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From Wikipedia, the free encyclopedia
(Redirected from Permanent magnet)
This article is about objects and devices that produce magnetic fields. For a
description of magnetic materials, see Magnetism. For other uses, see Magnet
(disambiguation).

A magnetite rock is being pulled by

a neodymium magnet on top.

Articles about

Electromagnetism
  Electricity
 Magnetism
 Optics
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A magnet is a material or object that produces a magnetic field. This magnetic field
is invisible but is responsible for the most notable property of a magnet: a force that
pulls on other ferromagnetic materials, such as iron, steel, nickel, cobalt, etc. and
attracts or repels other magnets.

A permanent magnet is an object made from a material that is magnetized and

creates its own persistent magnetic field. An everyday example is a refrigerator
magnet used to hold notes on a refrigerator door. Materials that can be magnetized,
which are also the ones that are strongly attracted to a magnet, are
called ferromagnetic (or ferrimagnetic). These include the
elements iron, nickel and cobalt and their alloys, some alloys of rare-earth metals,
and some naturally occurring minerals such as lodestone. Although ferromagnetic
(and ferrimagnetic) materials are the only ones attracted to a magnet strongly
enough to be commonly considered magnetic, all other substances respond weakly
to a magnetic field, by one of several other types of magnetism.

Ferromagnetic materials can be divided into magnetically "soft" materials

like annealed iron, which can be magnetized but do not tend to stay magnetized, and
magnetically "hard" materials, which do. Permanent magnets are made from "hard"
ferromagnetic materials such as alnico and ferrite that are subjected to special
processing in a strong magnetic field during manufacture to align their
internal microcrystalline structure, making them very hard to demagnetize. To
demagnetize a saturated magnet, a certain magnetic field must be applied, and this
threshold depends on coercivity of the respective material. "Hard" materials have
high coercivity, whereas "soft" materials have low coercivity. The overall strength of
a magnet is measured by its magnetic moment or, alternatively, the total magnetic
flux it produces. The local strength of magnetism in a material is measured by
its magnetization.

An electromagnet is made from a coil of wire that acts as a magnet when an electric
current passes through it but stops being a magnet when the current stops. Often,
the coil is wrapped around a core of "soft" ferromagnetic material such as mild steel,
which greatly enhances the magnetic field produced by the coil.

Discovery and development

[edit]
Main article: History of electromagnetic theory
See also: Magnetism history
Ancient people learned about magnetism from lodestones (or magnetite) which are
naturally magnetized pieces of iron ore. The word magnet was adopted in Middle
English from Latin magnetum "lodestone", ultimately from Greek μαγνῆτις
[λίθος] (magnētis [lithos])[1] meaning "[stone] from Magnesia",[2] a place
in Anatolia where lodestones were found (today Manisa in modern-day Turkey).
Lodestones, suspended so they could turn, were the first magnetic compasses. The
earliest known surviving descriptions of magnets and their properties are from
Anatolia, India, and China around 2,500 years ago.[3][4][5] The properties of lodestones
and their affinity for iron were written of by Pliny the Elder in his
encyclopedia Naturalis Historia in the 1st century AD.[6]

In 11th century China, it was discovered that quenching red hot iron in the Earth's
magnetic field would leave the iron permanently magnetized. This led to the
development of the navigational compass, as described in Dream Pool Essays in
1088.[7][8] By the 12th to 13th centuries AD, magnetic compasses were used in
navigation in China, Europe, the Arabian Peninsula and elsewhere.[9]

A straight iron magnet tends to demagnetize itself by its own magnetic field. To
overcome this, the horseshoe magnet was invented by Daniel Bernoulli in 1743.[7][10] A
horseshoe magnet avoids demagnetization by returning the magnetic field lines to
the opposite pole.[11]
In 1820, Hans Christian Ørsted discovered that a compass needle is deflected by a
nearby electric current. In the same year André-Marie Ampère showed that iron can
be magnetized by inserting it in an electrically fed solenoid.[12] This led William
Sturgeon to develop an iron-cored electromagnet in 1824.[7] Joseph Henry further
developed the electromagnet into a commercial product in 1830–1831, giving people
access to strong magnetic fields for the first time. In 1831 he built an ore separator
with an electromagnet capable of lifting 750 pounds (340 kg).[13]

