Velocity of Three Charges Released from Equilateral Triangle

[Ichigo449]

Homework Statement

Three equal charges with charge q and mass m are placed into an equilateral triangle of side length L. Find the speed of each when they are infinitely far from one another.

Homework Equations

-ΔU =ΔK (since the electric force is conservative), U= 1/4πε Σq1q2 /r

The Attempt at a Solution

Since the charges are equal and in an equilateral triangle U =1/4πε (3q^2 /L). Conservation of energy gives that ΔK =U, since U at infinity is 0. By conservation of momentum each charge will move at the same velocity so 1/2mv^2 +1/2mv^2 +1/2mv^2 = 1.5mv^2 =U. Implying v = √(1/6πε [3q^2 /L]).
Any errors in the above reasoning or a better way of laying out the solution?

 

[ehild]

It is correct, but you can simplify the result.