Current in ideal conductor

[antonantal]

Main Question or Discussion Point

Why is it that the current in an ideal electric conductor resides in a very thin layer at the surface of the conductor?

 

[lzkelley]

what makes an ideal conductor an ideal conductor is that there is an effectively infinite supply of electrons than can move perfectly freely.
That being the case, if there is ANY electric field whatsoever inside the conductor, the electrons will almost instantly move to cancel it out. Electrons can't, however, escape the physical boundaries of the conductor -> so they can accumulate and move along the outside.
Does that help?

 

[rbj]

what makes an ideal conductor an ideal conductor is that there is an effectively infinite supply of electrons than can move perfectly freely.
That being the case, if there is ANY electric field whatsoever inside the conductor, the electrons will almost instantly move to cancel it out. Electrons can't, however, escape the physical boundaries of the conductor -> so they can accumulate and move along the outside.
Does that help?

remember the leftover protons from when the electrons slosh over to the other side, those guys are tied into nuclii that don't move from their lattice positions.

i think the fact is that for DC the current density as a function of radius from the axial line or curve of the conductor is much more constantly distributed, more that the current density in the center is the same as the current density closer to the conductor edge.

now as the frequency increases, you get this skin effect where the current density in the center is less than the current density closer to the conductor edge. at very high frequencies, virtually all of the current is at the cylinderical edge of the conductor. on a linear scale, the current density vs. radius function would look spike-like (perhaps approximated with a dirac-impulse function). that is the extreme end of skin effect.

 

[antonantal]

...at very high frequencies, virtually all of the current is at the cylinderical edge of the conductor...

The thing that got me confused was that in an ideal electric conductor the phenomenon occurs at any frequency.

But looking at the formula for the skin depth $$\delta = \sqrt{\frac{2}{\sigma\omega\mu}}$$ it can be seen that, for infinite conductivity, the skin depth is zero no matter what the frequency is.

I'm still confused about what would be the skin depth at DC in an ideal conductor (superconductor).

 

[lzkelley]

rbj is totally correct, but he's appealing to the practical situation where everything except superconductors have non-negligible resistance.

In a theoretical, perfect, ideal conductor (effectively superconductors count) the skin-depth is infinitesimal... effectively zero.

 

[cabraham]

The thing that got me confused was that in an ideal electric conductor the phenomenon occurs at any frequency.

But looking at the formula for the skin depth $$\delta = \sqrt{\frac{2}{\sigma\omega\mu}}$$ it can be seen that, for infinite conductivity, the skin depth is zero no matter what the frequency is.

I'm still confused about what would be the skin depth at DC in an ideal conductor (superconductor).

I don't know about the equation you've given. That equation, if my memory is correct, is for a planar sheet, not a cylindrical wire. I'll check my reference book when I get home, but I remember a different equation for wires. In grad school in the late '70's, we studied the math for skin effect. It involved "ber" and "bei" functions, which are derived from Bessel functions of the first kind. I'll look it up and post again. What happens when sigma becomes infinite is a good question, and my curiosity is now piqued. BR.

Claude