Finding Electric Field at Rectangle Center: A Problem

[spoonthrower]

Here is the problem i am stuck on: There are 4 charges arranged in a rectangle pictured with side lengths .03m and .05m. The top 2 charges are negative and the bottom 2 charges are positive. All 4 charges have the same magnitude of 8.60*10^-12 C. Find the magnitude of the electric field at the center of the rectangle as pictured:

1 2
-***-
* *
* *
* *
* *
* *
+***+
3 4

So first i found the radius to each charge which is the same for all the charges. so the radius is the square root of (.015m^2+.025^2) = .0292 m
So i know that E1=E2=E3=E4 since the radius is the same for all the charges. So E=kq/(r^2)=8.99*10^9(8.6*10^-12)/(.029^2)=91.9. The Electric field is doubled though for the top 2 charges because the positive electric field points away from itself and the negative electric field points toward itself so i know that this combined electric field is 2*91.9 = 184. I know this is right because i got this part of the question right. Now to find the electric field at the center of the rectangle, i would think to use the pythagorean theorom and say Enet= square root of (184^2+184^2)= 260. However, the CPU tells me this is wrong. Please help me out. Thanks.

 

[member 553083]

The electric field at the center of the rectangle is not just the sum of the two electric fields from charges 1 and 3. You need to take into account the electric fields from charges 2 and 4 as well. The electric field at the center of the rectangle is the vector sum of the four electric fields, which can be found using the superposition principle (https://en.wikipedia.org/wiki/Superposition_principle).