Simplifying Complicated Concepts: Explained with Examples

[TimeRip496]

I do not understand this even the one in Wikipedia. Can anyone explain it to me as simple as possible as well as give me some simple examples?
Thanks a lot!

 

[Nugatory]

I do not understand this even the one in Wikipedia. Can anyone explain it to me as simple as possible as well as give me some simple examples?
Thanks a lot!

Intuitively...

Imagine a body of water with some currents flowing in it. At every point, the water is moving in some direction at some speed, and we can describe this motion with a vector at that point. That's an example of a vector field and we can write the current at a point as vector-valued function of position: $\vec{F}(x,y,z)$.

Now, imagine a tiny particle of silt floating around in the water, moving along with the water in whichever direction the currents are pushing it. If that particle of silt would tend to rotate as it moves, then the vector field has non-zero curl at that point. We represent the curl as a vector by adopting the convention that it points perpendicular to the plane of rotation and has a magnitude proportional to the strength of the rotation.