How close will body approach fixed point charge?

[Aleksandre]

Homework Statement

Charged sphere with a mass of 15 mg and charge 2 nC moves with a speed of 15 cm/s towards a fixed point charge of 3 nC. How close will sphere approach charge?

Homework Equations

K=(1/2)*mv²
U=k*(Q1Q2/r)

The Attempt at a Solution

So I am not sure I approached correctly but that's all I could think of. As system initial energy = final energy I used formulae of kinetic energy and potential energy. At first, I assumed that initial distance was infinity. In that case, the initial energy in system would be expressed as :

Einitial=(1/2)*(mv²) = 1.6875 * 10^-4 Joules

Then when the sphere reached to the point where electric field vector of point charge was so big that it had to stop, sphere stopped so v=0. That brings us to the Efinal equation:

Efinal=U=kQ1Q2/x
Here everything is known except x. So if we equate this equation to Einital we can find x distance easily. Also as units work out, I think this may be correct solution?

 

[haruspex]

I think this may be correct solution?

It is.