What is phi? Understanding Conservative Forces

[Nusc]

When you define $$\vec F(\vec r) = \phi(r') (\vec r)/r$$
Now U is usually denoted

$$U(\vec r) = -\int_0^r \phi(r') dr'$$

What is phi?

 

[Matterwave]

It would appear that phi is just the magnitude of the Force vector...

EDIT: after looking at it a bit more, I don't believe the first equation can be true in general. Since the only vector on the RHS is the r vector, that means this equation would only work for central forces. In that case, phi should indeed be the magnitude of the force vector. If the forces are not central forces...then you can't get the equation to hold no matter what you set phi to.

 

[Nusc]

Yeah they are central, thx.