- #1

- 30

- 0

## Homework Statement

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.

## Homework Equations

U=kq

_{1}q

_{2}/r

## 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(kQ

^{2}/a) + kQ

^{2}/sqrt(2)*a (1)

How this makes sense to me:

2(kQ

^{2}/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.

kQ

^{2}/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 (a

^{2}+a

^{2}) 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)kQ

^{2})/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?