Computing Central Force Potential: Bound from |r| to Infinity

[mystraid]

Hello,

I am trying to compute the potential for a central force of the form: F(r) = f(r)r
where r=|r|

Using the conservative force information, equation1 comes for potential V(r):

equation1: V(r) = \int (-F(r))= \int (-f(r) r)

In http://en.wikipedia.org/wiki/Central_force" it is stated that this integral is bounded from |r| to infinity. However I could not understand the reason.

Could someone help me?
Thanks..

 

[tiny-tim]

Welcome to PF!

Hello mystraid! Welcome to PF!

It has to be bounded from |r| to somewhere …

we can choose that somewhere to be anywhere, but it makes it simplest if we choose it to be ∞ (so the potential is always 0 at ∞).

 

[mystraid]

Thank you for the reply tiny-tim.

And, I have another question. What if the function is dependent on the position vector r but not the magnitude of it?

So:

F(r) = f(r)r

Then is there any potential for such a force, and if so, under what conditions it exists?

Thanks

 

[tiny-tim]

I'm sorry, I don't understand.

 

[mystraid]

Me, too