# E-field inside a conductor

If you place a conductor in an external E-field the charges inside it will move so as to cancel off the field making the field inside the conductor zero.
My question is: Is this also true if you place some net charge on a conductor? Will the field inside it then still be zero? The net charge will flow to the surface yes, but will it also be true that the charges are able to cancel off the field produced by the net charge?
And why is it that net charge always resides on the surface of a conductor. You could say I suppose that it always minimizes the mutual potential energy between the point charges originating from the net charge, but don't you have to take into account how the positive and negative charges from the conductor itself position themselves?

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mfb
Mentor
Is this also true if you place some net charge on a conductor? Will the field inside it then still be zero?
In equilibrium, yes. Every field inside the conductor would lead to currents along the field lines, which cannot exist in equilibrium.

Okay I guess that makes sense. But a new problem arose for me. Suppose you have a conductor and put an amount of free negative charges on it. My book then says that in order to minimize their mutual potential energy they must always go to the surface. I guess that's hard to argue with, but! Don't you have to take into account the configuration of the charges originally sitting in the conductor (i.e. the atoms consist of a + and -)?
So say you find that the potential energy between the free charges is a minimum if they are all at the surface, how does that help if the equilibrium situation that it produces has a higher potential energy when you take ALL the charges into account than in another situation where the free charges are generally not sitting on the surface?

mfb
Mentor
Don't you have to take into account the configuration of the charges originally sitting in the conductor (i.e. the atoms consist of a + and -)?
No. The initial material is neutral, so all contributions from positive and negative charges cancel.

well yes but the field from the negative charges pull them apart such that they gain a potential energy?

either way I also think there is some problems involved with the whole idea that in a conductor electrons are free to roam. Because you "proove" the argument that the field inside a conductor is zero by showing how the field that the moved electrons in the conductor has creaeted is opposite to the external field. But on the other hand, if these charges inside the conductor are able to produce a field how does that not contradict the idea that the electrons can roam around free at will?

mfb
Mentor
well yes but the field from the negative charges pull them apart such that they gain a potential energy?
There is no field inside, remember? ;)

But on the other hand, if these charges inside the conductor are able to produce a field how does that not contradict the idea that the electrons can roam around free at will?
I don't see a contradiction. Electrons do not have their own will, they move according to the electric field.

there is a field inside. That field just quickly disappears because the charges move around so as to cancel off the external field. Since the process is practically instantaneous we might as well say that there is no field inside a conductor ever.
But don't you see the contradiction? If a conductor supports completely free movement of electrons then there can't be any field binding them. But then in another argument you use the fact that the field created by separating the electrons from the nuclei creates a field that tends to cancel of the external. Now if that is not a contradiction I dont know what is.

mfb
Mentor
The electrons are "free" to move in the direction of the electric field. If you consider individual electrons (which is a bit tricky in quantum mechanics, but well...), they can travel freely - but the net velocity has to stay 0, so for every electron moving in one direction you have another electron moving in the opposite direction.

but if what you say is correct then what is the basic difference between an insulator and a conductor?
Because in an insulator you exactly have that when you separate the electrons from their respective nuclei a field is pulling them backwards leaving them only polarized. If in a conductor the atoms are free to move in the direction of the electric field what is it then that produces the field point in the opposite direction as the E-field - remember we can't say that its the mutual attraction between the electrons and their nuclei because then we would have an insulator.