Central potential

  1. 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..
     
    Last edited: May 3, 2010
  2. jcsd
  3. tiny-tim

    tiny-tim 26,055
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hello mystraid! Welcome to PF! :wink:

    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 ∞). :smile:
     
  4. 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
     
  5. tiny-tim

    tiny-tim 26,055
    Science Advisor
    Homework Helper

    I'm sorry, I don't understand. :confused:
     
  6. Me, too:smile:
     
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