Magnetic Reluctance

Magnetic reluctance which is also known as reluctance, magnetic insulator, or a magnetic resistance is defined as the resistance provide by a magnetic circuit to the flow or production of magnetic flux (magnetic field lines). It is the property of the material that opposes the creation of magnetic flux in a magnetic circuit.
The concept of magnetic reluctance is similar to the resistance of a material to the flow of charge (current) ) is determined for electric circuits by the equation:
$$R = \rho {L \over A} \quad \text{(ohm, Ω)}$$
Where the reluctance of a material to the setting up of magnetic flux lines in the material is determined by the following equation:
$$S = R_m = {l \over \mu A} \quad \text{(rels, A.t/wb)}$$
where $S$ is the reluctance, $l$ is the length of the magnetic path, and $A$ is the cross-sectional area. The $t$ in the units $At/Wb$ is the number of turns of the applied winding. More is said about ampere-turns ($At$) in the next section.
Note that the resistance and reluctance are inversely proportional to the area, indicating that an increase in area will result in a reduction in each and an increase in the desired result: current and flux.
For an increase in length the opposite is true, and the desired effect is reduced.
The reluctance, however, is inversely proportional to the permeability, while the resistance is directly proportional to the resistivity. The larger the $\mu$ or the smaller the $r$, the smaller the reluctance and resistance, respectively.
Obviously, therefore, materials with high permeability, such as the ferromagnetic, have very small reluctances and will result in an increased measure of flux through the core. There is no widely accepted unit for reluctance, although the rel and the At/Wb are usually applied.

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