Why can't the charge carriers leave the conductor?

Question

I see that electrons are quite small in size, moreover it is moving fast but I have a question why do free electrons not leave a conductor (like a wire) ? but they can only move at the edge of the conductor?

Answer 1

Fundamentally they can't leave because they are attracted to the fixed positively charged atomic nuclei in the material.

This results in the work function, meaning an amount of energy required to free an electron from the material. Given a big enough stimulus (for example in the photoelectric effect) the work function can be overcome and the electron can be freed.

Answer 2

Suppose the conductor is copper.
A copper atom has $29$ protons in its nucleus and $29$ orbiting electrons.
In the solid state each copper atom gives up one election to form a copper ion which on average is located at a fixed position, the 28 electrons being bound to the copper nucleus to form a lower energy state with the process forming what is called metallic bonds.
The free (unbound / liberated) electrons are free to move within the copper lattice (boundary of the solid) but are bound by the overall effect of the copper ions.
The motion of the free electrons with the copper can be liken to that of gas molecules within a box and they have a kinetic energy distribution like that of the molecules in a gas.
To remove the a free electron from its bound state within the copper requires a certain amount of energy which is called the work function energy.
If a free electron has sufficient kinetic energy (greater than the work function energy) when it is near the surface of the copper there is a possibility of it escaping from the copper.
If the The kinetic energy of the free electrons can be increased by heating the copper and when the temperature is sufficiently high a significant number of electron can escape from the copper, the process being called [thermionic emission(https://en.wikipedia.org/wiki/Thermionic_emission).
Another mechanism by which the free electrons can gain sufficient energy to escape in numbers is by irradiating the copper with electromagnetic radiation, the process being called photoelectric emission.

Answer 3

An exact answer requires quantum mechanics, but here is a sort of rationale.

Imagine a big flat sphere of conductor, that is negatively charged. The movable electrons spread out on the surface. They repel each other so each of them tries to get as far as it can from the others, and that's how they do it.

So each of them gets most of its repelling charge from the electrons that are close to it, to the sides. And they get most of their attractive force from the immovable charged atoms which are a little bit inside. So there's a larger force pulling them in than pushing them out. That force can be overcome, but it takes a lot to do it.

Now imagine the same sphere with a thin conducting needle sticking out of it. Electrons will climb the needle because they can, and because that puts them farther away from the other electrons.

By the time they reach the tip of the needle, they have other electrons behind them pushing them forward, and not much force pulling them back. They can escape much easier.

So if you want to make a conducting surface that can build up a large charge, you want to make it nice and smooth.

Answer 4

Due to quantum mechanical properties of conductor material and charges. Charge typically needs a lot of energy in order to leave the surface of the conductor. You may be interested in a thing called vaccum level.