Physics
[edit]
Magnetic field
[edit]

Iron filings that have oriented in the magnetic field

produced by a bar magnetDetecting magnetic field with compass and with iron filings
Main article: Magnetic field
The magnetic flux density (also called magnetic B field or just magnetic field, usually
denoted by B) is a vector field. The magnetic B field vector at a given point in space
is specified by two properties:

1. Its direction, which is along the orientation of a compass needle.

2. Its magnitude (also called strength), which is proportional to how
strongly the compass needle orients along that direction.
In SI units, the strength of the magnetic B field is given in teslas.[14]

Magnetic moment
[edit]
Main article: Magnetic moment
A magnet's magnetic moment (also called magnetic dipole moment and usually
denoted μ) is a vector that characterizes the magnet's overall magnetic properties.
For a bar magnet, the direction of the magnetic moment points from the magnet's
south pole to its north pole,[15] and the magnitude relates to how strong and how far
apart these poles are. In SI units, the magnetic moment is specified in terms of
A·m2 (amperes times meters squared).

A magnet both produces its own magnetic field and responds to magnetic fields. The
strength of the magnetic field it produces is at any given point proportional to the
magnitude of its magnetic moment. In addition, when the magnet is put into an
external magnetic field, produced by a different source, it is subject to
a torque tending to orient the magnetic moment parallel to the field.[16] The amount of
this torque is proportional both to the magnetic moment and the external field. A
magnet may also be subject to a force driving it in one direction or another,
according to the positions and orientations of the magnet and source. If the field is
uniform in space, the magnet is subject to no net force, although it is subject to a
torque.[17]

A wire in the shape of a circle with area A and carrying current I has a magnetic
moment of magnitude equal to IA.

Magnetization
[edit]
Main article: Magnetization
The magnetization of a magnetized material is the local value of its magnetic
moment per unit volume, usually denoted M, with units A/m.[18] It is a vector field,
rather than just a vector (like the magnetic moment), because different areas in a
magnet can be magnetized with different directions and strengths (for example,
because of domains, see below). A good bar magnet may have a magnetic moment
of magnitude 0.1 A·m2 and a volume of 1 cm3, or 1×10−6 m3, and therefore an average
magnetization magnitude is 100,000 A/m. Iron can have a magnetization of around a
million amperes per meter. Such a large value explains why iron magnets are so
effective at producing magnetic fields.

Modelling magnets
[edit]

Field of a cylindrical bar magnet computed accurately

See also: Two definitions of moment
Two different models exist for magnets: magnetic poles and atomic currents.

Although for many purposes it is convenient to think of a magnet as having distinct

north and south magnetic poles, the concept of poles should not be taken literally: it
is merely a way of referring to the two different ends of a magnet. The magnet does
not have distinct north or south particles on opposing sides. If a bar magnet is
broken into two pieces, in an attempt to separate the north and south poles, the
result will be two bar magnets, each of which has both a north and south pole.
However, a version of the magnetic-pole approach is used by professional
magneticians to design permanent magnets.[citation needed]

In this approach, the divergence of the magnetization ∇·M inside a magnet is treated
as a distribution of magnetic monopoles. This is a mathematical convenience and
does not imply that there are actually monopoles in the magnet. If the magnetic-pole
distribution is known, then the pole model gives the magnetic field H. Outside the
magnet, the field B is proportional to H, while inside the magnetization must be
added to H. An extension of this method that allows for internal magnetic charges is
used in theories of ferromagnetism.

