Why does flux linkage use Ienclosed/I for coaxial cable but N*Ψ for solenoids?

[ElieMakdissi]

TL;DR

I don't understand why we multiply by Ienclosed/I the total flux linkage

In Sadiku, he used the formula dλ=dΨ * Ienclosed/I
to determine the total flux linkage for coaxial cable for ρ<a and for a<ρ<b, but I applied this formula for the solenoid and it didn't work, the way that works for the solenoid is by using λ=N*Ψ.

So why we multiply by Ienclosed/I in the coaxial cable?

 

[vanhees71]

Without context and even a definition of your symbols I have no clue what you are talking about. E.g., are you looking at the coax cable from the point of view of the "telegrapher's equation", which is a quasistationary approximation, or the full wave-guide theory a la Maxwell and Hertz? What's $\Psi$?

 

[ElieMakdissi]