Magnetic reluctance
Encyclopedia
Magnetic reluctance, or magnetic resistance, is a concept used in the analysis of magnetic circuit
s. It is analogous to resistance
in an electrical circuit
, but rather than dissipating magnetic 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 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
.
Reluctance is usually represented by a curly capital R, as can be displayed using such fonts as Monotype
” (MMF) in a passive magnetic circuit
to 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-turn
s 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
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:
or
where
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).
Reluctance can also be applied to:
Magnetic circuit
A magnetic circuit is made up of one or more closed loop paths containing a magnetic flux. The flux is usually generated by permanent magnets or electromagnets and confined to the path by magnetic cores consisting of ferromagnetic materials like iron, although there may be air gaps or other...
s. It is analogous to resistance
Electrical resistance
The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...
in an electrical circuit
Electrical network
An electrical network is an interconnection of electrical elements such as resistors, inductors, capacitors, transmission lines, voltage sources, current sources and switches. An electrical circuit is a special type of network, one that has a closed loop giving a return path for the current...
, but rather than dissipating magnetic energy it stores magnetic energy. In likeness to the way an electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
causes an electric current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...
to follow the path of least resistance
Path of least resistance
The path of least resistance describes the physical or metaphorical pathway that provides the least resistance to forward motion by a given object or entity, among a set of alternative paths. The concept is often used to describe why an object or entity takes a given path.In physics, the path of...
, a magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
causes magnetic flux
Magnetic flux
Magnetic flux , is a measure of the amount of magnetic B field passing through a given surface . The SI unit of magnetic flux is the weber...
to follow the path of least magnetic reluctance. It is a scalar
Scalar (physics)
In physics, a scalar is a simple physical quantity that is not changed by coordinate system rotations or translations , or by Lorentz transformations or space-time translations . This is in contrast to a vector...
,
extensive quantity, akin to electrical resistance.
History
The term was coined in May 1888 by Oliver HeavisideOliver Heaviside
Oliver Heaviside was a self-taught English electrical engineer, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, invented mathematical techniques to the solution of differential equations , reformulated Maxwell's field equations in terms of electric and...
. The notion of “magnetic resistance” was first mentioned by James Joule and the term "magnetomotive force
Magnetomotive force
Magnetomotive force is any physical driving force that produces magnetic flux. In this context, the expression "driving force" is used in a general sense of "work potential", and is analogous, but distinct from force measured in newtons...
” (MMF) was first named by Bosanquet. The idea for a magnetic flux
Magnetic flux
Magnetic flux , is a measure of the amount of magnetic B field passing through a given surface . The SI unit of magnetic flux is the weber...
law, similar to Ohm's law
Ohm's law
Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points...
for closed electric circuits, is attributed to H. Rowland
Henry Augustus Rowland
Henry Augustus Rowland was a U.S. physicist. Between 1899 and 1901 he served as the first president of the American Physical Society...
.
Reluctance is usually represented by a curly capital R, as can be displayed using such fonts as Monotype
Definition
The total reluctance is equal to the ratio of the "magnetomotive forceMagnetomotive force
Magnetomotive force is any physical driving force that produces magnetic flux. In this context, the expression "driving force" is used in a general sense of "work potential", and is analogous, but distinct from force measured in newtons...
” (MMF) in a passive magnetic circuit
Magnetic circuit
A magnetic circuit is made up of one or more closed loop paths containing a magnetic flux. The flux is usually generated by permanent magnets or electromagnets and confined to the path by magnetic cores consisting of ferromagnetic materials like iron, although there may be air gaps or other...
to the magnetic flux
Magnetic flux
Magnetic flux , is a measure of the amount of magnetic B field passing through a given surface . The SI unit of magnetic flux is the weber...
in this circuit. In an AC field, the reluctance is the ratio of the amplitude values for a sinusoidal MMF and magnetic flux
Magnetic flux
Magnetic flux , is a measure of the amount of magnetic B field passing through a given surface . The SI unit of magnetic flux is the weber...
. (see phasors)
The definition can be expressed as:
where
("R") is the reluctance in ampere-turnAmpere-turn
The ampere-turn was the MKS unit of magnetomotive force , represented by a direct current of one ampere flowing in a single-turn loop in a vacuum...
s per weber
Weber (unit)
In physics, the weber is the SI unit of magnetic flux. A flux density of one Wb/m2 is one tesla.The weber is named for the German physicist Wilhelm Eduard Weber .- Definition :...
(a unit that is equivalent to turns per henry). "Turns
Turn (geometry)
A turn is an angle equal to a 360° or 2 radians or \tau radians. A turn is also referred to as a revolution or complete rotation or full circle or cycle or rev or rot....
" refers to the winding number
Winding number
In mathematics, the winding number of a closed curve in the plane around a given point is an integer representing the total number of times that curve travels counterclockwise around the point...
of an electrical conductor comprising an inductor.