Another model is the Ampère model, where all magnetization is due to the effect of
microscopic, or atomic, circular bound currents, also called Ampèrian currents,
throughout the material. For a uniformly magnetized cylindrical bar magnet, the net
effect of the microscopic bound currents is to make the magnet behave as if there is
a macroscopic sheet of electric current flowing around the surface, with local flow
direction normal to the cylinder axis.[19] Microscopic currents in atoms inside the
material are generally canceled by currents in neighboring atoms, so only the
surface makes a net contribution; shaving off the outer layer of a magnet
will not destroy its magnetic field, but will leave a new surface of uncancelled
currents from the circular currents throughout the material.[20] The right-hand rule tells
which direction positively-charged current flows. However, current due to negatively-
charged electricity is far more prevalent in practice.[citation needed][21]

Polarity
[edit]
The north pole of a magnet is defined as the pole that, when the magnet is freely
suspended, points towards the Earth's North Magnetic Pole in the Arctic (the
magnetic and geographic poles do not coincide, see magnetic declination). Since
opposite poles (north and south) attract, the North Magnetic Pole is actually
the south pole of the Earth's magnetic field.[22][23][24][25] As a practical matter, to tell
which pole of a magnet is north and which is south, it is not necessary to use the
Earth's magnetic field at all. For example, one method would be to compare it to
an electromagnet, whose poles can be identified by the right-hand rule. The
magnetic field lines of a magnet are considered by convention to emerge from the
magnet's north pole and reenter at the south pole.[25]

Magnetic materials
[edit]
Main article: Magnetism
The term magnet is typically reserved for objects that produce their own persistent
magnetic field even in the absence of an applied magnetic field. Only certain classes
of materials can do this. Most materials, however, produce a magnetic field in
response to an applied magnetic field – a phenomenon known as magnetism. There
are several types of magnetism, and all materials exhibit at least one of them.

The overall magnetic behavior of a material can vary widely, depending on the
structure of the material, particularly on its electron configuration. Several forms of
magnetic behavior have been observed in different materials, including:

 Ferromagnetic and ferrimagnetic materials are the ones normally thought

of as magnetic; they are attracted to a magnet strongly enough that the
attraction can be felt. These materials are the only ones that can retain
magnetization and become magnets; a common example is a
traditional refrigerator magnet. Ferrimagnetic materials, which
include ferrites and the longest used and naturally occurring magnetic
materials magnetite and lodestone, are similar to but weaker than
 ferromagnetics. The difference between ferro- and ferrimagnetic materials
is related to their microscopic structure, as explained in Magnetism.
 Paramagnetic substances, such as platinum, aluminum, and oxygen, are
weakly attracted to either pole of a magnet. This attraction is hundreds of
thousands of times weaker than that of ferromagnetic materials, so it can
only be detected by using sensitive instruments or using extremely strong
magnets. Magnetic ferrofluids, although they are made of tiny
ferromagnetic particles suspended in liquid, are sometimes considered
paramagnetic since they cannot be magnetized.
 Diamagnetic means repelled by both poles. Compared to paramagnetic
and ferromagnetic substances, diamagnetic substances, such
as carbon, copper, water, and plastic, are even more weakly repelled by a
magnet. The permeability of diamagnetic materials is less than
the permeability of a vacuum. All substances not possessing one of the
other types of magnetism are diamagnetic; this includes most substances.
Although force on a diamagnetic object from an ordinary magnet is far too
weak to be felt, using extremely strong superconducting magnets,
diamagnetic objects such as pieces of lead and even mice[26] can
be levitated, so they float in mid-air. Superconductors repel magnetic
fields from their interior and are strongly diamagnetic.
There are various other types of magnetism, such as spin
glass, superparamagnetism, superdiamagnetism, and metamagnetism.

Shape
[edit]
Main article: Demagnetizing field
The shape of a permanent magnet has a large influence on its magnetic properties.
When a magnet is magnetized, a demagnetizing field will be created inside it. As the
name suggests, the demagnetizing field will work to demagnetize the magnet,
decreasing its magnetic properties. The strength of the demagnetizing field is
proportional to the magnet's magnetization and shape, according to

Here, is called the demagnetizing factor, and has a different value depending on
the magnet's shape. For example, if the magnet is a sphere, then .

