A square of side a has a charge +Q at each corner. What is the electric potential energy of this system of charges?
Express your answer in terms of the variables a, Q and appropriate constants.
The Attempt at a Solution
I figured I could find the electric potential energy of one charge and multiply this quantity by 4 to obtain the total electric potential energy of the system. Here's what I did:
U = 2(kQ2/a) + kQ2/sqrt(2)*a (1)
How this makes sense to me:
2(kQ2/a) -----> this part is for two of the +Q charges, one parallel to the charge we're looking at and the other is perpendicular. The distance between the charges is a.
kQ2/sqrt(2)*a ------> this part is for the +Q charge that is diagonal from the charge we're looking at. The distance separating them is sqrt (a2+a2) which simplifies to sqrt(2)*a
Then I took (1) and multplied it by 4. I simplified the expression and ended up with
U = (8+sqrt(8)kQ2)/a
When I inputted this answer, I got a message saying "Your answer either contains an incorrect numerical multiplier or is missing one."
Does anyone know what I'm doing wrong?