## Central potential

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 wikipedia it is stated that this integral is bounded from |r| to infinity. However I could not understand the reason.

Could someone help me?
Thanks..
 Blog Entries: 27 Recognitions: Gold Member Homework Help Science Advisor 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 ∞).
 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

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