# Flux Linkage - what, where, why?

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.

Last edited:

tiny-tim
Homework Helper
hi lntz! 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 ):

B = µH = µnI

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

B flux linkage (through the M-turn secondary) = µMNIA/L webers 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