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I thought that the electric field within a conductor is always 0 because the charges would otherwise experience an electric force and therefore would move through the conductor until they attain an equilibrium distribution in which the electric field is 0 so that they no longer experience a force. However, in Purcell and Morin’s Electricity and Magnetism, the force experienced by a layer of charge is discussed, and the force is found to be proportional to the mean of the electric fields on the two sides of the layer.enter image description hereenter image description here

Could someone help me understand how these two concepts fit together? I am thinking that it has to do with the forces of atomic structure and cohesion of matter that are discussed at the end of the section. Is it correct that in a conductor, these forces would not be experienced until the charge carriers reach the edge of the surface; therefore, the only place where the electric force would be balanced by these structural forces would be when the charges are at the edges? Whereas in an insulator, these structural forces would exist everywhere, allowing the electric force experienced by a charge to be balanced regardless of the location of charge?

Or, was my original understanding about the reason that the electric field within a conductor had to be 0 incorrect?

Thank you for the clarification.

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I don't 100% follow the argument in your textbook. But I can add some points that might help you understand it better.

When they talk about the force on the charges in the surface layer they seem to be talking specifically about the Coulomb force due to the other charge elements in the layer. They can't be talking about the total force on the charge because that must be 0, otherwise the charge wouldn't remain at its location on the surface of the sphere.

There are other forces acting on the surface charge to balance the force being discussed here. You could say these forces are the forces that form the potential that confines the electrons within the material of the sphere, whatever that is. This force would actually be the attractive Coulomb force due to the fixed proton charge in the nuclei of the material.

Is it correct that in a conductor, these forces would not be experienced until the charge carriers reach the edge of the surface; therefore, the only place where the electric force would be balanced by these structural forces would be when the charges are at the edges?

No this happens throughout the material. If it were not so, all the electrons (rather than just a tiny fraction of them) in the material would repel each other and flow to the outer surface of the material.

There are fixed nuclear charges (protons) throughout the material so they exert electrical forces on electrons anywhere in the material.

Whereas in an insulator, these structural forces would exist everywhere, allowing the electric force experienced by a charge to be balanced regardless of the location of charge?

The difference in an insulator is that (speaking in very rough terms) the nuclear forces are strong enough (relative to the allowed energy levels of the electrons due to QM considerations) to localize the electrons around individual atoms, rather than allowing them to flow freely throughout the material.

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