Let C be the unit circle $x ^ { 2 } + y ^ { 2 } = 1$ oriented in a counter-clockwise direction.Say whether the following statements are true or false.
If $\int_{c} \vec{H} \cdot d \vec{r}=0$ , we can conclude that $\vec { F }$ is path-independent field.

Question

Quizplus · Accepted Answer

The statement incorrectly refers to vector field $\vec{H}$ in the integral and then suddenly switches to talking about a different vector field $\vec{F}$ being path-independent. The conclusion about $\vec{F}$ being path-independent cannot be made based on information given about $\vec{H}$.

Let C Be the Unit Circle x2+y2=1x ^ { 2 } + y ^ { 2 } = 1x2+y2=1

Let C Be the Unit Circle $x ^ { 2 } + y ^ { 2 } = 1$