Velocity of a particle kicked into four point charge square

[jlmccart03]

Homework Statement

Consider the arrangment of charges (fixed in place) shown in the figure. The square has side length d. (Figure 1)

Now suppose the particle with charge q is released. It is "kicked" so that it's initial speed is v. After an unspecified trajectory, it is observed that the particle ends up at the center of the original square and is momentarily at rest. If the mass of this particle is m, what was its initial speed v?
Express your answer in terms of q, d, m, and appropriate constants. Use k instead of 14πϵ0. The numeric coefficient should be a decimal with three significant figures.

Homework Equations

U = kq₁q₂/r
KE = 1/2mv^2

The Attempt at a Solution

So I know I have to find the initial and final U of each total charge on a charge q. The problem is how does one do that besides doing kQ₁q₂/d + kQ₃q₄/d...etc? I would just add all of the contributions right? The little q would stay little q, but big Q would be the charge of each of the four point charges. Then I have to find final Potential Energy, but what would that even be? 0? Then I know that I have to use kinetic energy since I have to use the law of conservation of energy. I am confused on what I need to do from here since I can't figure out the potential energies. I know I will have this in the end KE_i + U_i = KE_f + U_f where KE_f is zero. Thanks for any help!

 

[kuruman]

The best way to do this problem is
1. Pretend that the charge q that is kicked is not there.
2. Find the electric potential V_i at the corner where the charge is.
3. Find the electric potential V_f at the center of the square where the charge ends up.
4. Conserve energy where PE_i = q V_i and PE_f = q V_f, KE_i = ½mv² and KE_f = 0.