In vector calculus, the curl, also known as rotor, is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional Euclidean space. The curl at a …

In this section, we examine two important operations on a vector field: divergence and curl. They are important to the field of calculus for several reasons, including the use of curl and …

Jul 23, 2025 · Curl of a vector field is a measure of its rotation at a particular position. Curl of a vector shows how much the vector field rotates or circulates around that location.

Nov 16, 2022 · In this section we will introduce the concepts of the curl and the divergence of a vector field. We will also give two vector forms of Green’s Theorem and show how the curl can …

The curl of a vector field allows us to measure the rotation of a vector field. The resulting value of a vector’s curl can tell us whether a vector field is rotational or not.

Curl is the amount of pushing, twisting, or turning force when you shrink the path down to a single point. Let's use water as an example. Suppose we have a flow of water and we want to …

Roughly speaking, divergence measures the tendency of the fluid to collect or disperse at a point, and curl measures the tendency of the fluid to swirl around the point. Divergence is a scalar, …

As we saw earlier in this section, the vector output of curl (F) represents the rotational strength of the vector field F as a linear combination of rotational strengths (or circulation densities) from …

Generally, the curl of a vector field result is in another vector field whose magnitude is positive in some regions of space, negative in other regions, and zero elsewhere.

The magnitude of the curl vector at P measures how quickly the particles rotate around this axis. In other words, the curl at a point is a measure of the vector field’s “spin” at that point.