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Homework Help: Maximum potential given a charge

  1. Sep 4, 2013 #1
    1. The problem statement, all variables and given/known data

    So the question states that we have a hollow metal sphere of radius 2cm that is charged up. We take the breakdown field of air to be 1MV/m. We are asked to:

    a) Calculate the maximum amount of charge which can be placed on the sphere.
    b) Calculate the maximum potential on the surface of the sphere.

    2. Relevant equations

    [itex]E = \frac{Q}{4\Piε_{0}r^{2}}[/itex]

    3. The attempt at a solution

    a) [itex]1\cdot10^{6} = \frac{Q}{4\Piε_{0}0.02^{2}}[/itex]
    So we get Q as being [itex]4.4\cdot10^{-8}C[/itex]​

    However, I'm stuck with what to do next to get the potential. I'm not entirely sure I understand the question? Is it the potential between that space on the surface and the center of the sphere?

    I know the answer (or at least it is given as 20kV) but I'm not sure how to arrive at that answer.

  2. jcsd
  3. Sep 4, 2013 #2
    I think I might have cracked it. I realised that I also need the equation for potential which is:

    [itex]V = \frac{Q}{4\Piε_{0}r}[/itex]

    Could someone please explain why it is [itex]r^{2}[/itex] for electric field but [itex]r[/itex] for potential?
  4. Sep 4, 2013 #3
    You just need to recall how the potential and the field are related to Coulomb's force.
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