The value of the demagnetizing factor also depends on the direction of the
magnetization in relation to the magnet's shape. Since a sphere is symmetrical
from all angles, the demagnetizing factor only has one value. But a magnet that
is shaped like a long cylinder will yield two different demagnetizing factors,
depending on if it's magnetized parallel to or perpendicular to its length. [16]

Common uses
[edit]
 Hard disk drives record data on a thin magnetic

coating Magnetic hand separator for heavy

minerals

 Magnetic recording media: VHS tapes contain a reel of magnetic tape.

The information that makes up the video and sound is encoded on the
magnetic coating on the tape. Common audio cassettes also rely on
magnetic tape. Similarly, in computers, floppy disks and hard
disks record data on a thin magnetic coating.[27]
 Credit, debit, and automatic teller machine cards: All of these cards
have a magnetic strip on one side. This strip encodes the information
to contact an individual's financial institution and connect with their
account(s).[28]
 Older types of televisions (non flat screen) and older large computer
monitors: TV and computer screens containing a cathode-ray
tube employ an electromagnet to guide electrons to the screen.[29]
 Sensor: Permanent magnets are useful components for fabricating
magnetic sensors for the detection of motion, displacement, position,
and so forth.[30]
 Speakers and microphones: Most speakers employ a permanent
magnet and a current-carrying coil to convert electric energy (the
signal) into mechanical energy (movement that creates the sound).
The coil is wrapped around a bobbin attached to the speaker cone and
carries the signal as changing current that interacts with the field of the
permanent magnet. The voice coil feels a magnetic force and in
response, moves the cone and pressurizes the neighboring air, thus
generating sound. Dynamic microphones employ the same concept,
but in reverse. A microphone has a diaphragm or membrane attached
to a coil of wire. The coil rests inside a specially shaped magnet. When
sound vibrates the membrane, the coil is vibrated as well. As the coil
moves through the magnetic field, a voltage is induced across the coil.
 This voltage drives a current in the wire that is characteristic of the
original sound.
 Electric guitars use magnetic pickups to transduce the vibration of
guitar strings into electric current that can then be amplified. This is
different from the principle behind the speaker and dynamic
microphone because the vibrations are sensed directly by the magnet,
and a diaphragm is not employed. The Hammond organ used a similar
principle, with rotating tonewheels instead of strings.
 Electric motors and generators: Some electric motors rely upon a
combination of an electromagnet and a permanent magnet, and, much
like loudspeakers, they convert electric energy into mechanical energy.
A generator is the reverse: it converts mechanical energy into electric
energy by moving a conductor through a magnetic field.
 Medicine: Hospitals use magnetic resonance imaging to spot problems
in a patient's organs without invasive surgery.
 Chemistry: Chemists use nuclear magnetic resonance to characterize
synthesized compounds.
 Chucks are used in the metalworking field to hold objects. Magnets are
also used in other types of fastening devices, such as the magnetic
base, the magnetic clamp and the refrigerator magnet.
 Compasses: A compass (or mariner's compass) is a magnetized
pointer free to align itself with a magnetic field, most commonly Earth's
magnetic field.
 Art: Vinyl magnet sheets may be attached to paintings, photographs,
and other ornamental articles, allowing them to be attached to
refrigerators and other metal surfaces. Objects and paint can be
applied directly to the magnet surface to create collage pieces of art.
Metal magnetic boards, strips, doors, microwave ovens, dishwashers,
cars, metal I beams, and any metal surface can be used magnetic
vinyl art.
 Science projects: Many topic questions are based on magnets,
including the repulsion of current-carrying wires, the effect of
temperature, and motors involving magnets.[31]

Magnets have many uses in toys. M-tic uses

magnetic rods connected to metal spheres for construction.

