Curl

$$\nabla \times \vec{F}=\text{curl}\vec{F}$$

1. Vector that shows swirliness and rotation direction
2. Swirliness based on magnitude of curl
3. Rotation direction about the axis of the vector, according to Right Hand Rule

• Uses Del operator
• if $\vec{F}$ is Conservative, then $\nabla \times \vec{F}=\vec{0}$
  • $⟹$ if $\nabla \times \vec{F}\ne 0$, then $\vec{F}$ is not conservative
• if the domain of $\vec{F}$ is Simply-Connected
  • then $\vec{F}$ is Conservative iff $\nabla \times \vec{F}=\vec{0}$