Magnetic reluctance, or magnetic resistance, is a concept used in the
analysis of magnetic circuits. It is analogous to resistance in an electrical
circuit, but rather than dissipating electric energy it stores 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. The unit for
magnetic reluctance is inverse henry, H−1.
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” 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.
Reluctance is usually represented by a cursive capital .
Definition In a DC field, the reluctance is the
ratio of the "magnetomotive force” in a magnetic circuit to the magnetic flux in
this circuit. In a pulsating DC or AC field, the reluctance is the ratio of
the amplitude of the "magnetomotive force” in a magnetic circuit to the
amplitude of the magnetic flux in this circuit.
The definition can be expressed as follows:
where is the reluctance in ampere-turns per
weber. "Turns" refers to the winding number of an electrical conductor
comprising an inductor. is the magnetomotive force in
ampere-turns Φ 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.
The reluctance of a uniform magnetic circuit can be calculated as:
or where
l is the length of the circuit in metres is the permeability of vacuum, equal to
4π × 10−7 henry per metre is the relative magnetic permeability of
the material is the permeability of the material
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. Applications
Constant air gaps can be created in the core 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.
Variable air gaps can be created in the cores by a movable keeper to create a
flux switch that alters the amount of magnetic flux in a magnetic circuit
without varying the constant magnetomotive force in that circuit.
Variation of reluctance is the principle behind the reluctance motor and the
Alexanderson alternator. Another way of saying this is that the reluctance
forces strive for a maximally aligned magnetic circuit and a minimal air gap
distance. 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 pickups See also
Dielectric complex reluctance Magnetic capacitivity
Magnetic capacitance Magnetic circuit
Magnetic complex reluctance Reluctance motor
References ^ Heaviside O., Electrical Papers, Vol 2
– L.; N.Y.: Macmillan, 1892, p.166 ^ Joule J., Scientific Papers, vol 1 –
1884, p.36 ^ Bosanquet, Phil. Mag., vol 15, 1883,
p.205 ^ Rowland H., Phil. Mag., vol 46, 1873,
p.140 External links