# Work to create a square of charges

1. Jun 16, 2007

### supersunshine

hi,
i'm completely stuck on this problem

1. The problem statement, all variables and given/known data
the problem asks for an expression for the work required to create a square charge configuration starting with the charges starting at infinity:
each side is length a. on the top left corner the charge is +q, top right: -q, bottom left: -q, bottom right +q

2. Relevant equations
change in potential energy= work
U= kqq/r

3. The attempt at a solution
Since the charges begin at infinity, the work will equal the final potential energy. I think potential energies can be added, but if you add all the charges at equal distances you will get zero. I also tried chosing a corner and adding the potential energies relative to the corners but did not get the right answer.

The work required to bring the second charge will be $\frac{k q_1 q_2}{r_{12}}$ where r_12 is the distance between those two charges at the final position. The work required to bring the third charge is $\frac{k q_1 q_3}{r_{13}} +\frac{k q_2 q_3}{r_{23}}$ since q_2 and q_3 are already there. You can guess the formula for the work to bring the last charge :tongue2: !