Curl
A vector differential operator measuring the local circulation or rotation density of a 3D vector field around a point.
Governing formula
curl F = ∇ × F = det|[î, ĵ, k̂], [∂/∂x, ∂/∂y, ∂/∂z], [F_x, F_y, F_z]|
SI unit
[Vector Field Unit] / m
In depth
The direction of the curl vector indicates the rotation axis via the right-hand rule, and its magnitude represents circulation intensity. A field with zero curl (∇ × F = 0) is irrotational and conservative.
Examples in the real world
Faraday's law ∇ × E = -∂B/∂t showing time-varying magnetic fields create rotational electric field curls.