# Why can't excess charges leave the surface of a conductor?

• lawsonfurther
In summary, the conversation discusses the work function and two possible origins of it. One possible origin is the coulombic charge and the other is the excess charges coming from contact with an external charged object. The conversation also touches on the concept of equilibrium and the relationship between the energy of the electron arrangement and the work function. The final comment mentions that adding too many charges to a conductor can cause it to emit charges spontaneously.
lawsonfurther
My question is basically similar to a thread that was posted 12 years ago:
I was glad to see that there was already a thread which asked my question in the forum. But when I read through all of the discussion, I don't quite understand the two possible origin of the work function.
(See #7 post from ZapperZ.)
He mentioned that one possible origin is coulombic charge and explained it as following, "When an electron tries to leave a conductor, it is going to leave a neutral object and causing it to be positively charged momentarily."
So I am wondering what if those excess charges(or electrons) actually came from contacting with external charged object. In this case, those excess electrons on the conductor will repel each other, thus giving a force to one another. So what force is actually keeping them from leaving the surface of a conductor? And microscopically speaking, where does this force come from? Besides, when those electrons are trying to leave the conductor, should there be a tendency to make the conductor neutral? If so, how was the work function introduced in physics?
Or maybe someone can explain the second possible origin more plainly to me. I am still in the first year of university.
Thanks.

I think what you are having some trouble to understand is that a charged metal can still be in equilibrium. Think about a metal bar. If one supposedly charge it with some negative charge, those new electrons (that will swap over time with the internal electrons) will be orbiting mainly the external (surface) of the bar. This is because this state of equilibrium has minimum energy. Each atom has an electron cloud that shapes a probability density function of the electron be in that point at that time. When all the atoms join to become the bar, all of these clouds interact with one another and merge, and for the case of metals the energy that is necessary for an electron to pass from one metal atom to another is surpassed by this new rearrangement of clouds, making the electrons of the valence shell “free to move between the atoms” (of course there are some places with higher probability density as usual). When you charge a metal, the new electrons change mainly the external clouds. This results in an EQUILIBRIUM with higher energy, but it’s still an equilibrium. It’s easier to take this electrons out than it was to take the electrons out of the neutral bar. But the energy of the arrangement is still negative, that means the electrons prefer to stay at the bar than to stay flying to the infinity. Now you can understand the work function. For the electrons to escape the bar/ be absorbed by another molecule out of the bar (e.g. air molecules) you have some things to consider: Is the new equilibrium more energily viable than the first? If so all of the electrons tend to go to the new equilibrium if given some incentive (an energy to overcome the still negative energy of the charged bar). But in almost all cases the bar will not be electronically isolated so that a fotoelectric experiment will not be consider as an equilibrium. This way if one gives enough energy for the surface electrons to pass that negative energy of the bar, they will leave and never go back. That energy is the work function, it has to overcome the external electrical clouds.

A few charges spread out over a large conductor don't change the explanation in the linked thread.
If you try to keep adding charges, there is some point where the charges start getting emitted spontaneously, but that needs a huge charge. In capacitors this will typically destroy the capacitor.

jaumzaum said:
I think what you are having some trouble to understand is that a charged metal can still be in equilibrium. Think about a metal bar. If one supposedly charge it with some negative charge, those new electrons (that will swap over time with the internal electrons) will be orbiting mainly the external (surface) of the bar. This is because this state of equilibrium has minimum energy. Each atom has an electron cloud that shapes a probability density function of the electron be in that point at that time. When all the atoms join to become the bar, all of these clouds interact with one another and merge, and for the case of metals the energy that is necessary for an electron to pass from one metal atom to another is surpassed by this new rearrangement of clouds, making the electrons of the valence shell “free to move between the atoms” (of course there are some places with higher probability density as usual). When you charge a metal, the new electrons change mainly the external clouds. This results in an EQUILIBRIUM with higher energy, but it’s still an equilibrium. It’s easier to take this electrons out than it was to take the electrons out of the neutral bar. But the energy of the arrangement is still negative, that means the electrons prefer to stay at the bar than to stay flying to the infinity. Now you can understand the work function. For the electrons to escape the bar/ be absorbed by another molecule out of the bar (e.g. air molecules) you have some things to consider: Is the new equilibrium more energily viable than the first? If so all of the electrons tend to go to the new equilibrium if given some incentive (an energy to overcome the still negative energy of the charged bar). But in almost all cases the bar will not be electronically isolated so that a fotoelectric experiment will not be consider as an equilibrium. This way if one gives enough energy for the surface electrons to pass that negative energy of the bar, they will leave and never go back. That energy is the work function, it has to overcome the external electrical clouds.
So you were saying that the reason why the excess charges can't leave the surface is that they are still under control of the external electron cloud of the outermost atomic layer of the charged metal. Compared with the surface without being charged, the only thing that has changed is that the external electron cloud of that layer in a charged metal has more energy than the cloud of the counterpart in an uncharged metal. Am I saying the right thing?
And I know that the electrons of an atom can have different energy levels. So can I understand it in this way? The new electrons of a conductor may occupy a higher unoccupied energy level in the outermost atoms of the conductor, namely, the atoms on the surface of the metal. Therefore, the electric force exerted by other excess electrons on a specific excess electron can be balanced out by the coulombic force given by the nuclei of the outermost atoms on that electron.

## 1. Why do excess charges accumulate on the surface of a conductor?

Excess charges accumulate on the surface of a conductor because of the repulsive forces between like charges. This causes the charges to spread out as much as possible, resulting in an accumulation on the surface of the conductor.

## 2. Why can't excess charges leave the surface of a conductor?

Excess charges can't leave the surface of a conductor because the electric field inside a conductor is zero. This means that there is no force acting on the charges to move them away from the surface.

## 3. What happens if excess charges are introduced to the inside of a conductor?

If excess charges are introduced to the inside of a conductor, they will immediately redistribute themselves to the surface of the conductor. This is due to the repulsive forces between like charges causing them to spread out as much as possible.

## 4. Can excess charges ever leave the surface of a conductor?

Yes, excess charges can leave the surface of a conductor if an external electric field is applied. This will create a force on the charges, causing them to move away from the surface.

## 5. How does the shape of a conductor affect the distribution of excess charges on its surface?

The shape of a conductor can affect the distribution of excess charges on its surface. For example, sharp edges and points can result in a higher concentration of charges, while smoother surfaces will have a more even distribution. This is due to the electric field being stronger at sharp points, causing the charges to accumulate more heavily there.

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