# Vector Field

1. Nov 21, 2012

### 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 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?

#### Attached Files:

• ###### vector field.jpg
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2. Nov 21, 2012

### LCKurtz

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.

3. Nov 21, 2012

### Miike012

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?

#### Attached Files:

• ###### vector field.jpg
File size:
7.7 KB
Views:
69
4. Nov 21, 2012

### LCKurtz

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?

5. Nov 21, 2012

### haruspex

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

6. Nov 22, 2012

### Miike012

Even if I picked a path around the origin I dont know what Im looking at. What are you focusing your attention on when evaluating the field?

7. Nov 22, 2012

### LCKurtz

Did you read my post #4? Would it be the same going around the circle either way?

8. Nov 22, 2012

### haruspex

Imagine going in a circle anticlockwise around the origin in the left-hand picture. At each point, the field E is making some angle to your direction of travel. As you advance a distance element vector dS, the energy transfer will be E.dS. If that scalar always has the same sign its integral cannot be zero.