 Toys: Given their ability to counteract the force of gravity at close

range, magnets are often employed in children's toys, such as
the Magnet Space Wheel and Levitron, to amusing effect.
  Refrigerator magnets are used to adorn kitchens, as a souvenir, or
simply to hold a note or photo to the refrigerator door.
 Magnets can be used to make jewelry. Necklaces and bracelets can
have a magnetic clasp, or may be constructed entirely from a linked
series of magnets and ferrous beads.
 Magnets can pick up magnetic items (iron nails, staples, tacks, paper
clips) that are either too small, too hard to reach, or too thin for fingers
to hold. Some screwdrivers are magnetized for this purpose.
 Magnets can be used in scrap and salvage operations to separate
magnetic metals (iron, cobalt, and nickel) from non-magnetic metals
(aluminum, non-ferrous alloys, etc.). The same idea can be used in the
so-called "magnet test", in which a car chassis is inspected with a
magnet to detect areas repaired using fiberglass or plastic putty.
 Magnets are found in process industries, food manufacturing
especially, in order to remove metal foreign bodies from materials
entering the process (raw materials) or to detect a possible
contamination at the end of the process and prior to packaging. They
constitute an important layer of protection for the process equipment
and for the final consumer.[32]
 Magnetic levitation transport, or maglev, is a form of transportation that
suspends, guides and propels vehicles (especially trains) through
electromagnetic force. Eliminating rolling resistance increases
efficiency. The maximum recorded speed of a maglev train is 581
kilometers per hour (361 mph).
 Magnets may be used to serve as a fail-safe device for some cable
connections. For example, the power cords of some laptops are
magnetic to prevent accidental damage to the port when tripped over.
The MagSafe power connection to the Apple MacBook is one such
example.
Medical issues and safety
[edit]
Because human tissues have a very low level of susceptibility to static magnetic
fields, there is little mainstream scientific evidence showing a health effect
associated with exposure to static fields. Dynamic magnetic fields may be a
different issue, however; correlations between electromagnetic radiation and
cancer rates have been postulated due to demographic correlations
(see Electromagnetic radiation and health).

If a ferromagnetic foreign body is present in human tissue, an external magnetic

field interacting with it can pose a serious safety risk.[33]

A different type of indirect magnetic health risk exists involving pacemakers. If

a pacemaker has been embedded in a patient's chest (usually for the purpose of
monitoring and regulating the heart for steady electrically induced beats), care
should be taken to keep it away from magnetic fields. It is for this reason that a
patient with the device installed cannot be tested with the use of a magnetic
resonance imaging device.
Children sometimes swallow small magnets from toys, and this can be
hazardous if two or more magnets are swallowed, as the magnets can pinch or
puncture internal tissues.[34]

Magnetic imaging devices (e.g. MRIs) generate enormous magnetic fields, and
therefore rooms intended to hold them exclude ferrous metals. Bringing objects
made of ferrous metals (such as oxygen canisters) into such a room creates a
severe safety risk, as those objects may be powerfully thrown about by the
intense magnetic fields.

Magnetizing ferromagnets
[edit]
See also: Remanence
Ferromagnetic materials can be magnetized in the following ways:

 Heating the object higher than its Curie temperature, allowing it to cool
in a magnetic field and hammering it as it cools. This is the most
effective method and is similar to the industrial processes used to
create permanent magnets.
 Placing the item in an external magnetic field will result in the item
retaining some of the magnetism on removal. Vibration has been
shown to increase the effect. Ferrous materials aligned with the Earth's
magnetic field that are subject to vibration (e.g., frame of a conveyor)
have been shown to acquire significant residual magnetism. Likewise,
striking a steel nail held by fingers in a N-S direction with a hammer
will temporarily magnetize the nail.
 Stroking: An existing magnet is moved from one end of the item to the
other repeatedly in the same direction (single touch method) or two
magnets are moved outwards from the center of a third (double
touch method).[35]
 Electric Current: The magnetic field produced by passing an electric
current through a coil can get domains to line up. Once all of the
domains are lined up, increasing the current will not increase the
magnetization.[36]
Demagnetizing ferromagnets
[edit]
This section does not cite any sources. Please help improve
this section by adding citations to reliable sources. Unsourced
material may be challenged and removed. (February
2025) (Learn how and when to remove this message)
Magnetized ferromagnetic materials can be demagnetized (or degaussed) in the
following ways:

