User Tools

Site Tools


Sidebar


Add a new page:

basic_tools:vector_calculus:curl

Curl

Intuitive

Circulation is the amount of force that pushes along a closed boundary or path. It's the total "push" you get when going along a path, such as a circle.

A vector field is usually the source of the circulation. If you had a paper boat in a whirlpool, the circulation would be the amount of force that pushed it along as it went in a circle. The more circulation, the more pushing force you have.

Curl is simply the circulation per unit area, circulation density, or rate of rotation (amount of twisting at a single point). Imagine shrinking your whirlpool down smaller and smaller while keeping the force the same: you'll have a lot of power in a small area, so will have a large curl. If you widen the whirlpool while keeping the force the same as before, then you'll have a smaller curl. And of course, zero circulation means zero curl.Vector Calculus: Understanding Circulation and Curl by Kalid Azad

Concrete

Abstract

The motto in this section is: the higher the level of abstraction, the better.

Why is it interesting?

The curl of a quantity: $\nabla \times F$ is a crucial tool that allows us how much a given system "rotates". For example, when we try to describe water, the curl of the quantity that we use to describe the water, tells us how much rotation is going on in the water.

The curl is especially important in electrodynamics, because the fundamental equations of electrodynamics (called Maxwell equations) contain the curl of the electric and magnetic fields.

basic_tools/vector_calculus/curl.txt · Last modified: 2018/03/28 12:25 by jakobadmin