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(less commonly), reluctancy
Physics a measure of the resistance of a closed magnetic circuit to a magnetic flux, equal to the ratio of the magnetomotive force to the magnetic flux


A property of a magnetic circuit analogous to resistance in an electric circuit.

Every line of magnetic flux is a closed path. Whenever the flux is largely confined to a well-defined closed path, there is a magnetic circuit. That part of the flux that departs from the path is called flux leakage.

For any closed path of length l in a magnetic field H, the line integral of H cos α dl around the path is the magnetomotive force (mmf) of the path, as in

Eq. (1), where α is the angle between H and the path. If the path encloses N conductors, each with current I, Eq. (2) holds.

Consider the closely wound toroid shown in the illustration. For this arrangement of currents, the magnetic field is almost entirely within the toroidal coil, and there the flux density or magnetic induction B is given by

Eq. (3), where l is the mean circumference of the toroid and μ is the permeability. The flux Φ within the toroid of cross-sectional area A is given by either form of
Eqs. (4), which is similar in form to the equation for the electric circuit, although nothing actually flows in the magnetic circuit. The factor l/μA is called the reluctance of the magnetic circuit. The reluctance is not constant because the permeability μ varies with changing flux density.

A toroidal coilenlarge picture
A toroidal coil



a characteristic of a magnetic circuit; the reluctance R m is equal to the ratio of the magnetomotive force F acting on a magnetic circuit to the magnetic flux Φ developed in the circuit. For a uniform section of a magnetic circuit the reluctance can be calculated from the formula Rm = l/μμ0S, where l and S are the length and cross section of the section of the magnetic circuit, respectively; μ is the relative magnetic permeability of the material in the circuit; and μ0 is the magnetic constant.

In the case of a nonuniform magnetic circuit composed of successive uniform sections having different values of l, S, and μ, the reluctance is equal to the sum of the values of Rm for the uniform sections. Such a computation is approximate, since the formula does not take into account “magnetic leakage” (the diffusion of magnetic flux into the space surrounding the magnetic circuit), the nonuniformity of the magnetic field in the circuit, and the nonlinear dependence of the reluctance on the field. In a variable magnetic field the reluctance is a complex quantity, because in this case μ, is a function of the frequency of the electromagnetic oscillations. The unit of reluctance in the International System of Units is the ampere or ampere-turn per weber (A/Wb), and in the cgs system of units, the gilbert per maxwell (Gb/Mx); 1 A/Wb = 4 × 10-9 Gb/Mx ≈ 1.2566 × 10-8 Gb/Mx.


A measure of the opposition presented to magnetic flux in a magnetic circuit, analogous to resistance in an electric circuit; it is equal to magnetomotive force divided by magnetic flux. Also known as magnetic reluctance.
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I am discovering how all the learning and even all the reluctancy have been built into my present mission.
In addition to the reluctancy of industrialists to adopt changes in the plant and investment on the treatment, land availability and land use restrictions are also factors which result into higher treatment costs for older facilities.
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Although the company is benefiting from a steady flow of work from the rail industry, Mr Mitten did say that he would support an extension of rail franchise lengths by the Government, as he believes that those lasting only six to seven years led to a reluctancy to invest in refurbishment work.
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Due to regulations which penalize banks for financing borrowers in or just out of bankruptcy, institutions generally have a reluctancy to lend in situations where bankruptcy is a factor," comments Fefferman.
Yet only over the past 10 years have building owners and managers, spurred by the public's reluctancy to live or work in buildings containing these materials, been inclined to view total removal as the most viable way to deal with asbestos.
The Sunderland boss hopes for talks with Steed Malbranque, Pascal Chimbonda, Teemu Tainio and Younes Kaboul, despite the players' reluctancy to go north.