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Calculating charge transferred between metal spheres

  1. Apr 11, 2012 #1
    Suppose I have two metal spheres, radius 1 metre and 1 cm.
    I charge the small one to 100V.
    The self-capacitance of the sphere is 4µϵR, so the charge Q = CV = 4µϵ coulombs
    Then I touch the two spheres together. I assume charge flows between them so that the voltage equalizes. As charge builds on the surface of the large sphere, electrostatic forces increase which prevent further charge from being transferred. Charge is conserved, I know the capacitance of both, so I get a final voltage of 0.99V and a charge of 0.99*4µϵ coulombs on the large sphere and 0.0099*4µϵ coulombs on the small one (to 2 places).
    If I move them apart, that's what they will have. I think.

    If instead I drill a 3cm hole in the large sphere, and lower the small one through so it touches the inside of the large sphere, the charge on the small one discharges to the large one. There is no charge on the inside of the large sphere, because it immediately migrates to the outside, and there is no electrostatic field on the inside to prevent more charge being transferred. Does the small sphere lose all its charge ? That would imply that when I remove it the two spheres have different voltages, which doesn't make sense as they were shorted together. What am I getting wrong here ?

    (this is not actually homework - the numbers are arbitrary for the purposes of illustration)
  2. jcsd
  3. Apr 11, 2012 #2
    Charge is conserved, voltage is not. The reason voltage (electrical potential energy) is not conserved is mechanical energy is exchanged in separating the spheres
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