Editing Vector field (section)

===Curl in three dimensions===
{{Main|Curl  (mathematics)}}
The [[Curl (mathematics)|curl]] is an operation which takes a vector field and produces another vector field. The curl is defined only in three dimensions, but some properties of the curl can be captured in higher dimensions with the [[exterior derivative]].  In three dimensions, it is defined by
<math display="block">\operatorname{curl}\mathbf{F} = \nabla \times \mathbf{F} = \left(\frac{\partial F_3}{\partial y} - \frac{\partial F_2}{\partial z}\right)\mathbf{e}_1 - \left(\frac{\partial F_3}{\partial x} - \frac{\partial F_1}{\partial z}\right)\mathbf{e}_2 + \left(\frac{\partial F_2}{\partial x}- \frac{\partial F_1}{\partial y}\right)\mathbf{e}_3.</math>

The curl measures the density of the [[angular momentum]] of the vector flow at a point, that is, the amount to which the flow circulates around a fixed axis.  This intuitive description is made precise by [[Stokes' theorem]].