# Finding particle potential

1. Feb 3, 2009

### implet

1. The problem statement, all variables and given/known data
"A particle at position $${\mathbf r}$$ experiences a force $$(ar^{-3}+br^{-4}){\mathbf r}$$. 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
$$-\nabla {\mathbf V} = {\mathbf F}$$

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. Feb 3, 2009

### CompuChip

Actually,
$$-\mathbf{\nabla} V = {\mathbf F}$$
because V is not really a vector.

Anyway, you need a function $V_n$ whose gradient looks like
$$\nabla V_n = \frac{\mathbf{r}}{r^n},$$
right?

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