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Charge on spherical conducting shells

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

    There are two spherical conducting shells one inside the other. If the total charge on the inside shell is -3q and the total charge on the outside shell is +5q whats is the charge on the inner and outer surface of each shell?

    Attempt at solution

    My teacher said i can assume there is no charge in the center so i think the inner surface of the small shell has a charge of -6q and the outer surface +3q and the larger shell has inner surface charge of -3q and outer surface charge of +8q
     
  2. jcsd
  3. Mar 10, 2015 #2

    BvU

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    Hello TP,

    I grant you that this isn't about relevant equations. So the 2 from the template can be left out. But thinking up a solution isn't physics. What are your considerations to come to e.g. this -6 q ?
     
    Last edited: Mar 10, 2015
  4. Mar 10, 2015 #3
    Since there is no charge in the center i wanted to use the smallest numbers that could make the net charge cancel to negative three. I know inside the conductor must be 0 so the charge is on the surfaces so i picked -6 for the inside surface and postive 3 for the outside
     
  5. Mar 10, 2015 #4

    BvU

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    Wouldn't the -6 q race to the outer surface in a flash ? All the little charge carriers repel each other like crazy and they want to sit as far away from each other as possible !

    Remember that inside a conductor there is no electric field: if there were, the charge carriers would simply move with the field until either the field is zero or they can't go any further !

    Do you know about Gauss's law ?
     
  6. Mar 10, 2015 #5
    the internmost charge is the same as the one on the outer surface?
     
  7. Mar 10, 2015 #6

    BvU

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    Still don't know if you know about Gauss's law. Let's assume you do. Else look it up, e.g. on hyperphysics.

    Imagine a gauss sphere halfway inner and outer surfaces of the inner shell. No field (it's a conductor) hence no (net) charge within. No charge inside the inner surface, so no charge on the inner surface either. Conclusion: on the outer surface of the inner shell there is sitting -3q .

    Now it's your turn to find out how much charge is sitting on the inner surface of the outer shell ...
     
  8. Mar 10, 2015 #7
    Oops sorry I do know gausses law and I know the electric field would be E = Qencl/ε4πr^2 it is the Qencl I am having trouble with.
    I was confused because I though that if there was charge on one surface then there must be charge on the other one. If the only charge on the inner sphere is -3q on the outer surface then the inner surface of the outer sphere would have a +3q charge and the outer surface of the outer sphere would have a + 2q charge. this also confused me when i was trying the problem on my own because I thought the same polarity of charge could not be on both surfaces of the conductor
     
  9. Mar 11, 2015 #8

    BvU

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    The shells are prepared by charging (they are not neutral and not connected to ground). The distribution is as you now describe: the +3 is pulled inwards. That way a Gauss suface halfway inner and outer surfaces of the outer shell encloses zero Coulomb: no flux, no E field inside that conductor. The remaining +2 is distributed evenly over the outer surface of the outer shell (*). The outside world observes +2, e.g. using Gauss. (and has no way of telling what's inside !).


    (*) even if the inner shell isn't centered wrt the outer. Clear from Gauss's law and the outer shell being a conductor !
     
  10. Mar 11, 2015 #9
    thank you!
     
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