Straight wire inductance vs wire radius

[supernano]

TL;DR Summary

I am looking for an intuitive explanation to why the inductance of a straight wire is larger for thinner wires.

I know that the whole topic of inductance in a straight wire is complicated (and has led to some heated discussions in this forum ). I followed Rosa's derivation and can see that it leads to an inverse relation of the inductance to the wire radius, and from what could understand, the point is that with thinner wires there is more "space" between the edge of the wire and infinity to integrate across. Is that it, or does someone have a better intuitive explanation for this relationship?

 

[Baluncore]

Start by thinking of say 6 parallel filaments on the surface of the wire.

The filaments of current flowing on the thin wire are close together, so their magnetic fields have good coupling. On thicker wires, the individual filaments are more separated, so are less well coupled.

Then increase the number of filaments until you are thinking of a current sheet on the surface of a round wire.

 

[supernano]

Start by thinking of say 6 parallel filaments on the surface of the wire.

The filaments of current flowing on the thin wire are close together, so their magnetic fields have good coupling. On thicker wires, the individual filaments are more separated, so are less well coupled.

Then increase the number of filaments until you are thinking of a current sheet on the surface of a round wire.

Thanks @Baluncore, so I thought about this as well and it makes sense for high frequency signals where the skin depth is much smaller than the radius of the wire.. but from what I understand, Rosa's derivation applies to DC currents, which is what makes it less intuitive to me

 

[Baluncore]

.. but from what I understand, Rosa's derivation applies to DC currents, which is what makes it less intuitive to me

OK, so add a central filament, to the six peripheral filaments, making seven. Allocate one seventh of the sectional area to each filament. Place the filaments at the geometric mean of the sub-area they represent. The concept then fits the DC model, and the exact same logic follows. As the wire diameter is increased, the coupling between the filaments is reduced.

 

[Baluncore]

The part that slows me down is Maxwell's Geometric Mean Distance.
I find the GMD of an area from itself to be a particularly difficult concept to understand.

The work by Rosa (and his team at NBS) during that period was magnificent.
https://archive.org/browse.php?field=subject&mediatype=texts&collection=NISTJournalofResearch

 

[marcusl]

Baluncore's visualization of filaments of current within the wire leads us in the right direction. The mutual inductance between filaments increases as the wire diameter shrinks. (If the filament separation and total current in the wire are both held constant, then the current per filament increases, increasing the magnetic coupling.)