# Dictionary Definition

reluctance

### Noun

1 (physics) opposition to magnetic flux (analogous to electric resistance)
2 a certain degree of unwillingness; "a reluctance to commit himself"; "after some hesitation he agreed" [syn: hesitancy, hesitation, disinclination, indisposition]

# User Contributed Dictionary

## English

### Noun

1. Unwillingness to do something.
2. Hesitancy in taking some action.
3. That property of a magnetic circuit analogous to resistance in an electric circuit.

#### Translations

unwillingness to do something
hesitancy in taking some action
magnetic resistance

# Extensive Definition

Magnetic reluctance or "magnetic resistance", is analogous to resistance in an electrical circuit (although it does not dissipate magnetic energy). In likeness to the way an electric field causes an electric current to follow the path of least resistance, a magnetic field causes magnetic flux to follow the path of least magnetic reluctance. It is a scalar, extensive quantity, akin to electrical resistance.

## History

The term was coined in May 1888 by Oliver Heaviside. The notion of “magnetic resistance” was first mentioned by James Joule and the term "magnetomotive force” (MMF) was first named by Bosanquet. The idea for a magnetic flux law, similar to Ohm's law for closed electric circuits, is attributed to H. Rowland.

## Definition

The total reluctance is equal to the ratio of the "magnetomotive force” (MMF) in a passive magnetic circuit and the magnetic flux in this circuit. In an AC field, the reluctance is the ratio of the amplitude values for a sinusoidal MMF and magnetic flux. (see phasors)
The definition can be expressed as:
\mathfrak R = \frac
where
\mathfrak R ("R") is the reluctance in ampere-turns per weber (a unit that is equivalent to turns per henry). "Turns" refers to the winding number of an electrical conductor comprising an inductor.
\mathfrak F ("F") is the magnetomotive force (MMF) in ampere-turns
Φ ("Phi") is the magnetic flux in webers.
It is sometimes known as Hopkinson's law and is analogous to Ohm's Law with resistance replaced by reluctance, voltage by MMF and current by magnetic flux.
Magnetic flux always forms a closed loop, as described by Maxwell's equations, but the path of the loop depends on the reluctance of the surrounding materials. It is concentrated around the path of least reluctance. Air and vacuum have high reluctance, while easily magnetized materials such as soft iron have low reluctance. The concentration of flux in low-reluctance materials forms strong temporary poles and causes mechanical forces that tend to move the materials towards regions of higher flux so it is always an attractive force(pull).
The reluctance of a uniform magnetic circuit can be calculated as:
\mathfrak R = \frac
where
l is the length of the circuit in metres
\mu_0 is the permeability of free space, equal to 4 \pi \times 10^ henry per metre
\mu_r is the relative magnetic permeability of the material (dimensionless)
A is the cross-sectional area of the circuit in square metres
The inverse of reluctance is called permeance.
\mathfrak P = \frac
Its SI derived unit is the henry (the same as the unit of inductance, although the two concepts are distinct).

## Applications

• Air gaps can be created in the cores of certain transformers to reduce the effects of saturation. This increases the reluctance of the magnetic circuit, and enables it to store more energy before core saturation. This effect is also used in the flyback transformer.
• Multimedia loudspeakers are typically shielded magnetically, in order to reduce magnetic interference caused to televisions and other CRTs. The speaker magnet is covered with a material such as soft iron to minimize the stray magnetic field.
Reluctance can also be applied to:

## References

Tutorial on magnetic reluctance and mmf
reluctance in Catalan: Reluctància
reluctance in German: Magnetischer Widerstand
reluctance in French: Réluctance
reluctance in Korean: 자기저항
reluctance in Italian: Riluttanza
reluctance in Dutch: Magnetische weerstand
reluctance in Polish: Reluktancja
reluctance in Portuguese: Relutância magnética
reluctance in Finnish: Reluktanssi