Curl of Some Vector Fields

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.

Details

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External Links

Curl (Wolfram MathWorld)

Permanent Citation

Ryan Zhan
​
​"Curl of Some Vector Fields"​
​http://demonstrations.wolfram.com/CurlOfSomeVectorFields/​
​Wolfram Demonstrations Project​
​Published: February 19, 2016