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

In summary, in the conversation, the formula dλ=dΨ * Ienclosed/I was discussed for determining total flux linkage in a coaxial cable for ρ<a and a<ρ<b. However, when applied to a solenoid, this formula did not work and instead, the formula λ=N*Ψ was found to be effective. The question of why Ienclosed/I is multiplied in the coaxial cable was also raised, but without further context or definition of symbols, the purpose of this calculation is unclear.
  • #1
ElieMakdissi
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TL;DR Summary
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?
 
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  • #2
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##?
 
  • #3
IMG_20230527_160545.jpg
 

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

What is total flux linkage?

Total flux linkage (λ) is a measure of the magnetic flux (Ψ) linked with a coil or a set of coils. It is an important parameter in electromagnetism and electrical engineering, especially in the context of inductors and transformers.

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

The correct formula for total flux linkage is λ = N * Ψ, where N is the number of turns in the coil and Ψ is the magnetic flux through a single turn. The formula λ = dΨ * Ienclosed / I is not standard and may be a misunderstanding or misinterpretation of related concepts.

What do the symbols in the formula λ = N * Ψ represent?

In the formula λ = N * Ψ, λ represents the total flux linkage, N represents the number of turns in the coil, and Ψ represents the magnetic flux through a single turn of the coil.

Why is the formula λ = N * Ψ used in electromagnetism?

The formula λ = N * Ψ is used in electromagnetism because it directly relates the total flux linkage to the number of turns in the coil and the magnetic flux through each turn. This relationship is fundamental in analyzing and designing electromagnetic devices like transformers and inductors.

Can you provide an example of how to calculate total flux linkage?

Sure! Suppose you have a coil with 50 turns (N = 50) and the magnetic flux through a single turn (Ψ) is 0.02 Weber (Wb). The total flux linkage (λ) would be calculated as follows: λ = N * Ψ = 50 * 0.02 Wb = 1 Weber-turn (Wb-turn).

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