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Finding particle potential

  1. Feb 3, 2009 #1
    1. The problem statement, all variables and given/known data
    "A particle at position [tex]{\mathbf r}[/tex] experiences a force [tex](ar^{-3}+br^{-4}){\mathbf r}[/tex]. Sketch the potential as a function of r in the different cases that arise according to the signs of a and b."


    2. Relevant equations
    [tex]-\nabla {\mathbf V} = {\mathbf F}[/tex]


    3. The attempt at a solution
    I just can't see where to start with this one. I haven't done much vector calculus...

    Many thanks :)
     
  2. jcsd
  3. Feb 3, 2009 #2

    CompuChip

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    Science Advisor
    Homework Helper

    Actually,
    [tex]-\mathbf{\nabla} V = {\mathbf F}[/tex]
    because V is not really a vector.

    Anyway, you need a function [itex]V_n[/itex] whose gradient looks like
    [tex]\nabla V_n = \frac{\mathbf{r}}{r^n},[/tex]
    right?

    My hint to you is: try differentiating
    [tex]\frac{1}{r^{n - 1}}[/tex]
    with respect to x, y and z and see what you get.
     
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