I understand that, by definition, a vector field is irrotational if the rotation is zero, but what does this intuitively mean?
I have an idea of what it could physically be, which I've concluded by reading various things online, but I'm not sure if it's completely correct:
A gravitational field is an irrotational vector field (and so the rotation will be zero). This also means that the field is conservative (no matter what path you follow, the net work will always be the same), this is approximately how it is defined in my coursebook, though in there it's pure mathematically.
Intuitively this would mean that all vectors in the field are in the same direction, just with different starting points and magnitudes.
Also: What would be a physical example of a non-irrotational (rotational?) vector field?
Thanks in advance!
Best Answer
Edward Purcell's undergraduate book on electromagnetism does a good job building intuitions about vector fields.
An example of a non-irrotational vector field that you might think about is the current flowing in a wide river. The water flows faster in the middle of the river. Near the banks, it flows more slowly. As you move from the bank toward the center, the velocity increases. The velocity vectors in the flow are increasing in a direction perpendicular to their length. This is a non-irrotational vector field.