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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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But advocates of limited government make a potentially fatal error in assuming that homosexual revolutionaries share this principled reluctance to use state power.
Any claimed private sector reluctance to share important data with the government grows out of, at best, a misperception of current law" EPIC's Sobel said in his July 9 testimony.
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In a letter to the Fiji RFU administration manager, Tevita Ratuva, SRU secretary, Bill Hogg, wrote: "I would advise you that this decision has been taken with the greatest reluctance.
Law enforcement agencies that understand the human reluctance to kill and the effects of conditioning can develop training programs that will allow their officers, first, to successfully and appropriately employ deadly force and, second, to survive the emotional and psychological aftereffects of deadly force incidents.
But they still exhibit some reluctance to share the classroom or to take the time to plan library instruction, still overestimate students' abilities to use library resources, and still do not really understand how improving that ability can help make students more independent, more interested, and more interesting, and thus more rewarding to teach.
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The reluctance to complete timely, relevant evaluations can, in large part, be explained by the old axiom that "few are willing to do something they have never been taught to do.
These makers of fine wines are now turning to the bag-in-box format to drive market share, overcoming a traditional market reluctance to use this type of packaging.