Electronic – Proximity effect misunderstanding

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.

This is a nice question.

Explanation 1: We know that a circular current produces a magnetic field whose pattern is exactly that of a magnetic dipole:

So the sheet simply constructs the currents in answer a to exactly oppose the fields from the bar magnet.

A better and more accurate explanation is the below ones, which I believe should now tube easier to understand.

Explanation 2: We know from Lenz's law that the currents will oppose the fields generating it.

It will help if you consider the rod stationery for a moment. For a 2d cross section The fields just behind the rod will come out of the sheet, and just in front of it, they go inside.

As the rod moves forward, this field gets weaker. So the currents behind the rod must counter this CHANGE IN FIELDS. For the region behind the rod, the change is a decrease in fields.

Now look at option a. The currents behind attempt to maintain the the status quo. To do this they attempt to increasing the net field. At the front, the change is an increase. So the currents must decrease it. So at the front, the opposite must be true.

At the center the chance is maximum, so the eddy current is the strongest.

So as the rod moves forward the center does too. The fields due to the eddy current decrease behind the rod as the center moves forward, so effectively, their diminishing effect weakens (they attempt to counter the decrease in field by reducing their contribution to the decrease in the net field, ie as per Lenz's law they attempt to increase the field).

At the front they increase their contribution to the decrease in net field by increasing themselves, (closer to centre), the exact opposite of above para.

Note that when I say increase the fields behind the rod, I simply mean eddy currents decrease their negative contribution to the net field. The net field however will keep on decreasing behind the rod and increase in front of it.