What binds electrons to a negatively charged material?

This is probably a very stupid question but I couldn't find an answer on google.

Consider a neutral material - say, some block of metal. There is exactly as many electrons as protons and the electrons are bound to the nuclei with the electromagnetic force.

Now, add some electrons to it. It becomes negatively charged, until something with a lower charge contacts it.

The electromagnetic force makes negative charges away from other negative charges.

So why doesn't the object directly repel its overload of electrons? What prevents them to escape into the vacuum? Is there another interaction that I don't know which is occuring?

• It is a mobility of electrons in metal that makes the metal locally charged positively due to going away the metallic electrons. So the resulting attraction may become sufficient to bind an extra electron to the bulk of metal. Aug 25, 2019 at 8:44

1 Answer

The electrons do feel mutual repulsions and so will spread out, to an extent that their repulsion will be overcome by attractions of nearby protons. Increasing distance reduce the force, and attration due to protons don't let them fly off into space.

But this happens only to an extent. Keep adding more negative charge, and you'll reach a point when electrons are able to fly off. This results in phenomenon such as Corona discharge.

• Why do the protons stop electrons from flying into space when the amount of negative charge is greater than positive charge? Remember, conductors start with large amounts of positive and negative charges distributed throughout them. Sure, the protons pull each electron back, but there are more electrons in the conductor pushing them away. Sep 14, 2021 at 4:53
• In classical electrostatics, we learn that the excess charges of a conductive sphere will distribute themselves uniformly around the edge due to their repulsive forces - what stops them from being repelled just a tiny bit further? The attraction from the protons in the sphere? But there is an equal density of electrons inside the sphere causing the inside of the conductor to be electrically neutral. Perhaps this is a quantum effect. Sep 14, 2021 at 4:55
• In fact we even learn that there will be an electric field at the surface of a charged conductor (in electrostatic equilibrium) that is normal to the surface. If there is a net outwards electric field at the surface, then there should be a net outward force on surface charges - that is unless the region where the electric field is zero includes the (infinitely thin) surface itself, but this is just mathematical nitpicking that I wouldn't intuitively expect to matter in real life on a quantum level. Sep 14, 2021 at 5:04
• See the answers to this question. It appears to be a quantum mechanical phenomenon that requires quite a large electric field to overcome. I don't fully understand the answers, but the point is that it cannot be explained with classical electrodynamics, which would predict a net outwards force on any surface charge. Sep 16, 2021 at 4:13