Find mag. of net electric field at the center

[mdawg467]

Homework Statement

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

my figure: (image each charge represents a corner of the square)
(+q₁)(+q₂)
(-q₃)(-q₄)


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 ?
Express your answer in terms of the variables q, a, and appropriate constants.

Homework Equations

E=F/q
F=Kq²/r²

The Attempt at a Solution

I uploaded my work as an attachment..I'm getting the wrong answer. The correct answer is E=(4kq√2)/a², whereas I kept getting E=(kq√2)/2a²

any ideas? thanks

 

[SammyS]

Homework Statement

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

my figure: (image each charge represents a corner of the square)
(+q₁)(+q₂)
(-q₃)(-q₄)


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 ?
Express your answer in terms of the variables q, a, and appropriate constants.

Homework Equations

E=F/q
F=Kq²/r²

The Attempt at a Solution

I uploaded my work as an attachment..I'm getting the wrong answer. The correct answer is E=(4kq√2)/a², whereas I kept getting E=(kq√2)/2a²

any ideas? thanks

You need to keep only the y -component of the electric field due to each charge.