Can the electric field at the surface of a conductor be determined exactly?

[Cyrus]

I have a question about the surface charge and the potential. My physics book states that the potential inside the conductor is the same at the surface. But the potential is just the electric field times the radial distance. Does this mean that it is possible to determine the electric field at a point EXACTLY on the surface of a conductor. I was not sure that was possible or not. If it is possible, would it simply be 1/4pi e R^2, which means that at exactly the surface of a conductor, the electric field is like a point charge at the center of the conducting sphere, R units away.

 

[Tide]

Things get a little dodgy when you talk about EXACTLY on the surface! On the one hand, real material at the atomic level is not smoothly and evenly distributed so you cannot specify the location exactly, in a strict sense. You can only do that within the average spacing between atoms or, at best, to the within the size of an atom. And we haven't even invoked Heisenberg yet!

On the other hand, all materials have finite temperature which means that there will be some jitter motion of the charges (electrons in particular) in effect smoothing the transition from "inside" to "outside." That scale is called the Debye length (thermal speed divided by plasma frequency).

For most applications people ignore those two aspects of surface charge and simply accept a discontinuity of the electric field "at the surface" of a conductor. In the case of the ideal spherical conductor the field at the surface (approaching it from the outside!) is e/R^2 but, of course, it's zero on the "inside."

 

[Cyrus]

Oh ok tide, thanks!

 

[Cyrus]

Hey tide, I have a question about the last time we talked. If it is metastable as you say, according to my physics text it is equipotential inside the conductor, then wouldent that suggest that the charge does not move if placed inside a uniform charge distribution. Because the potential is the same everywhere, the charge should not want to move to higher or lower potential, since there is none.

 

[Tide]

Hey tide, I have a question about the last time we talked. If it is metastable as you say, according to my physics text it is equipotential inside the conductor, then wouldent that suggest that the charge does not move if placed inside a uniform charge distribution. Because the potential is the same everywhere, the charge should not want to move to higher or lower potential, since there is none.

Your textbook is referring to an equilibrium situation with no discussion of how that equilibrium is achieved. Your original question, relating to the stability of a state, is about an intrinsically nonequilibrium condition the moment you introduce a perturbation.