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Homework Help: Yukawa potential energy function

  1. Sep 18, 2010 #1
    1. The problem statement, all variables and given/known data
    This is not yet an attempt at solving a problem. I just need confirmation on that I'm on the right track. So, I am supposed to derive an expression for the radial force function from the given Yukawa-function.


    2. Relevant equations

    U(r) = -(r/r0)U0 exp-(-r/r0)

    3. The attempt at a solution

    I'm thinking about two possibilities here. First: Derivation of said function with respect to r (normal differential). Second: Partial differentiation to solve for the gradient (although I think this is not necessary since r is a fixed value, and no coordinates are given in the context of the problem)
     
  2. jcsd
  3. Sep 18, 2010 #2
  4. Sep 18, 2010 #3
    Ah true, since this function only has one variable which is r. What I am a bit concerned about is that if the system for spherical coordinates should be used in this derivation... Or they aren't needed since the radial force is dependant only on r (in this given situation)?
     
  5. Sep 18, 2010 #4
    It doesn't matter, you have only one axis specified in the problem, and that's the radial axis. The way to take the gradient with respect to the radial axis is [tex]\frac{\partial f}{\partial r}\hat r[/tex]
    It doesn't matter what the other two axes are.
     
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