Flux Linkage - what, where, why?

  1. Hi,

    we have been doing lots of work recently on magnets. we have learnt 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.
    Last edited: Mar 16, 2012
  2. jcsd
  3. tiny-tim

    tiny-tim 26,016
    Science Advisor
    Homework Helper

    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:
  4. 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
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