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Does electricity flow on the surface of a wire or in the interior?

http://www.ux1.eiu.edu/~cfadd/1360/24Gauss/SphrChrg.html

Charge on a conductor always remains on the surface. In that case, why is it that charge flow through the interior of a wire? How would it not just flow on the surface of the wire?

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Short answer: a wire is not made of free charges that can move freely, and current flow in a realistic wire is not an equilibrium condition.

Charge distributing itself on the surface, thereby maximising the distance between neighbouring repulsive charges and minimising the overall potential energy, is an equilibrium condition. That it, if you left the system for an infinitely long time to settle, that's the state it would end up in.

In reality a wire is made up of atoms with delocalised electrons, that is electrons that are still bound to the nuclei, but loosely so as to be easily knocked out. To move towards the outer surface of the wire, it would take them many scattering events with other atoms and electrons, which would result in recoil kicks and change of directions in random directions. And with a constant potential difference at the ends of the wire you always have a fresh supply of new forward (or backward) moving electrons ready to maintain the random kicking and knocking out.

By the way, AC current does flow on the outside of a wire, because of something called the skin effect.

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  • $\begingroup$ Why would it take them many scattering events? Don't electrons exert an electric force on each other, so it's not merely diffusion? In that case, there will still be a net force to the outside of the wire that should after a while yield a noticeable result $\endgroup$ – JobHunter69 Sep 11 '16 at 22:02
  • $\begingroup$ The electric force between electron would probably be less than the attractive force provided by a high $Z$ nucleus. Hence they'd be attracted towards neighbouring atoms - this is what I meant by 'scattering events'. I.e. bouncing off nuclei here and there. $\endgroup$ – SuperCiocia Sep 11 '16 at 22:04
  • $\begingroup$ It doesn't require scattering events. The current exists throughout the cross section because the electric field due to the surface charges (plus any external fields) is uniform across the cross-section. $\endgroup$ – garyp Sep 12 '16 at 0:21
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    $\begingroup$ I'd rather say AC current doesn't flow on the outside of a wire, but in a shallow region beneath the surface: down to approximately the skin depth $\delta = \sqrt{\frac{2\rho}{\mu\omega}}$. For mains AC this actually turns out to be much thicker than any wire you could practically use – effectively the current density is homogeneous in the entire conductor. The effect becomes really relevant at high frequencies. $\endgroup$ – leftaroundabout Sep 12 '16 at 10:27
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    $\begingroup$ Any excess charge distributes itself on the surface. All those conduction band electrons on the interior are nicely balanced by the atomic cores. And, in a solid, those electrons are not localized, but occupy Bloch functions throughout the lattice and move quite happily (with scattering) in the bulk. $\endgroup$ – Jon Custer Sep 12 '16 at 15:28
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Charge can be either positive or negative. It's therefore possible to have equal numbers of positive and negative charges within an infinitesimal volume maintaining a net charge of zero, yet charges still being there. This wouldn't be possible if there was only one type of charge.

So when people say "charge on a conductor always resides on the outside", what's true is that local net charge resides on the outside of a conductor.

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