 Heating a magnet past its Curie temperature; the molecular motion

destroys the alignment of the magnetic domains, completely
demagnetizing it
  Placing the magnet in an alternating magnetic field with intensity
above the material's coercivity and then either slowly drawing the
magnet out or slowly decreasing the magnetic field to zero. This is the
principle used in commercial demagnetizers to demagnetize tools,
erase credit cards, hard disks, and degaussing coils used to
demagnetize CRTs.
 Some demagnetization or reverse magnetization will occur if any part
of the magnet is subjected to a reverse field above the magnetic
material's coercivity.
 Demagnetization progressively occurs if the magnet is subjected to
cyclic fields sufficient to move the magnet away from the linear part on
the second quadrant of the B–H curve of the magnetic material (the
demagnetization curve).
 Hammering or jarring: mechanical disturbance tends to randomize the
magnetic domains and reduce magnetization of an object, but may
cause unacceptable damage.
Types of permanent magnets
[edit]
Magnetic metallic elements
[edit]
Many materials have unpaired electron spins, and the majority of these materials
are paramagnetic. When the spins interact with each other in such a way that the
spins align spontaneously, the materials are called ferromagnetic (what is often
loosely termed as magnetic). Because of the way their regular crystalline atomic
structure causes their spins to interact, some metals are ferromagnetic when
found in their natural states, as ores. These include iron
ore (magnetite or lodestone), cobalt and nickel, as well as the rare earth
metals gadolinium and dysprosium (when at a very low temperature). Such
naturally occurring ferromagnets were used in the first experiments with
magnetism. Technology has since expanded the availability of magnetic
materials to include various man-made products, all based, however, on naturally
magnetic elements.

Composites
[edit]

A stack of ferrite magnets

Ceramic, or ferrite, magnets are made of a sintered composite of powdered iron
oxide and barium/strontium carbonate ceramic. Given the low cost of the
materials and manufacturing methods, inexpensive magnets (or non-magnetized
ferromagnetic cores, for use in electronic components such as portable AM radio
antennas) of various shapes can be easily mass-produced. The resulting
magnets are non-corroding but brittle and must be treated like other ceramics.

Alnico magnets are made by casting or sintering a combination

of aluminium, nickel and cobalt with iron and small amounts of other elements
added to enhance the properties of the magnet. Sintering offers superior
mechanical characteristics, whereas casting delivers higher magnetic fields and
allows for the design of intricate shapes. Alnico magnets resist corrosion and
have physical properties more forgiving than ferrite, but not quite as desirable as
a metal. Trade names for alloys in this family include: Alni, Alcomax, Hycomax,
Columax, and Ticonal.[37]

Injection-molded magnets are a composite of various types of resin and magnetic

powders, allowing parts of complex shapes to be manufactured by injection
molding. The physical and magnetic properties of the product depend on the raw
materials, but are generally lower in magnetic strength and resemble plastics in
their physical properties.

Flexible magnet
[edit]
Flexible magnets are composed of a high-coercivity ferromagnetic compound
(usually ferric oxide) mixed with a resinous polymer binder.[38] This is extruded as
a sheet and passed over a line of powerful cylindrical permanent magnets. These
magnets are arranged in a stack with alternating magnetic poles facing up (N, S,
N, S...) on a rotating shaft. This impresses the plastic sheet with the magnetic
poles in an alternating line format. No electromagnetism is used to generate the
magnets. The pole-to-pole distance is on the order of 5 mm, but varies with
manufacturer. These magnets are lower in magnetic strength but can be very
flexible, depending on the binder used.[39]

For magnetic compounds (e.g. Nd2Fe14B) that are vulnerable to a grain

boundary corrosion problem it gives additional protection.[38]

Rare-earth magnets
[edit]
 Ovoid-shaped magnets (possibly hematine), one
hanging from another
Main article: Rare-earth magnet
Rare earth (lanthanoid) elements have a partially occupied f electron shell (which
can accommodate up to 14 electrons). The spin of these electrons can be
aligned, resulting in very strong magnetic fields, and therefore, these elements
are used in compact high-strength magnets where their higher price is not a
concern. The most common types of rare-earth magnets are samarium–
cobalt and neodymium–iron–boron (NIB) magnets.

