Calculate the magnitude of the electric field at the center of a square with sides 22.4 cm long if the corners, taken in rotation, have charges of 1.02 μC, 2.04 μC, 3.06 μC, and 4.08 μC (all positive).

Answer 1

let A=1.02Coulomb

now the four corners contain 1,2,3,4 of these A charges.

1 and 3 are in opposition, so a net 2
now change the corners to 0,2,2,4
The corners 2 and 4 are in opposition, so now we can have a net 0,2
so now the corners are 0,0,2,2
These are at 45 degrees to each other (draw the figure), so each is cos45 times net charge.
So now, the final net charge a distance 1/2 (.224)*.707 from the center.

Etotal= kA(2*2*.707)/(.112*.707)^2
=kA*4*sqrt2/.112^2

check all that. If you wish, you can do it the long way, watch vector addition.