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Work done by moving electrons through electric potential?

  1. Jul 23, 2012 #1
    1. The problem statement, all variables and given/known data
    A parallel-plate capacitor is charged to an electric potential of 100 V by moving 4x10^19 electrons from one plate to the other. How much work was done?


    2. Relevant equations
    How much work was done?


    3. The attempt at a solution
    Work is then simply equals to -q*deltaV. Q= number of electrons times charge per electron.

    W= +4E19 * 1.6E-19 * 100= 640 J

    But the answer I was given was 320 J. I don't see a divisible of 2 anywhere that I can account for.

    Please help. Thanks.
     
  2. jcsd
  3. Jul 23, 2012 #2

    cepheid

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    Staff Emeritus
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    Gold Member

    Welcome to PF!

    The conceptual error you're making here is that V is not constant during the movement of the charges. In other words, the 100 V was not always there from the beginning, but rather it built up slowly from 0 V as the charge accumulated. So W = q*V won't work. Instead you need W = qdV = CVdV.

    If you haven't done integrals before, then use the following (totally equivalent) method: look up the equation for the total energy stored in a capacitor.
     
  4. Jul 23, 2012 #3
    I see the error. Thank you much.
     
  5. Jul 24, 2012 #4
    The voltage built up from zero to 100V by transferring the charge. For a capacitor Q is proportional to V so to calculate the work done you need average voltage (V/2) x charge
     
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