Single-molecule magnets (SMMs) and single-chain

magnets (SCMs)
[edit]
Main article: Single-molecule magnet
In the 1990s, it was discovered that certain molecules containing paramagnetic
metal ions are capable of storing a magnetic moment at very low temperatures.
These are very different from conventional magnets that store information at a
magnetic domain level and theoretically could provide a far denser storage
medium than conventional magnets. In this direction, research on monolayers of
SMMs is currently under way. Very briefly, the two main attributes of an SMM
are:

1. a large ground state spin value (S), which is provided by

ferromagnetic or ferrimagnetic coupling between the paramagnetic
metal centres
2. a negative value of the anisotropy of the zero field splitting (D)
Most SMMs contain manganese but can also be found with vanadium, iron,
nickel and cobalt clusters. More recently, it has been found that some chain
systems can also display a magnetization that persists for long times at higher
temperatures. These systems have been called single-chain magnets.

Nano-structured magnets
[edit]
Some nano-structured materials exhibit energy waves, called magnons, that
coalesce into a common ground state in the manner of a Bose–Einstein
condensate.[40][41]

Rare-earth-free permanent magnets

[edit]
The United States Department of Energy has identified a need to find substitutes
for rare-earth metals in permanent-magnet technology, and has begun funding
such research. The Advanced Research Projects Agency-Energy (ARPA-E) has
sponsored a Rare Earth Alternatives in Critical Technologies (REACT) program
to develop alternative materials. In 2011, ARPA-E awarded 31.6 million dollars to
fund Rare-Earth Substitute projects.[42] Iron nitrides are promising materials for
rare-earth free magnets.[43]

Costs
[edit]
The current cheapest permanent magnets, allowing for field strengths, are
flexible and ceramic magnets, but these are also among the weakest types. The
ferrite magnets are mainly low-cost magnets since they are made from cheap
raw materials: iron oxide and Ba- or Sr-carbonate. However, a new low cost
magnet, Mn–Al alloy,[38][non-primary source needed][44][45] has been developed and is now
dominating the low-cost magnets field.[citation needed] It has a higher saturation
magnetization than the ferrite magnets. It also has more favorable temperature
coefficients, although it can be thermally unstable. Neodymium–iron–boron
(NIB) magnets are among the strongest. These cost more per kilogram than
most other magnetic materials but, owing to their intense field, are smaller and
cheaper in many applications.[46]

Temperature
[edit]
Temperature sensitivity varies, but when a magnet is heated to a temperature
known as the Curie point, it loses all of its magnetism, even after cooling below
that temperature. The magnets can often be remagnetized, however.

Additionally, some magnets are brittle and can fracture at high temperatures.

The maximum usable temperature is highest for alnico magnets at over 540 °C
(1,000 °F), around 300 °C (570 °F) for ferrite and SmCo, about 140 °C (280 °F)
for NIB and lower for flexible ceramics, but the exact numbers depend on the
grade of material.

Electromagnets
[edit]
Main article: Electromagnet
An electromagnet, in its simplest form, is a wire that has been coiled into one or
more loops, known as a solenoid. When electric current flows through the wire, a
magnetic field is generated. It is concentrated near (and especially inside) the
coil, and its field lines are very similar to those of a magnet. The orientation of
this effective magnet is determined by the right hand rule. The magnetic moment
and the magnetic field of the electromagnet are proportional to the number of
loops of wire, to the cross-section of each loop, and to the current passing
through the wire.[47]

If the coil of wire is wrapped around a material with no special magnetic

properties (e.g., cardboard), it will tend to generate a very weak field. However, if
it is wrapped around a soft ferromagnetic material, such as an iron nail, then the
net field produced can result in a several hundred- to thousandfold increase of
field strength.

Uses for electromagnets include particle accelerators, electric motors, junkyard

cranes, and magnetic resonance imaging machines. Some applications involve
configurations more than a simple magnetic dipole; for
example, quadrupole and sextupole magnets are used to focus particle beams.

