# Why does current follow a conductor above a ground plane

Suppose there is a conductor above a ground plane. Current flows from a source through the conductor to a load on the other side. Depending on the frequency of the current the return path through the ground plane can take a variety of paths. At DC the return current takes a straight line. As the frequency starts to increase the current starts following the path under the conductor. Why is that?

Initially I thought that the current path under the conductor minimizes the current loop area. But why does the current path change depending on the frequency? I guess that has something to do with the impedance at different frequencies.

Edit Here is a diagram of what is going on:

I'm looking for an explanation why this is happening.

• In a superconducting plane the DC path wouldn't take a "straight path", either, because the magnetic field could not penetrate the superconductor, i.e. the field could not spread out beyond the conductor about the plane. Only in the case that the penetration depth into the metal is large can there be significant field components far away from the conductor and only in that case can a current be induced in the plane far away from the conductor. Jun 15 '16 at 17:32
• It is not clear to me what the scenario is which you are asking about. Perhaps a diagram would make it clear. Are you claiming that this effect does happen, what is your authority? Where is this stated? If this is what you think will happen, please can you explain why you think so? Have you seen it happen? Jun 16 '16 at 1:56
• @sammygerbil I'm saying it does happen and is widely known in the electrical engineering community. Pretty much all of digital PCB layout is based on this principle in order to meet regulatory compliance. Jun 16 '16 at 17:54
• Thanks for the diagram but personally I'm still having trouble visualising it. Are you describing a PCB? If this is well known in the EE community, have you tried asking on Elec Eng Stack Exchange? Jun 16 '16 at 20:16
• @sammygerbil Yes, it is a PCB. It's a track on the top layer with a ground plane on the bottom layer. I am looking for an explanation why this is happening from an EM perspective i.e. Maxwell's equations. That is why I asked it here. Jun 16 '16 at 20:20

I did a bit of research and will give my own answer to my question for those that are interested. The return current follows the path of least impedance in the ground plane. There are two sources of impedance: the resistivity of the conductor, and the coupling between the trace and the ground plane: $$Z = R + jX\omega$$ At low frequencies the resistivity dominates. The path of least impedance is a straight line. As frequency increases the inductive coupling starts affecting the path, because it is dependent on the frequency.