One property of a three dimensional vector field is called the CURL, and it measures the degree to which the field induces spinning in some plane. This is a local property, which means there could be a different curl at each point, in contrast to a more global property like the circulation around a larger curve. We've actually seen the "kth component of curl" previously when we were talking about the analogous concept in two dimensions, and then we called it circulation density. In this video we will also look at the del operator which provides a quick way to compute the curl of a vector field. We finally note the curl of a gradient field is zero, and connect this back to the notion of a conservative vector field.

0:00 Definition of Curl
0:55 Geometric Meaning in 2D
2:16 Geometric Meaning in 3D
4:02 del operator formula
5:55 Curl of Gradient
6:43 Test for Conservative


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