1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Science Advisor
    Homework Helper

    [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]

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook