How to calculate Net electric force?

Question

three positve point charges +Q are placed at three corners of a square and a negative point charge -Q is placed at the fourth corner. the side of the square is L. Calculate the net electric force that the positive charges exert on the negative charge.

Answer 1

using coloumbs law F = kQ1Q2/r^2

assuming charges are of equal magnitude

net electric force = 2kQ^2 + kQ^2/2

=3kQ^2/2

as a square, r for 2 of the charges can be assumed 1, and the furthest away one assumed sqrt(2) due to only being a ratio.

k is constant 1/[4(pi)(epsilon0)]

Answer 2

Position the square on the x-y axes with the center on the origin and the negative charge on the positive y-axis. The positive charges are on the positive and negative x-axis and the negative y-axis.

Divide the force produced by the two  particles on x-axis into components in the x and y directions. These components will have a magnitude of (1/(4πε))(Q^2/L^2)/√2.

The components in the x direction cancel out. The components in the y direction add: 2*(1/(4πε))(Q^2/L^2)/√2 = √2(1/(4πε))(Q^2/L^2).

The force due to the charge on the negative y axis is (1/(4πε))(Q^2/(√2L)^2) = (1/(4πε))(Q^2/(2L^2)) = (1/2)(1/(4πε))(Q^2/(L^2)). Add this to the forces due to the other two charges:√2(1/(4πε))(Q^2/L^2) + (1/2)(1/(4πε))(Q^2/(L^2)) = (√2+1/2)(1/(4πε))(Q^2/(L^2)).