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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.
References in periodicals archive ?
"PwC has had some widely publicised fines in recent years and we understand there is a reluctance to engage based on our ownership structure."
'My reluctance was not because I have not kissed a woman before, but it is one thing to kiss a woman in your own space and another on the screens.
Chiba, "Current Waveform for Noise Reduction of a Switched Reluctance Motor Under Magnetically Saturated Condition," in IEEE Transactions on Industry Applications, vol.
"It is with great reluctance and disappointment that I announce my retirement from concert touring," he said in a statement on his website.
India also lost hosting the Under-19 Asia Cup, also over the country's reluctance to host Pakistan's junior side.
This paper proposes fuzzy logic controller for the converter of switched reluctance motor in closed loop control.
[31], the reluctance of the soft magnetic materials was included to consider the nonlinear magnetization characteristic, but the most important B-H magnetizing curve was determined based on B-H experimental data by a trial and error method for calculating the reluctance of soft magnetic materials.
(I think that those who know me, our party for example, I have a reluctance to take on the leadership.)
Iranian president Hassan Rouhani has said that reluctance by foreign banks to deal with Iran for fear of retribution from US authorities could stymie economic growth in the nation.
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MIDLAND business leaders say firms have a "growing reluctance" to deal with banks after a sharp lending fall.
Thanks to rapid urbanisation and banks' reluctance, Pakistan is short of 90 lakh houses.