Is total flux linkage λ=dΨ*Ienclosed/I or λ=N*Ψ?

[ElieMakdissi]

Homework Statement

Calculate the flux linkage inside a coaxial cable

Relevant Equations

total flux linkage λ=dΨ*Ienclosed/I or λ=N*Ψ

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?

 

[Steve4Physics]

Homework Statement: Calculate the flux linkage inside a coaxial cable
Relevant Equations: total flux linkage λ=dΨ*Ienclosed/I or λ=N*Ψ

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?

I’m guessing (don’t have the textbook), but maybe this helps…

In a (long) solenoid, the direction of current-flow is around the axis; the direction of the internal magnetic field is parallel to the axis. The opposite applies in a coaxial cable. So you can’t apply results/equations for a solenoid to a coaxial cable. Differently oriented areas are needed when calculating fluxes.

Make sure you know exactly what $l_{enclosed}$ and $l$ represent.