# Homework Help: Potential of conservative force

1. Nov 18, 2011

### Uku

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

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

$\vec{F(\vec{r})}=\vec{r}f(\vec{r})$

2. Relevant equations

$\vec{F}=-\nabla U$

3. The attempt at a solution

I can integrate by components?

$F_{x}=-\frac{\partial U}{\partial x}$

Getting: $U_{x}=-\int xf(x)dx$

Not sure on this..

2. Nov 18, 2011

### dextercioby

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

$$U = - \int x f(x,y,z) dx + g(y,z)$$