Curl of Some Vector Fields

vector field



2

x

yz,x

2

y

z,xy

2

z



xy

2

z

,

2

x

y

2

z

,

2

x

2

y

z

2xy,

2

x

+2yz,

2

y



z

curl F at point {0,0,0} = {0.,0.,0.}

y

x

The curl

∇×F

of a vector field

F

produces another vector field. Pictorially, the direction of rotation of the field

F

produced by operation of the curl in an infinitesimal neighborhood of a point

p

in 3D space defines the direction of

∇×F

at the point

p

. A curl of positive magnitude spins in a counterclockwise direction around

p

, in accordance with the "right-hand rule". The angular speed of the rotation equals 1/2 the magnitude of the curl at the point

p

.

The third Snapshot shows a conservative vector field that has a constant curl equal to zero at every point.