Curl
Table of Contents
1. Curl of a Vector Field
The curl of a vector field \(\vec{F} = \langle M, N \rangle\) is:
\[ \text{curl}(\vec{F}) = N_x - M_y \]
This measures the failure of a field to be conservative, as for simply connected regions and vector fields that are defined everywhere, \(N_x=M_y\) shows that it is conservative.
Additionally, for a velocity field, curl measures the rotation component of the motion. For example, if our vector field \(\vec{F}\) is constant where \(\vec{F} = \langle a,b \rangle\), the curl is 0.