R.h. corkscrew rule

Note the direction of the flux is given by Maxwell's 'R.H. corkscrew rule' and that the flux lines are continuous
Applying  Ampere's  Law  to  a  concentric circular path inside the ring gives:

H.l=N.I

so

H=N.I/l

where l is the  length of the chosen path inside the former. (If  the   radius   of  the   former   is   large compared to the width, then l =2 .pi .r )

Where ℜ=l/µµ₀ A  is called  the reluctance of the magnetic path It has been written in this way to show the identical form of the equation to  current flowing in the conductor ie:

I=V/R

where   the   current   I   flows   through   a conductor of resistance R.

Hence the name 'magnetic circuit'

Here,    
Φ is analogous to current I
N.I is analogous to V
ℜ is analogous to R
 
The analogy is so strong that the product N.I is often referred to as the 'magnetomotive force' (m.m.f) in analogy with the electro-motive force (e.m.f. or voltage) and

(σ = conductivity of the material).So we may write:
 
flux Φ =  m.m.f / circuit reluctance (Analogous to:  I = voltage/resistance in an electrical circuit).

Hence the flux flows more 'easily' through  a material with high µ material - i.e. it requires less m.m.f to produce a given flux in the material, just as current flows more easily through a high conductivity material. If an air gap were now introduced into the core,