# E-field & electric potential of a metal conductor

A few questions about electric field here:

1. Why do charges have to be on the outer surface of the conductor?
2. Why no charge on the inner surface of a hollow conductor?
3. If charges cannot be inside the conductor, how come the electric potential is constant throughout the conductor when an electrostatic equilibrium is reached? Isn't it that charges won't be able to redistribute throughout the conductor?

Must be wrong concepts. Please correct.

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Born2bwire
Gold Member
In a conductor, classically, there is an inifinite amount of charges that can move throughout the material without any appreciable amount of interference. Any electric field applied throughout a conductor will create a force on these charges. This causes the charges to move, the negative charges move in one direction and the positive charges move in the opposite direction. The charges collect on the surfaces because that is the only barrier to their movements since they have free movement throughout the conductor. Since we now have a collection of opposite charges on the surfaces, these charges will create their own electric field in accordance with Coulomb's law. This field will oppose the applied field. As long as any net field exists in the conductor, charges will be moved because they will experience a net force. Once the charges have configured themselves in such a manner that the electric field produced by the charges perfectly cancels the applied field, then we now have equilibrium because there will no longer be any net fields or forces inside the conductor.

Since there are no net fields inside the conductor, there are no opposing forces for a single test charge when it is placed inside the conductor. Since there are no net forces, the amount of work it takes to move the test charge anywhere inside the conductor is zero. Thus, the electric potential difference between any two points inside the conductor is also zero (because electric potential difference is a measure of the amount of work required to move a test charge from point A to point B).

In actuality, a real conductor has a finite supply of electrons and the positive charges, the ions left behind when an electron is stripped from an atom, are immobile as they are held in the metal's lattice. However, the amount of electrons on the surface of a good conductor, like copper, is still astronomical. We can still only strip off the electrons from the surface of a piece of copper and move them to the opposite surface of the copper and be able to produce an electric field that is much higher than most fields we will ever encounter. So, the approximation of infinite charges to move about is a very good one since the limit of this approximation requires very very large fields. The free movement of the electrons is still a good approximation. The electrons will meet resistance, as they bump into the atoms in the lattice (Drude model) but in the static case this is immaterial. The electrons will dissipate very little energy, which will be supplied from the applied field, and they can still move to respond to the applied fields. With statics, these transients are ignored and indeed they occur very very quickly.

So, I guess the salient points on a physical description are:
1. Charges move about freely in a conductor and will move in response to an applied electric field.
2. The charges separate to create local areas of net charge which in turn create secondary electric fields that cancel out the applied fields.
3. The charges collect at the surface because that is the only boundary to their movement and because any net field inside the conductor will cause charges to move and create secondary fields fighting the applied field.
4. In the end, the net field inside the conductor is zero which means the potential difference between points in a conductor is also zero.

Very sound and thorough explanation! Now I finally know what's happening in the conductor... Thanks!!

Dale
Mentor
2. Why no charge on the inner surface of a hollow conductor?
Be careful with this one. There can in fact be charge on the inner surface of a hollow conductor. The key point is that (in electrostatics) the e-field must be 0 within the conductor as described by Born2bwire. If you have a hollow conductor that encloses a charge then according to Gauss' law the inner surface must have an opposite charge in order to result in 0 e-field within.

Be careful with this one. There can in fact be charge on the inner surface of a hollow conductor. The key point is that (in electrostatics) the e-field must be 0 within the conductor as described by Born2bwire. If you have a hollow conductor that encloses a charge then according to Gauss' law the inner surface must have an opposite charge in order to result in 0 e-field within.
It states that in my book "There is no charge on the inner surface of a hollow conductor." Is it really a wrong concept? Or it actually means a NET charge can only be located on the outside of the conductor...

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Meir Achuz
Homework Helper
Gold Member
It states that in my book "There is no charge on the inner surface of a hollow conductor." Is it really a wrong concept? Or it actually means a NET charge can only be located on the outside of the conductor...
The book meant an empty hollow conductor.

Dale
Mentor
Is it really a wrong concept?
It is, at a minimum, an oversimplification.

The book meant an empty hollow conductor.
Huh? Sorry but I can't understand. Isn't it that empty = hollow in this case?

Dale
Mentor
Huh? Sorry but I can't understand. Isn't it that empty = hollow in this case?
Hollow means that there is an open space on the inside, for instance a Faraday shield around a room would be a hollow conductor. Empty means that there is nothing in the open space. A Faraday shielded room filled with sensitive equipment would be an example of a hollow conductor that is not empty.

If there is a net charge inside the hollow conductor (e.g. non-conducting charged sphere inside a Faraday shield) then there will be an equal and opposite net charge on the inner surface of the hollow conductor. If the hollow conductor is empty then there is obviously no net charge inside it and so there will be no net charge on the inner surface of the conductor.