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Charge and energy of a conducting sphere

  1. Dec 10, 2015 #1
    1. The problem statement, all variables and given/known data

    A conducting sphere of radius 100cm is charged to a potential of 30 volts.
    a) What is the charge on the sphere?
    b) What is the energy stored in the field?
    c) If the sphere is connected to a second identical uncharged sphere by a long wire, what is the final energy in the system? You can neglect any interference.


    2. Relevant equations

    Q=CV
    C=4πεr
    U=(1/2)CV^2

    3. The attempt at a solution

    For part A I find the capacitance of the sphere so I can then apply Q=CV to find the charge.
    C=4π(8.85X10^-12)(100)=1.1X10^-8

    Q=(1.1X10^-8)(30)=3.3X10^-7

    For part B I used the energy equation U=(1/2)(1.1X10^-8)(900)=4.95X10^-6

    I am pretty much stuck on part C. Since it is a conducting sphere the potential for both of them should be the same. So I tried equating both potential equations such as V=(kq1)/(r)=(kq2)/(r). Both spheres are identical so I get that q1=q2. Not really clear on how to find the final energy.
     
  2. jcsd
  3. Dec 10, 2015 #2

    TSny

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    Gold Member

    The wire connecting the two spheres is "long", so you can treat each sphere as being isolated.
     
  4. Dec 10, 2015 #3
    So since each sphere has the same charge does that mean the final energy will double?
     
  5. Dec 10, 2015 #4

    gneill

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    Staff: Mentor

    What are the units? I see you've used "100" for the radius. 100 what? So what are the capacitance units you end up with?
    Again, what are the units for these?
     
  6. Dec 10, 2015 #5

    TSny

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    No. The final charge on each sphere is not the same as the initial charge on the one sphere (before the wire was connected).
     
  7. Dec 10, 2015 #6
    If the initial sphere has charge Q and then you connect the spheres by a long wire then
    charge q will be transferred to the uncharged sphere.
    Now using what you know about electrical potential and electric currents
    you should be able to calculate the final charge configuration.
     
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