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A person standing on insulating stool touches a charged insulated conductor. Is the conductor discharged completely?

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No. You can think of the person as an uncharged capacitor: Charges will move between the person and the conductor until the voltage/potential in both equilibrates.

So, although the conductor is partly discharged, it is still at a non-zero voltage, ie. charged.

This of course assumes that the person is not charged. If the person was originally charged with the exact opposite charge of the conductor, then the equilbrium would lead to both being uncharged.

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