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Effect of an uncharged sphere touched to charged sphere

  1. Jul 21, 2011 #1
    1. The problem statement, all variables and given/known data
    Two identical metal spheres, each with a positive charge q, are separated by a centre-to-centre distance r. What effect will the following change have on the magnitude of the electric force exerted on each sphere by the other:

    -one sphere is touched by an identical neutral sphere, which is then taken far away


    2. Relevant equations
    F2 / F= q1q2 / q1q2

    where F is the initial electrical force, and F2 is the final electrical force.

    3. The attempt at a solution
    I looked at the solutions manual and it says this:

    14wzi11.jpg

    I just don't understand why one of the charges is halved. What does this have to do with the neutral sphere?

    Thank you!
     
  2. jcsd
  3. Jul 21, 2011 #2

    gneill

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    Think about what happens when the neutral metal sphere is touched to a charged metal sphere. Do the charges stay put?
     
  4. Jul 21, 2011 #3
    Since the stationary sphere is positive, that means that when a neutral sphere approaches it, the electrons in the neutral sphere will move towards the stationary sphere.

    I don't know how that explains the halving of the charge, though.
     
  5. Jul 21, 2011 #4

    gneill

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    The sphere's touch. Are the electrons going to be satisfied moving only to the surface of the neutral sphere?

    Also, you need not think about what the particular charge carriers are. Just think about the net charges on each sphere. The positive sphere has q positive charges. The neutral sphere has no charge. The positive charges on the charged sphere would like to get away from each other...
     
  6. Jul 21, 2011 #5
    The electrons will move to the side with a positive charge. So the neutral sphere will become positively charged, and the previously positive sphere becomes negatively charged?
     
  7. Jul 21, 2011 #6

    gneill

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    Almost right. The previously positively charged sphere will become LESS positively charged. Charges stop moving once there is no potential difference to drive them. If the spheres have identical dimensions, then the charge will be split equally between them.
     
  8. Jul 21, 2011 #7
    So you mean that q1 = q2 now? And since the charge is split equally, q1 = q2 = q/2?
     
  9. Jul 21, 2011 #8

    gneill

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    That would appear to be the logical conclusion :smile:
     
  10. Jul 21, 2011 #9
    Great!! Thanks a lot!

    So this relationship holds true involving any two spheres of equal dimensions, as long as one is neutral and the other is either positive or negative to any magnitude, right?
     
  11. Jul 21, 2011 #10

    SammyS

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    I agree with you that to say the excess charge is equally shared by the two spheres coming in contact is questionable. In my opinion, it's a HUGE assumption.

    I would only be confident in the halving of the charge if when the two spheres are in contact, then each of them is the same distance from the third sphere. Otherwise, the third sphere will tend to push more than half of the excess charge onto the more distant of the two spheres.
     
  12. Jul 21, 2011 #11
    What if there is no third sphere? Just two spheres?
     
  13. Jul 21, 2011 #12

    SammyS

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    Which two spheres?
     
  14. Jul 21, 2011 #13
    The ones in my original question. There were only 2 to start with.
     
  15. Jul 21, 2011 #14

    gneill

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    We can be sneaky and specify that the two contacting spheres are equidistant from the third sphere.

    It's not clear that poster 5.98e24 has covered induction charges in his course as yet.
     
  16. Jul 21, 2011 #15

    SammyS

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    If your question is: "What if two identical conducting spheres touch, will any excess charge be equally shared by the two spheres?" , then the answer is: "Yes, provided that they are isolated from any other charges object or externally produced electric field."
     
  17. Jul 21, 2011 #16
    I'm a her .. :)

    I did learn about induction, but that was a while ago. I haven't touched physics in a few years.

    Thanks for all the help! Greatly appreciated!
     
  18. Jul 21, 2011 #17

    gneill

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    My apologies :smile:
     
  19. Jul 21, 2011 #18

    SammyS

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    It's still not clear whether 5.98e24 has covered induction charges, even after her response.

    We could also move the single charged sphere to a very distant location while the other two touch, then bring it back to the original position after the other two separate.

    5.98e24 is a puzzling name. It could represent a bit less than 10 moles.
     
  20. Jul 21, 2011 #19

    gneill

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    Or the mass of the Earth in kg.
     
  21. Jul 21, 2011 #20

    SammyS

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    That makes much more sense. Gives me an idea for 5.98e24's name, but I'll only post the guess if she's game.
     
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