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..
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 ∞).
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