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Question: Which vector field is conservative?

I added two pictures of the vector fields in the paint document.

So far the only things I know about conservative vector fields are..

1. Net change is 0 for a closed path

2.there is some function f such that F = ∇f (F being the conserv. vector field)

3. Net change is independent of the path

4. Energy is always conserved

I dont know how to apply the top four facts to a picture of a vector field. So how can I determine if they fields are conservative?

I added two pictures of the vector fields in the paint document.

So far the only things I know about conservative vector fields are..

1. Net change is 0 for a closed path

2.there is some function f such that F = ∇f (F being the conserv. vector field)

3. Net change is independent of the path

4. Energy is always conserved

I dont know how to apply the top four facts to a picture of a vector field. So how can I determine if they fields are conservative?