Electric Potential of Charge Distribution

[metgt4]

Homework Statement

Two point charges, -q and q/3, are situated at the origin and at the point (a,0,0) respectively. At what point on the x-axis does the Electric Field Vanish? Find the potential function and show that the V = 0 equipotential surface is a sphere

Homework Equations

I have found that the electric field can be described as:

E = [tex]\frac{q}{4pi\epsilon_{o}}[/tex][[tex]\frac{-1}{r^2}\widehat{r}[/tex]+[tex]\frac{q}{3(r^2 + a^2 - 2racos\alpha}\widehat{r'}[/tex]]

where alpha is the angle between r and r', but I'm not sure how to find the potential field. I know that the potential is the negative integral of the electric field, but I get stuck when trying to integrate the potential due to the positive charge. I'm sure that the solution is something SUPER obvious that I simply am overlooking in my sleep deprived state, but any hints or help would be greatly appreciated.

Thanks!
Andrew

 

[vela]

You don't need to do any integrals. For any point, find the potential there for each point charge and sum them.