find the net electric field at the center of an square

Question

find the net electric field at the center of the square of charges A(+5), B(+5), C(-5), D(-5) microcoulomb at the corners of the square ABCD separated by a distance of 1cm from each other

Answer 1

Firstly, from the geometry you can see that (putting A and B at the top of the square and C and D at the bottom of the square) all of the points will have the same magnitude effect of k_eQ/(s/sqrt(2))² where s is the side of the square (i.e. 2k_eQ/s²). Secondly, the x components of E fields from A and B will balance at the center, as will the x components of the E fields from C and D. Thirdly, the y components will all result in a pull in the - y direction (C and D pulling down and A and B pushing down). The y component magnitude from any of the points is (sqrt(2)/2) (2k_eQ/s²) = sqrt(2)k_eQ/s² and because each point contributes: |E_y | = 4sqrt(2) k_eQ/s²

When you plug in you must use: Q = 5 x 10^-6C and s = .01m in order to obtain N/C. Please check my math as there are lots of sqrt(2) twists.