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Potential of conservative force

  • Thread starter Uku
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  • #1
Uku
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Homework Statement



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

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

Homework Equations



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

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..
 

Answers and Replies

  • #2
dextercioby
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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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