Electric field at some distance from a plate?

[m84uily]

Homework Statement

A thin horizontal 0.1m by 0.1m plate is charged with 10^10 electrons. If the electrons are uniformly distributed on the surface, what is the strength of the electric field 0.0001m above the center of the top of the surface of the plate?

Homework Equations

Eplane = n/(2(ε0))
n = Q/A

The Attempt at a Solution

I thought that because the distance to the edges of the plate is 1000 times greater than the distance that the electric field is being calculated from, that the equation for electric field of a plane could be used.

Eplane = n/(2(ε0))

= 10^10/(2A(ε0))

However this gives me the wrong answer by a very large margin! Thanks in advance for your help.

 

[Bhumble]

Charge of an electron is 1.602x10^-19 C.