What is the significance of mutual inductance in electromagnetism?

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Discussion Overview

The discussion centers on the concept of mutual inductance in electromagnetism, particularly in the context of two coils wound on a soft iron core and connected to an AC power source. Participants explore theoretical questions, practical implications, and the underlying principles of mutual inductance, including its dependence on geometry and the effects of induced currents.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question why the mutual inductance (M) of each coil is equal, suggesting it is determined by the geometry of the conductors.
  • There is a discussion about whether mutual inductance is specific to a particular circuit, with some asserting it depends on the geometry of the coils.
  • Participants explore the idea that when current flows through the secondary coil, it should generate additional flux, but this is countered by the primary coil's response, leading to questions about the nature of the currents involved.
  • One participant explains that the primary coil's current is influenced by both the applied voltage and the induction effects, indicating a complex interaction between these factors.
  • Another participant discusses the mathematical derivation of mutual inductance, referencing the Neumann equation and its implications for the equality of mutual inductance in both directions.
  • There is a debate about the nature of the voltage source connected to the primary coil, with some clarifying that it is a sinusoidal wave rather than a constant voltage.
  • Concerns are raised about the completeness of existing derivations, particularly regarding the treatment of induced electromotive force (emf) and the applied voltage in the primary coil.

Areas of Agreement / Disagreement

Participants express various viewpoints on the nature of mutual inductance, its dependence on geometry, and the interactions between the primary and secondary coils. No consensus is reached on several key questions, indicating ongoing debate and exploration of the topic.

Contextual Notes

Participants note that the discussion involves complex interactions between induced currents and applied voltages, with some mathematical steps and assumptions remaining unresolved. The implications of these interactions on the behavior of the coils are not fully agreed upon.

  • #31
Regarding the latest questions, my response is verified in many textbooks, which anyone can obtain. The "coupling coefficient" can be called "k". If k12 represents the coupling *from 1 to 2*, and k21 represents coupling from 2 to 1, then the overall coupling is given by:

k = sqrt (k12*k21).

As far as the coax cable goes, I don't think that the shield is a shorted turn. If we sketch an iron core xfmr, add a shorted secondary turn, and examine the direction of the core flux, we will see that the shorted turn is oriented normal to the flux. But the coax shield is along the flux of the center conductor, not normal.

The mutual inductance Lm, does equal the shield self inductance Ls, and Henry Ott of Bell Labs derives this relation in his highly acclaimed book "Noise Reduction Techniques In Electronic Systems". This is true for a general coaxial cable. When we say "in general" I presume that coax cable is under discussion. If "in general" refers to other configurations besides coax, then different relations are encountered.

In general, if 2 coils mutually interact, then k = sqrt (k12*k21), and Lm = k*sqrt(L1*L2). This can be derived but it is involved. An advanced fields text might have the derivation with illustrations. With grad school I have no time to derive it. Maybe in June when things slow down I might have time. Best regards.

Claude
 
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  • #32
cabraham said:
Regarding the latest questions, my response is verified in many textbooks, which anyone can obtain. The "coupling coefficient" can be called "k". If k12 represents the coupling *from 1 to 2*, and k21 represents coupling from 2 to 1, then the overall coupling is given by:

k = sqrt (k12*k21).

Actually it's me who seems to be getting mixed up.I had been thinking all this time that k depends exclusively on the individual coils themselves (no. of turns,length,etc.)...so we would have different k values for each...
also,as you said in an earlier post, the k values don't have to be the same for the coils,I thought that confirmed my idea,
However,you say,(like in my book )that k = sqrt (k12*k21).,which means there is only one value of k for a particular transformer...I can't really explain to myself why there is a unique value of k!

(As 'The Electrician' knows,my book often contains mistakes,so I was wondering if the fact that k has a unique value as stated in my book is one of those mistakes,however,you've just confirmed that it's not.)

cabraham said:
The mutual inductance Lm, does equal the shield self inductance Ls

I got that...then I tried to prove how the mutual inductances could be equal for both the core and the shield(and without success ofcourse)...
"Lm of core=Nc(k*phi_s)/Is Lm' of core =Ns(k'*phi_c)/Ic...and you said k' was less than unity and Ic=Is...since Nc>Ns (these are the magnetic heights,which is analogous to turns in coils,I suppose)...then (k*phi_s)<(k'*phi_c)...but k'<k...so phi_s>phi_c...but that's the opposite!"
 
  • #33
cabraham said:
As far as the coax cable goes, I don't think that the shield is a shorted turn. If we sketch an iron core xfmr, add a shorted secondary turn, and examine the direction of the core flux, we will see that the shorted turn is oriented normal to the flux. But the coax shield is along the flux of the center conductor, not normal.

The mutual inductance Lm, does equal the shield self inductance Ls, and Henry Ott of Bell Labs derives this relation in his highly acclaimed book "Noise Reduction Techniques In Electronic Systems". This is true for a general coaxial cable. When we say "in general" I presume that coax cable is under discussion. If "in general" refers to other configurations besides coax, then different relations are encountered.

In general, if 2 coils mutually interact, then k = sqrt (k12*k21), and Lm = k*sqrt(L1*L2). This can be derived but it is involved. An advanced fields text might have the derivation with illustrations.
Claude

I agree. Also, mutual induction are compex quantities & depend on plane of co-incidence resulting in lesser net magnitude of flux linkage.
 
  • #34
Could someone clear the confusion about the k values as I stated in post 32#, please.
 
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