# Math Help - potential function

1. ## potential function

If I calculate the curl of a vector field and it's 0 is it guaranteed that it has a potential function??

2. Originally Posted by TheRekz
If I calculate the curl of a vector field and it's 0 is it guaranteed that it has a potential function??
Let F be a three dimensional differentiable vector field with continuous partial derivatives. Then
$\nabla\times F = 0$
if and only if F is conservative

Vector potential - Wikipedia, the free encyclopedia

3. I just need a yes/no answer.. I didn't get what you mean

4. Originally Posted by TheRekz
I just need a yes/no answer.. I didn't get what you mean

If a vector field is conservative, then it is the gradient of some potential function.

5. and it's conservative if the curl is 0

6. Originally Posted by TheRekz
and it's conservative if the curl is 0
Yes

7. so indirectly saying my first statement is correct

8. Yes if the vector field satisfies the above hypothesis.