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

In summary, the formula dλ=dΨ * Ienclosed/I is used in Sadiku to calculate the total flux linkage for a coaxial cable with varying radii. However, this formula does not work for a solenoid, as the direction of current flow and internal magnetic field are different in a coaxial cable. This is due to the need for differently oriented areas when calculating fluxes. It is important to understand the definitions and representations of lenclosed and l when using this formula.
  • #1
ElieMakdissi
3
0
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?
 
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  • #2
ElieMakdissi said:
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.
 

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