electromagnetism - Intuitive explanation of Skin Effect?

I'm trying to wrap my head round Skin Depth, we've derived the wave equation from Maxwell's equations, using the conditions that it's a "good conductor" ρ = 0, σ >> ωε and therefore you get that the current density decreases exponentially from its value at the surface.

I'm happy that it pops out the maths however it's an intuitive sense I'm after, given that we've used Maxwell's equations I've sure it'll have something to do with self inductance and I think I've sort of got something with current "strands" being induced in the opposite direction (lenz's law) etc, and then thinking about the force between two strands of current flowing in the opposite direction (they'll repel) but then I've got current flowing two different ways on the surface of my wire and now I'm confused.

Any help would be greatly appreciated, I've looked round quite a lot but if anyone has an explanation or can link me one that isn't a mathematic proof that'd be super

Answer

If you want to understand this, instead of thinking of a transmission line as two wires with special behavior, you need to think of a transmission line as a guiding structure for electromagnetic waves. When we talk about currents and voltages and capacitance and inductance in a transmission line, that's a useful simplification for many cases. But to understand skin effect you should instead think about an electromagnetic wave that is guided by conductive structures. The currents and voltages that we measure on the transmission line are caused by the EM wave travelling along it, not the other way around.

So then, when an EM wave encounters a conductive material, what happens? The EM wave is reflected. It doesn't penetrate deeply into the conductor. But if the conductivity is not infinite, it does penetrate slightly. And up to the depth that it penetrates, it causes currents to flow in the conductor. That is the skin effect.

I'm slightly confused as to the co-ordinates of how you're defining your transmission line.

Normally we call the axial direction (along the length of the transmission line) the z-dimension. The transverse dimensions are x and y.

It's easiest to visualize in a parallel plate waveguide. There, the propagating mode can be seen as a sum of plane waves reflecting back and forth between the two plates. So these plane waves have a k-vector that has components in both the z and x directions. The reflections off the conductors is what causes the currents in the conductors, and the depth of penetration into the conductors is what determines the skin depth.