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There is a magnetic-potential drop across an air gap. If you represent a magnetic core with a winding current i as a magnetic circuit. The magneto-motive force will be your voltage source, where the mmf (magneto-motive force) = Ni; (number of turns on the core and current product) == ∫Hdl=mmf=N*i. The elements that would be in the circuit would be in series and it would be represented as two "resistors" or better known in magnetics as the reluctance of the material which has a parallel equivalence to the resistor's characteristics.

Reluctance=Rmk=length of material divided by the product of the Area and permeability of the material µ.


Rmk=lk / (µk*Ak); where k is the number of of "legs" of the core or different mediums you approach.


To answer the air gap problem, the air gap would have a Reluctance where µ = µ0, permeability of free space and the Area of the Magnetic flux would be the same size of the area of the core. Finally the length would be the size of the airgap=δ.

Now since you have the reluctance of the airgap rmδ= δ /(µ0*Area of core). The Magnetic Drop is now = Umk where k is δ = Umδ = mmf / Rmδ = µ0*Area*N*i/δ

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