Magnetic reluctance

Magnetic reluctance is the scalar value, which is equal to the relation of the magnetic tension on the part of a passive magnetic circuit and the magnetic flux in this part or to relation their amplitude values for the sinusoidal magnetic tension and magnetic flux.

   Magnetic reluctance [1-4] is measuring in units – [1/H] and determining by the formula:

                ${\displaystyle z_{\mu }={\frac {N}{\Phi }}={\frac {N_{m}}{\Phi _{m}}}}$
 
   If the energy loss in a magnetic of the magnetic circuit are absent, then existence of the magnetic reluctance (resistance for a magnetic flux) no causes to a consumption of an energy, though here the relationship, which is formality similar to Ohm’s Law for an electric circuit [1-5], and has a place. So for an uniform path of a magnetic circuit the magnetic reluctance  ${\displaystyle z_{\mu }}$ is determining by the expression: 

              ${\displaystyle z_{\mu }={\frac {1}{\mu \mu _{0}}}{\frac {l}{S}}}$

where

${\displaystyle l}$ , ${\displaystyle S}$ is the length and cross-section of the part of a magnetic circuit;
${\displaystyle \mu \mu _{0}}$ is the magnetic permeability. 
   The term “reluctance” for a magnetic resistance to a magnetic flux is proposed by O. Heaviside [1]. Itself idea about a applicability to a magnetic flux the law, which is formality similar to Ohm’s Law for a closed electric circuit, goes to H. Rowland [2]. The notion “magnetic resistance” in the first time is met with J. Joule [3]. The naming "magnetomotive force” in the first time is proposed by Bosanquet [4]. 

References

[1] Heaviside O., Electrical Papers. Vol.2. – L.; N.Y.: Macmillan, 1892, p. 166.

[2] Rowland H., Phil. Mag. (4), vol. 46, 1873, p. 140. [3] Joule J., Scientific Papers, vol. 1. – 1884, p. 36. [4] Bosanquet, Phil. Mag., vol. 15, 1883, p. 205.