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Work to create a square of charges

  1. Jun 16, 2007 #1
    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.

    thank you for your help!
  2. jcsd
  3. Jun 16, 2007 #2


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

    Hope this helps
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