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Please, don't mind if my question is silly, but I was always wondering...

Imagine we have a negatively charged metailc wire. Let's assume it's just hanging on a thin rope. What force keeps electrons to fall on the ground and discharge the wire?

Electrons have mass. And according to laws of physics, everything with the mass will fall onto the earth with constant acceleration g (if we skip the friction).

Moreover, electrons want to get away from each other. As we know, particles with same change repel each other. So why don't they just fall of the surface of the wire?

So there are two forces, thaw want extra elecrons out of the wire, but it does not happen. I just can't get it through my head.

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What force keeps electrons to fall on the ground and discharge the wire?

The electromagnetic force.

Electrons want to get away from each other, but they want to be near the positively charged nuclei with which they form atoms. Even in a metal, where the electrons are weakly bound to the positively charged ion cores, those positive charges are still there and still act on the negatively charged electrons.

If you remove an electron from a neutral wire you necessarily will still have an extra positive unit of charge on an ion core that wants that electron back. I.e., there is a electromagnetic force keeping the electron in the wire, which is much greater than the gravitational force pulling the electron towards the earth.

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The gravitational force is a very weak force it cannot compete with the electromagnetic forces which create all observed matter.

In addition to the neutrality of all matter, that there are positive charges in the nuclei with electrons around them, the framework is quantum mechanical. There are always spill over positive forces that attract and keep electrons in the material . Quantum mechanics in contrast to classical mechanics has stable locations for all particles caught in a potential.

So what one could call "free electrons" are not free in the sense that water drops on a wire are free to be attracted by gravity and fall. They exist in bands at special levels and cannot leave unless energy is given corresponding to the bound state. For example electrons leave a cathode ray source because energy is given by heating the element.

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