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1. The problem statement, all variables and given/known data

A point charge is placed at each corner of a square with side length a. The charges all have the same magnitude q. Two of the charges are positive and two are negative, as shown in the following figure.

The two positive charges are on top and the two negative charges are on the bottom

What is the magnitude of the net electric field at the center of the square due to the four charges in terms of q and a?

2. Relevant equations

E = k ( q / r^2), k = 9.0*10^9
3. The attempt at a solution

The distance from the middle to one of the charges a/(2^1/2)

The x-components cancel out, leaving only the y-components.

The electric field due to one of the charge to my guess is-
E1sinω = 9.0*10^9 ( 2q / a^2 ) * (1/ (2^1/2))

I assumed that each charge exerts the same electric field so the answer would\ be
4 * 9.0*10^9 ( 2q / a^2 ) * (1/ (2^1/2))

I am not sure what I did wrong.

Thanks so much

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