= Curl =

'''Curl''' measures the circulation density of a [[Calculus/VectorField|vector field]].

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== Description ==

Curl refers to how much rotation there is in a [[Calculus/VectorField|vector field]]. It is measured using [[Calculus/Derivative|differentiation]].

For a vector field given as ''F = <P(x,y), Q(x,y)>'', it is calculated as:

{{attachment:curl1.svg}}

where ''k̂'' is the [[Calculus/UnitVector|unit basis vector]].

For a vector field given as ''F = <P,Q,R>'', it is calculated as:

{{attachment:curl2.svg}}

where ''î'', ''ĵ'', and ''k̂'' are all unit basis vectors.

Note that curl returns a new vector field. Generally this vector field is then evaluated at a given point.



=== Properties ===

An '''irrotational''' [[Calculus/VectorField|vector field]] has zero curl.

The curl of a [[Calculus/VectorField#Cross-Partial_Property_of_Conservative_Fields|conservative vector field]] is always 0.



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CategoryRicottone