As shown in the figure, a square has sides of 8.0 cm with a charge of +6.0 µC at one corner (a) and with charges of -2.0 µC at the remaining three corners (b, c, and d).

Question

The figure is just a square with no measurements. Corner a being the top left corner, corner b top right corner, corner d is bottom left, and corner c is bottom right.

Find the electric field at the center of the square.
___ N/C towards corner C.

I've tried working this problem out a few ways. Like using (8.99e9)(6.0e-6)/8.0cm
&
(8.99e9)(2.0e-6)/8.0cm
I get answers ranging from 5.3e8 N/C to 11.22 N/C.
Any suggestions?

Answer 1

Well, if all the corners had the same charge, the E would be zero. So you are really just dealing with the excess charge: At a, you have a +8microC excess (assuming -2microC starting at each corner). Well, The E will be

E=kQexcess/distance^2

Qexcess is 8microC, distance is the distance from a to the center (8cm*.707)
, of course, distance has to be in meters.

Check my thinking.

Answer 2

Still couldn't get the correct answer :[