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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 ?
It is understood Cole (above) is also reluctant to accept a cut in his PS25,000-aweek wages.
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Criteria: An elegantly crafted novel, "The Reluctant First Lady" clearly documents author Venita Ellick as an exceptionally accomplished writer able to skillfully weave memorable characters into an riveting story line from beginning to end.
TOMMY'S TIPS SHAWFIELD Race 1 - Delmonte Town; Race 2 - Reluctant Ebony; Race 3 - Lynway Marina; Race 4 - Kilkenny Franco; Race 5 - Lemon Karen; Race 6 - Reluctant Jinty; Race 7 - Glenside Jen; Race 8 - Lagile Maldini; Race 9 - Moorfoot Lizzie; Race 10 - Moorfoot Bob; Race 11 - Nadurra Cartier.
34; 3rd - Lagile Maldini (4) 5-2Fav, Reluctant Jinty (5) 4-1 PS13.
He was just trying to find a way to encourage his 11 year-old reluctant reader son to give books a try.
RELUCTANT RITA (9-4) got up close home to land the re-run PS1,000 final of the Winning Lines British Bred Puppy Derby over 480m at Newcastle on Saturday, writes Jonathan Kay.
Club Modernity for Reluctant Christians" is a discussion of faith and the modern world from Leonard Swidler as he digs into his own Catholic faith and reflects on the nature of many topics of the modern day and how being faithful to one's belief does not mean turning one's head away from the world.
reluctant to leave Spain, even though United were willing to meet the pounds 18m asking price for the 20-year-old.
WILLIAM Douglas Home's romantic comedy The Reluctant Debutante (pictured) arrives in North Wales next week.
MANY reluctant landlords could fall foul of the law as they are ill-prepared and unaware of the potential pitfalls of being a buy-to-let landlord, according to a national tenant eviction and rent recovery firm.