Reluctance

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Magnetic reluctance is the resistance of a material to a magnetic field. It is defined as the ratio of magnetomotive force to magnetic flux. The term was coined in May 1888 by Oliver Heaviside.

The definition can be expressed as:

$S=\frac{F}{\Phi}$

where

S is the reluctance in ampere-turns per weber (a unit that is equivalent to turns per henry)

F is the magnetomotive force (MMF) in ampere-turns

Φ is the magnetic flux in webers.

This 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, whilst 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:

$S = \frac{l}{\mu_0 \mu_r A}$

where

l is the length of the circuit in metres

$μ 0$ is the permeability of free space, equal to $4 \pi \times 10^{-7}$ henry per metre

$μ r$ 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.

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.

Variation of reluctance is the principle behind the variable reluctance generator and the Alexanderson alternator.

The variation in the reluctance of a magnetic circuit, in which part of the circuit is moving, is used in measuring instruments called reluctance sensors. One of the major applications is in magnetic pickups for electric guitars.^{[citation needed]}