Our arrange looks like the following:
The potential energy in each individual point is given by:
[tex]E_p=k\frac{Q}{d}[/tex]As all points have the same distance from the center of the square, we can calculate a single distance. We'll need the pythagorean theorem in order to calculate the distance. It can be written as the following
[tex]c^2=a^2+b^2[/tex]Then we can calculate this using half the side of the square. We get
[tex]c^2=5.68^2+5.68^2[/tex]By isolating c we can find
[tex]c=\sqrt[2]{5.68^2+5.68^2}=8.03cm[/tex]This is the distance from each vertex to the center
We also need to take into account the fact that the total potential energy is the sum of potential energies
[tex]E_p=E_A+E_B+E_C+E_D[/tex]It can then be written as
[tex]E_p=k(\frac{q_1}{d}+\frac{q_2}{d}+\frac{q_3}{d}+\frac{q_4}{d})[/tex]Which, once we plug our values in, yields:
[tex]E=(9*10^9)(\frac{(10.46-11.34-16.6+14.95)*10^{-6}}{8.03*10^{-2}})=-283561.6438J[/tex]Thus, our final answer is 283561.6438J
