# Vector Field

Miike012
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 don't 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?

#### Attachments

• vector field.jpg
7.7 KB · Views: 337

Homework Helper
Gold Member
If you could find closed paths where the work going around wasn't zero that would show the field wasn't conservative. Or if you can convince yourself that you can't do that, it might be conservative.

Miike012
If you could find closed paths where the work going around wasn't zero that would show the field wasn't conservative. Or if you can convince yourself that you can't do that, it might be conservative.

Lets say I chose the closed path ... I created some randome one in the paint doc... how would you know if the work around the path is zero?

#### Attachments

• vector field.jpg
7.7 KB · Views: 335
Homework Helper
Gold Member
What if that field represented wind velocity and you were riding a bike. Could you could find a path where the "wind is at your back" the whole way?

Homework Helper
Gold Member
Lets say I chose the closed path ... I created some randome one in the paint doc... how would you know if the work around the path is zero?
For the path you've chosen, it's not clear whether it could be zero. Try a path around the origin instead.

Miike012
For the path you've chosen, it's not clear whether it could be zero. Try a path around the origin instead.

Even if I picked a path around the origin I don't know what I am looking at. What are you focusing your attention on when evaluating the field?