Work to create a square of charges

[supersunshine]

hi,
i'm completely stuck on this problem

Homework Statement

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

Homework Equations

change in potential energy= work
U= kqq/r

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.

thank you for your help!

 

[nrqed]

hi,
i'm completely stuck on this problem

Homework Statement

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

Homework Equations

change in potential energy= work
U= kqq/r

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.

thank you for your help!

The work required to bring the first charge is zero.
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 !

Hope this helps