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Microscopic surface charge distribution on a metal ball

Physics Asked on January 11, 2021

On a metal ball with perfectly smooth surface with negative charge on it, the charge will be distributed evenly on the surface, but microscopically where exactly will the charge reside?

Although the repulsion between the charge will send the charge to the surface, but the repulsion will also prevent the charge to pack too densily on the surface.

As the number of the extra net electrons increase, will they:

(1) Only fill up the atoms that are farest from the center of the ball, which means one atom may contain multiple extra charge which is very not possible.

or

(2) They first fill up all the atoms that are farest from the center of the ball, then begain to fill the inner atoms, every atom is filled at least one charge (maybe even two but not very many), from outer atoms to innter atoms, creating layers of net charges.

or

(3) They only fill some of the outer atoms, then because of the repulsion between them they begain to fill inner atoms, leave some outer atoms not filled, creating layers of net charges.

For (2) and (3), if there is enough net charge, there won’t be a surface charge, but a "thick shell of charge", finnaly there is net charge everywhere on the ball. It is also possible that electron begain to get ejected out of the ball before the thick shell forms – if so, then there will be a upper limmit of the number extra electrons a metal ball can carry.

What will happen in reality?

How will the filling sequence depend on the properties of the metal (e.g. element/crystal structure)?

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