or justify your answer.

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