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How is potential energy is derived from work here?

  1. Feb 25, 2016 #1
    Since capacitors can store electrical energy in the form of a electrostatic field between its plates, one can derive that potential energy by looking at the work it takes to "push" the charges around to create the voltage.

    Therefore Work =
    integral from 0 to Q of V(q) dq =
    integral from 0 to Q of (1/C)q dq =
    Q^2/2C =
    1/2 CV^2=
    1/2 VQ which consequently equals the potential energy stored in the capacitor

    so my question overall is::
    Why it is not negative 1/2 VQ for PE since PE is the negative of work?
    Everywhere I look there is never a -PE=W but they immediately equate the two being PE=W. I think I am missing something very simple here.
  2. jcsd
  3. Feb 25, 2016 #2


    User Avatar
    Science Advisor
    Gold Member

    The whole thing in this case, is the reference point you take. This can either be you (or whatever produces work for that matter) and system ( the capacitor in this case). You must be consistent with what you choose and use in order to derive the appropriate signs.
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