Electric Field Question?

Question

The magnitude of each of the charges in the figure is 9.00x 10^-12 C. The lengths of the sides of the rectangle are 3.00 cm and 6.00 cm. Find the magnitude of the electric field at the center of the rectangle in figures a and b.
figure a N/C
figure b N/C

http://www.webassign.net/CJ/18-21fig.gif

I have tried multiple ways of solving this problem to no avail. I am using coulomb's law to find the electric field (E=(kq)/r^2 and am not getting the right answer.

Here's what I'm doing:

E= ((8.99x10^9)(9.00x10^-12))/(.06708^2)

I obtained the radius using the pythagorean theorem.

Any help that anyone can offer would be greatly appreciated.

Answer 1

lets make it easier with easy numbers.
K=9.0 x 10^9 N • m2 / C2
E=F/Q1=K*Q2/D/D
D=sqrt(3*3+1.5*1.5)cm=3.35cm=.0335Meters=3.35*10^-2
E filed strength due to one corner in the direction of the corner is
(9*10^9)*(9*10^-12)/3.35*10^2/3.35*10^2
9*9/3.35/3.35*10^1
is about 72
the component of the vector that is parallel to the long direction of the rectangle is .707*72=51
There are 4 equal components each created by one of the four corners
The side to side forces are exactly balanced out
so the total E field is about 204