Chapter 15 - Topics In Vector Calculus - 15.3 Independence Of Path; Conservative Vector Fields - Exercises Set 15.3 - Page 1121: 27

The vector field is not conservative

From the given figure, a closed loop can be found whose tangent everywhere makes an angle $\theta < \pi$ with the vector field, then the line integral \[ \int_C \vec{F} \cdot d\vec{r} > 0 \] Hence the vector field is not conservative. Result The vector field is not conservative.