Flux Linkage - what, where, why?

In summary, flux linkage is the way that magnetic flux is shared between turns of wire in a magnetic field. It is important for understanding how transformers work and for calculating the magnetic field produced by a primary solenoid.
  • #1
lntz
54
0
Hi,

we have been doing lots of work recently on magnets. we have learned about the ideas of flux, and using them to describe induction and how transformers work etc.

i feel that i understand quite well about these ideas, but now i have come across this idea of 'flux linkage'.

i do not understand what this is. the definitions i have been reading don't seem very explicit.

so please can somebody explain to me what it is, and why the ideas are important/useful.

thanks in advance.
 
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  • #2
hi lntz! :smile:

a major difficulty in understanding magnetic flux linkage is that it has the same units as magnetic flux (Wb)

if there are N turns of wire round an area A, through which there is a magnetic field B at an angle θ,

then the magnetic flux through A is Φ = BAcosθ,

and the magnetic flux linkage through A is NΦ = NBAcosθ

the only difference is the number of turns, N, which has no units!

i find this easier to understand if we use the H field (instead of the B)

the H field is magnetic moment density, measured in amp-turns per metre (A/m)

the H flux is magnetic moment per length, measured in amp-turn-metres (Am)

eg if the magnetic field is produced by a primary solenoid with current I area A length L and turns N (and pitch n = N/L),

then H = nI amp-turns per metre (independent of A)

and H flux = nIA = NIA/L amp-turn-metres

if this flux then goes through a secondary solenoid with the same area and M turns,

the flux linkage is M times the flux, = MNIA/L amp-turn2-metres​

returning to the B field (where the concept of "turn" as a unit is unnatural :redface:):

B = µH = µnI

B flux (from the N-turn primary) = µNIA/L webers

B flux linkage (through the M-turn secondary) = µMNIA/L webers :smile:
 
  • #3
I agree with Tiny tim reference to number of turns, N,
If you have one turn of area A in a magnetic flux density of B tesla (webers/m^2) then the flux phi = B*A webers.
If there are N turns then the effective flux is N times greater = NBA
This is called magnetic flux linkage
 

What is flux linkage?

Flux linkage refers to the measurement of the amount of magnetic flux that passes through a specific area over a period of time. It is a fundamental concept in electromagnetism and is used to calculate the induced voltage in a circuit.

Where is flux linkage used?

Flux linkage is used in a variety of applications, including generators, transformers, and motors. It is also used in other fields such as magnetic levitation and magnetic resonance imaging (MRI).

Why is flux linkage important?

Flux linkage is important because it helps us understand and predict the behavior of electromagnetic systems. It is also a key parameter in the design and analysis of electrical devices and plays a crucial role in the study of electromotive force and inductance.

How is flux linkage calculated?

Flux linkage is calculated by multiplying the magnetic flux passing through a specific area by the number of turns in a coil. It is represented by the symbol Λ and is measured in units of webers (Wb).

What factors affect flux linkage?

The amount of magnetic flux passing through an area and the number of turns in a coil are the main factors that affect flux linkage. Other factors include the size and shape of the coil, the strength of the magnetic field, and the material the coil is made of.

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