Why does flux linkage increase toward the wire center in skin effect?

[physiks]

I'm struggling to understand a key detail about this.

My book divides the cross section of a wire into elementary filaments. It then states that the flux linked by the filament in the centre of the wire will be greatest, then this will decrease until at the outermost filaments the only flux linked is from external sources. This would then mean greater self inductance in the middle of the wire, and thus larger impedance so the current flow is greater towards the surface.

Firstly I know flux linkage refers the the magnetic flux crossing an area. Here the field lines in the wire are concentric circles so when dealing with flux linkage we can't be dealing with the linkage through the cross sectional area of the wire as this would be zero. It must be the flux through the cross section of the wire when viewed from above so the field lines penetrate it.

I'm struggling to understand how the flux linked is greatest in the centre. The wire could be thought of as a series of shells, and the B-field due to the wire increases linearly outwards. The field at the centre of the wire is zero. Therefore surely a central elementary filament links zero flux, and the filaments on the outside link the most flux?

 

[berkeman]

There is a long thread stickied at the top of the EE forum about this. Maybe have a look at the thread and its related links to see if that helps...