I think I have a handle on domain hysteresis and eddy currents but skin effect I do not understand. Why do electrons prefer scooting alone the skin of copper? If I hammer a copper round wire flat does it have less resistance as there is now more surface skin that the electrons like? If you can shed some light on this I would not mind hearing it.
As you go up in frequency, the changing magnetic field around the wire affects the wire itself.
Imagine a round wire (isolated in space, nothing near it) divided into concentric shells. The outermost shell encloses all the current carried by the interior, which therefore produces a magnetic field in the outermost shell (which is nearly the magnetic field at the surface of the wire -- just add the current of the outermost shell). This field is changing, so it induces a current in the conductor, which opposes the current flow. How much does it oppose? Depends on the resistance of the shell: circumference times resistivity of the material. As you go from inside to outside, the enclosed current increases, but so does the circumference; but area increases faster, so the current would actually be flipped, becoming negative on the outside -- as a result of assuming a constant (evenly distributed) current on the inside. This is a contradiction, so we know the current cannot be even!
In fact, it's a feedback mechanism, where most of the current flows on the outside, and the current inside is determined by what current (and magnetic field) is left after passing through the outer shell, and so on.
At very high frequencies, hardly any energy flows in the conductor itself, rather it's contained entirely within the space around the conductor. The conductor is a boundary condition, shaping the EM field, but not directly participating. This is true of ordinary TEM (stripline, coax, etc.) sorts of transmission lines, and even more explicit in waveguides (including the all-dielectric kind, and fiber optics), Goubau lines, and free waves.
It's maybe more convenient to assume the energy is contained in the space around the conductor, and 'seeps' into the conductor. If instead of AC steady state, we think in terms of transient time, then: when a step change occurs, first the change propagates at the speed of light, in the space around the conductor. This imposes a current on the surface of the conductor, and an opposing magnetic field.
Because the change is very rapid, the surface depth is very shallow (less than a micron, say). As time goes on, the rate of change outside the conductor remains zero (it's a step), but the rate of change within the conductor is nonzero: the magnetic field, and current flow, diffuse into the conductor.
Still another way to think of it: the conductor has a very high index of refraction. This is nonsense, right? I mean it's a conductor... Well, refractive index is determined by permeability and permittivity; and permittivity is how 'conductive' a substance is to electric fields. Normally it gives capacitance, but if we merely expand this to the complex plane -- as is normal for AC steady state problems, anyway -- we can consider a complex capacitor, which gives real resistance. Thus, bulk resistivity is identical to complex permittivity. The magnitude of the index is large, but it's very lossy as well. Indeed, this tells us metals are good shields -- incident radiation is primarily reflected (because of the huge index mismatch), and what's left is quickly absorbed. If we think about how a wave propagates through such a material, its amplitude decays as it goes (because of the loss), while being phase shifted. If we look at the average effect, we see diffusion.
Indeed, wave mechanics don't go away just because you've put down a conductor -- can you do standing waves in a conductor? Absolutely. For a moderately sized round wire (i.e., radius about 1-3 skin depths), the wave doesn't fully attenuate by the time it reaches the center; waves coming in from all sides means the center is a null. At certain frequencies, there are also zeroes away from center, so that current density is large at the surface, dropping to zero at some inner shell, then actually going backwards in the core (before again going to zero at the center).
Or for a sheet, a particular thickness of foil/film can have a color. Hold a CD-ROM up to the light, and see that it looks not completely opaque, but slightly bluish. That's a thin (100nm??) film of aluminum metal you're seeing through.
What does this mean for oddly shaped conductors? Transformers? Other structures? What if we want more current, or less (for that matter)?
A ribbon shaped conductor, in isolation, is worse than a round wire. Consider where the magnetic field must go: for the round case, it is evenly distributed around the wire, and current density can't be any lower. For an oblong shape, the magnetic field will clip into the peaks, increasing current density there, and reducing efficiency.
What if the conductor is not in isolation, but near other wires carrying currents? Well, all those currents act together, shaping the current distribution in each wire. A pair of wires carrying opposite currents (twin lead) has the magnetic field canceling out at far distances -- which means the back sides of the wires carry little current. The magnetic field is concentrated in the space between wires, and so the currents are concentrated on the facing sides of the wires.
Likewise, two wires carrying equal currents (same direction) repel. (Kind of like skin effect all over again, just with the conductor broken up into pieces.)
In a transformer, say you have a windup like this: 2 layers secondary, tape, 2 layers primary. Take a cross section, and you will see pairs of wires in the same direction (the two layers), and pairs opposing (the two layers separated by tape). The layers in the middle there have double trouble: they're being pinched by the currents outside of them, while also facing opposite currents. This double-pinches the current, so the inner layers have even worse distribution. This is proximity effect.
You avoid proximity effect by interleaving opposing currents. Suppose the transformer were wound: (1 layer each) P, S, P, S. The middle layers are pinched the same way in two directions at once, resulting in more even current distribution.
What else can we do? If we go back to the flat conductors, but use two carrying opposing currents, we can spread out the current by placing them broadside-facing. This works for transformers with single turn foil windings, PCB traces (particularly in multilayer boards when you need to move a lot of AC current around) and so on.
So, is flat conductor better? Not alone, but when used correctly -- near opposing currents, flat to flat, it's much better.
By the way, the space between wires -- that's carrying all that close-up magnetic field -- is the leakage inductance in a transformer. The interleaved case has less leakage, which is a big help for most switching converters.
Tim