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If we set the potential at infinity to be zero, we find that the potential of a grounded conductor is V=0. The conductor being grounded has no net charge and produces no external field, so I understand why in that situation we would say the potential of the conductor is zero.

However, in studying the classic image problem, we take a charge above an infinite, grounded conductor and assume the conductor to be at V=0 because it's grounded. In all the explanations I've seen of this, there's no explanation of why we can still take the potential to be zero, but that this is 'known' or 'obvious'.

So if we have a conductor that is grounded, but in the presence of a charge, we get some induced charge on the conductor and it's not obvious to me that the potential remains at zero here, in general. In the image problem it's shown that the image charge configuration does produce a zero potential at the conductor, but we got this by initially assuming the boundary condition that the potential would be zero at the conductor.

The only explanation I can see for why we can always assume that the grounded conductor has an electric potential of zero is that a conductor is an equipotential. Therefore if we tie a conductor to ground, where an effectively infinite amount of charge can be dissipated and is at zero potential, the entire conductor must remain at zero potential since the potential must be the same everywhere. Am I thinking about this correctly?

However, in studying the classic image problem, we take a charge above an infinite, grounded conductor and assume the conductor to be at V=0 because it's grounded. In all the explanations I've seen of this, there's no explanation of why we can still take the potential to be zero, but that this is 'known' or 'obvious'.

So if we have a conductor that is grounded, but in the presence of a charge, we get some induced charge on the conductor and it's not obvious to me that the potential remains at zero here, in general. In the image problem it's shown that the image charge configuration does produce a zero potential at the conductor, but we got this by initially assuming the boundary condition that the potential would be zero at the conductor.

The only explanation I can see for why we can always assume that the grounded conductor has an electric potential of zero is that a conductor is an equipotential. Therefore if we tie a conductor to ground, where an effectively infinite amount of charge can be dissipated and is at zero potential, the entire conductor must remain at zero potential since the potential must be the same everywhere. Am I thinking about this correctly?

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