Prove Radial Fields are conservative and at the origin.

[physics_197]

Prove Radial Fields are conservative... and at the origin.

1. Homework Statement

Prove the radial field F = r / |r|^p is conservative on any region not containing the origin. For what values of p is F conservative on a region that contains the origin?

2. Homework Equations

v x F = 0 (for conservation)

3. The Attempt at a Solution

I've proved the first part, but I don't know how to solve for p's such that F is conservative on a region that CONTAINS the origin.

 

[hunt_mat]

What about if r was a unit vector (p=1)