Magnetic Reluctance
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.
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:
where
(“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.
("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:
where
l is the length of the
circuit in metres
μ0 is the permeability of
free space, equal to henry per metre
μr 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.
Its SI derived unit is the henry (the same
as the unit of inductance, although the two concepts are distinct).
3.6.2
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 reluctance motor
(or the variable reluctance generator) and the Alexanderson alternator.
§
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:
§
Reluctance motors
§
Variable reluctance (magnetic) pickups
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