Show that the curl of

is zero but that

is not zero if C is the circle x² + y² = 1 in the xy-plane. (Theorem 7 does not apply here because the domain of F is not simply connected. The field F is not defined along the z-axis so there is no way to contract C to a point without leaving the domain of F.)

Transcribed Image Text:

F= -y x² + y² i+ X x² + y² j + zk