("F") is the magnetomotive forceMagnetomotive force
Magnetomotive force is any physical driving force that produces magnetic flux. In this context, the expression "driving force" is used in a general sense of "work potential", and is analogous, but distinct from force measured in newtons...
(MMF) in ampere-turns
- Φ ("Phi") is the magnetic fluxMagnetic fluxMagnetic flux , is a measure of the amount of magnetic B field passing through a given surface . The SI unit of magnetic flux is the weber...
in webers.
It is sometimes known as Hopkinson's law and is analogous to Ohm's Law
Ohm's law
Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points...
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
Maxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.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:
or
where
- l is the length of the circuit in metreMetreThe metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...
s
is the permeability of free space, equal to 
henry per metre
is the relative magnetic permeability of the material (dimensionless)
is the permeability of the material (
) - A is the cross-sectional area of the circuit in square metreSquare metreThe square metre or square meter is the SI derived unit of area, with symbol m2 . It is defined as the area of a square whose sides measure exactly one metre...
s
The inverse of reluctance is called permeance.
Its SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
derived unit is the henry (the same as the unit of inductance
Inductance
In electromagnetism and electronics, inductance is the ability of an inductor to store energy in a magnetic field. Inductors generate an opposing voltage proportional to the rate of change in current in a circuit...
, although the two concepts are distinct).
Applications
- Air gaps can be created in the cores of certain transformers to reduce the effects of saturationSaturation (magnetic)Seen in some magnetic materials, saturation is the state reached when an increase in applied external magnetizing field H cannot increase the magnetization of the material further, so the total magnetic field B levels off...
. This increases the reluctance of the magnetic circuit, and enables it to store more energyEnergyIn physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
before core saturation. This effect is also used in the flyback transformerFlyback transformerA flyback transformer , also called a line output transformer , is a special transformer, which is used for conversion of energy in electronic circuits. It was initially designed to generate high current sawtooth signals at a relatively high frequency...
.
- Variation of reluctance is the principle behind the reluctance motorReluctance motorA reluctance motor is a type of electric motor that induces non-permanent magnetic poles on the ferromagnetic rotor. Torque is generated through the phenomenon of magnetic reluctance.A reluctance motor, in its various incarnations, may be known as a:...
(or the variable reluctance generator) and the Alexanderson alternatorAlexanderson alternatorAn Alexanderson alternator is a rotating machine invented by Ernst Alexanderson in 1904 for the generation of high frequency alternating current up to 100 kHz, for use as a radio transmitter...
. Another way of saying this is that the reluctance forces strive for a maximally aligned magnetic circuit and a minimal air gap distance.
- MultimediaMultimediaMultimedia is media and content that uses a combination of different content forms. The term can be used as a noun or as an adjective describing a medium as having multiple content forms. The term is used in contrast to media which use only rudimentary computer display such as text-only, or...
loudspeakerLoudspeakerA loudspeaker is an electroacoustic transducer that produces sound in response to an electrical audio signal input. Non-electrical loudspeakers were developed as accessories to telephone systems, but electronic amplification by vacuum tube made loudspeakers more generally useful...
s are typically shielded magnetically, in order to reduce magnetic interference caused to televisionTelevisionTelevision is a telecommunication medium for transmitting and receiving moving images that can be monochrome or colored, with accompanying sound...
s and other CRTCathode ray tubeThe cathode ray tube is a vacuum tube containing an electron gun and a fluorescent screen used to view images. It has a means to accelerate and deflect the electron beam onto the fluorescent screen to create the images. The image may represent electrical waveforms , pictures , radar targets and...
s. 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 motorsElectric motorAn electric motor converts electrical energy into mechanical energy.Most electric motors operate through the interaction of magnetic fields and current-carrying conductors to generate force...
- Variable reluctance (magnetic) pickups
See also
- Dielectric complex reluctance
- Magnetic capacitivity
- Magnetic capacitanceMagnetic capacitanceMagnetic capacitance is a magnetic "reactance" which prevents magnetic "current" in oscillating magnetic circuits from rising...
- Magnetic circuitMagnetic circuitA magnetic circuit is made up of one or more closed loop paths containing a magnetic flux. The flux is usually generated by permanent magnets or electromagnets and confined to the path by magnetic cores consisting of ferromagnetic materials like iron, although there may be air gaps or other...
- Magnetic complex reluctanceMagnetic complex reluctanceMagnetic complex reluctance is a measurement of a passive magnetic circuit dependent on sinusoidal magnetomotive force and sinusoidal magnetic flux , and this is determined by deriving the ratio of their complex effective amplitudes.[Ref...
- Reluctance motorReluctance motorA reluctance motor is a type of electric motor that induces non-permanent magnetic poles on the ferromagnetic rotor. Torque is generated through the phenomenon of magnetic reluctance.A reluctance motor, in its various incarnations, may be known as a:...