Electric field involving 4 point charges in a rectangle

[dcarmichael]

Homework Statement

Consider 4 identical charges q arranged in a rectangle in the x-y plane. The rectangle has dimensions a x b.

Determine the electric field in the center of the rectangle.

Determine the electric field a distance c above the center of the rectangle.

Make sure you check your answer by looking at the limit as c goes to infinity and zero, and check the units of your final expression.

Relevant Equations

E=(Kq/r^2)*

I am stuck on the following question (Image attached of my work) appears to make sense until i try to take a limit as c--->0 because the result should be 0. Am i missing something, if so can't you point me in the right direction.
Thank you

 

[andrewkirk]

The image is hard to follow, but it appears to say something like:

$$\frac1{4\pi\varepsilon_0}\times \frac{4q}{c^2 + a^2/4 + b^2/4}\times \cos\theta$$
I presume $\theta$ is the angle to the vertical made by the ray from the point to a corner of the rectangle.

As $c\to \infty$ we have $\cos\theta\to 1$ and the second factor in the above formula goes to zero. So the whole thing goes to zero, as expected.