If the curl of a vector field is zero, what can we conclude about it?

[kritisk]

Homework Statement

Assume F⃗ is a vector field and ∇× F⃗ = 0 What can one conclude about F?

A. F=0
B. F=∇ƒ
C. F=∇*g
D. F=∇×g
E. Something else

Homework Equations

None

The Attempt at a Solution

I haven't really made a proper attemt at solving the problem since I'm confused. I though of curl f = 0 then F should be conservative but that doesn't always have to be the case. I also thought of Green's theorem but i think i'd be way of. I could really use a hint

 

[rude man]

Homework Statement

Assume F⃗ is a vector field and ∇× F⃗ = 0 What can one conclude about F?

A. F=0
B. F=∇ƒ
C. F=∇*g
D. F=∇×g
E. Something else

Homework Equations

None

The Attempt at a Solution

I though of curl f = 0 then F should be conservative but that doesn't always have to be the case.

Oh, but it does!
You should not have written curl f = 0. You should have written ∇ x F = 0.

So pick the right answer and justify it.