Central potential

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) = [tex]\int [/tex] (-F(r))= [tex]\int [/tex] (-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..

tiny-tim

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