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Charged Conductor

  1. Aug 8, 2005 #1
    I've been studying gauss' laws etc. at uni and I was thinking about charged conductors. When a conductor is charged the charge distributes itself in such a way that the electric field inside the conductor is zero, and hence if there is a cavity inside the conductor, the net force on a charged particle within the cavity will also be zero.

    Now my question is this. If we imagine a spherical, hollow, conductor with a positively charged particle contained within and then positively charge the conductor, nothing happens to the particle. But what happens if the conductor is not perfectly spherical but has a hole in it?

    Logically I think that there will be a net force on the particle in the direction of the hole, and as the size of the hole approaches zero so does the net force on the particle. But if you think about the field lines, then every field line originating at the interior surface of the conductor must leave the cavity through that hole, which would mean that as the size of the hole decreases, the force on a particle passing through the hole would increase. I'm pretty sure the first explanation is the correct one, as I don't think visualising field lines is a good way to approach this problem, but perhaps someone could explain what actually happens in this situation.
  2. jcsd
  3. Aug 8, 2005 #2
    Gauss' Law specifically states that the conductor must be closed. If there is a hole then there would be a net force on both the particle and the shell if they are both not fixed.
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