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Potential of conservative force

  1. Nov 18, 2011 #1

    Uku

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    1. The problem statement, all variables and given/known data

    Find the potential of the following conservative and central-symmetric force

    [itex]\vec{F(\vec{r})}=\vec{r}f(\vec{r})[/itex]

    2. Relevant equations

    [itex]\vec{F}=-\nabla U[/itex]

    3. The attempt at a solution

    I can integrate by components?

    [itex]F_{x}=-\frac{\partial U}{\partial x}[/itex]

    Getting: [itex]U_{x}=-\int xf(x)dx[/itex]

    Not sure on this..
     
  2. jcsd
  3. Nov 18, 2011 #2

    dextercioby

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    Homework Helper

    It's a system of PDE's for the same function Ux doesn't exist, since U is a scalar. You should have


    [tex] U = - \int x f(x,y,z) dx + g(y,z) [/tex]
     
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