# Curl Recall the idea of a [vector field](Vector-Fields.md). Consider the vector field below and think of it as representing a fluid flow.  We know that vector fields can behave as [sources and sinks](Divergence.md#Sources%20and%20Sinks). The **curl** of a vector field at a particular point in the plane tells you how much this imagined fluid tends to *rotate* around that particular point:  As in, if you were to drop a twig in the fluid at that point (somehow fixing it's center in place), would it tend to spin around. Regions where that rotation is clockwise are said to have positive curl, and regions where it is counter clockwise are said to have negative curl. As we saw with [Divergence](Divergence.md), to have non zero curl we do not need *all* vectors pointing counter clock wise or clockwise. For instance, below we will still have rotation due to high speed above compared to a lower speed below (resulting in a clockwise influence):  Now, the 2-d version of curl associates each point in space (a vector) with a single number:  In 3 dimensions each vector is associated with a single vector. ### Notation We often write the curl as the [Cross-Product](Cross-Product.md)between a the gradient operator and our field:    Watch [here](https://youtu.be/rB83DpBJQsE?t=653) for more details. --- Links to: [Divergence](Divergence.md) [Maxwell's-Equations](Maxwell's-Equations.md) References: * [Divergence and Curl - 3b1b](https://www.youtube.com/watch?v=rB83DpBJQsE&t=286s)