# Flux Linkage - what, where, why?

by lntz
Tags: flux linkage
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 P: 53 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.
 Sci Advisor HW Helper Thanks P: 26,148 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-metresreturning 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
 P: 1,506 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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