# What happens if we give a single electron charge to a hollow metal sphere?

I found this related question: What happens to 5 electrons on a sphere?

But this question describes the case when there can only be 5 electrons on that sphere at all times. The answer linked to the Thomson Problem, which gives a solution for the stable configuration of $N$ charges placed on a sphere.

• So my question is that, will it not repel the extra electrons inside the metal to produce a state of non-uniformly distributed + and - charges?

If not, it would mean that there is a net non-zero field inside the bulk of the sphere, so that configuration cannot be a steady state, i.e. It will cause the sea of electrons to flow and achieve another steady state, which can be said from the Electrostatic Shielding Effect.

• So, what steady state will be achieved?

• What if it is a solid sphere and not a hollow one? Will the extra electron still be on the surface of the sphere?

Any help is appreciated!

P.S. You can leave the last question for me to attempt, if its easily deducible from the answer for the first two!

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My guess would be that it remains where you add the electron, assuming it's an isolated system. As for your question "Is it necessary to continuously have N and only N electrons on the sphere at all times?", can you please clarify that? – mehfoos Jul 23 '13 at 10:35
@user1218748, changed the wording, hope it is clear now. – udiboy1209 Jul 23 '13 at 10:43
Sorry to be pedantic, but are you asking if the extra electron introduced will pull other electrons in the metal?? – mehfoos Jul 23 '13 at 10:51
I'm sorry, A typo... – udiboy1209 Jul 23 '13 at 10:52

When considering a big enough chunk of matter, as in your experiment, you are dealing with it's macroscopic observed effects, where granular effects of single electrons are smoothed out . So if you add $n$ electrons to the electron sea of the metal the observed effect will be a uniform increase of $-ne\over S$ in the surface charge density of the metal.