Units and calculations

[edit]
Main article: Magnetostatics
For most engineering applications, MKS (rationalized) or SI (Système
International) units are commonly used. Two other sets of
units, Gaussian and CGS-EMU, are the same for magnetic properties and are
commonly used in physics.[citation needed]

In all units, it is convenient to employ two types of magnetic field, B and H, as

well as the magnetization M, defined as the magnetic moment per unit volume.

1. The magnetic induction field B is given in SI units of teslas (T). B is

the magnetic field whose time variation produces, by Faraday's
Law, circulating electric fields (which the power companies
sell). B also produces a deflection force on moving charged
particles (as in TV tubes). The tesla is equivalent to the magnetic
flux (in webers) per unit area (in meters squared), thus giving B the
unit of a flux density. In CGS, the unit of B is the gauss (G). One
tesla equals 104 G.
2. The magnetic field H is given in SI units of ampere-turns per meter
(A-turn/m). The turns appear because when H is produced by a
current-carrying wire, its value is proportional to the number of
turns of that wire. In CGS, the unit of H is the oersted (Oe). One A-
turn/m equals 4π×10−3 Oe.
3. The magnetization M is given in SI units of amperes per meter
(A/m). In CGS, the unit of M is the oersted (Oe). One A/m equals
10−3 emu/cm3. A good permanent magnet can have a magnetization
as large as a million amperes per meter.
4. In SI units, the relation B = μ0(H + M) holds, where μ0 is the
permeability of space, which equals 4π×10−7 T•m/A. In CGS, it is
written as B = H + 4πM. (The pole approach gives μ0H in SI units.
A μ0M term in SI must then supplement this μ0H to give the correct
 field within B, the magnet. It will agree with the field B calculated
using Ampèrian currents).
Materials that are not permanent magnets usually satisfy the relation M = χH in
SI, where χ is the (dimensionless) magnetic susceptibility. Most non-magnetic
materials have a relatively small χ (on the order of a millionth), but soft magnets
can have χ on the order of hundreds or thousands. For materials
satisfying M = χH, we can also write B = μ0(1 + χ)H = μ0μrH = μH, where μr =
1 + χ is the (dimensionless) relative permeability and μ =μ0μr is the magnetic
permeability. Both hard and soft magnets have a more complex, history-
dependent, behavior described by what are called hysteresis loops, which give
either B vs. H or M vs. H. In CGS, M = χH, but χSI = 4πχCGS, and μ = μr.

Caution: in part because there are not enough Roman and Greek symbols, there
is no commonly agreed-upon symbol for magnetic pole strength and magnetic
moment. The symbol m has been used for both pole strength (unit A•m, where
here the upright m is for meter) and for magnetic moment (unit A•m2). The
symbol μ has been used in some texts for magnetic permeability and in other
texts for magnetic moment. We will use μ for magnetic permeability and m for
magnetic moment. For pole strength, we will employ qm. For a bar magnet of
cross-section A with uniform magnetization M along its axis, the pole strength is
given by qm = MA, so that M can be thought of as a pole strength per unit area.

Fields of a magnet
[edit]

Field lines of cylindrical magnets with various

aspect ratios
Far away from a magnet, the magnetic field created by that magnet is almost
always described (to a good approximation) by a dipole field characterized by its
total magnetic moment. This is true regardless of the shape of the magnet, so
long as the magnetic moment is non-zero. One characteristic of a dipole field is
that the strength of the field falls off inversely with the cube of the distance from
the magnet's center.

Closer to the magnet, the magnetic field becomes more complicated and more
dependent on the detailed shape and magnetization of the magnet. Formally, the
field can be expressed as a multipole expansion: A dipole field, plus
a quadrupole field, plus an octupole field, etc.
At close range, many different fields are possible. For example, for a long, skinny
bar magnet with its north pole at one end and south pole at the other, the
magnetic field near either end falls off inversely with the square of the
distance from that pole.

Calculating the magnetic force

[edit]
Main article: Force between magnets
Pull force of a single magnet
[edit]
The strength of a given magnet is sometimes given in terms of its pull force — its
ability to pull ferromagnetic objects.[48] The pull force exerted by either an
electromagnet or a permanent magnet with no air gap (i.e., the ferromagnetic
object is in direct contact with the pole of the magnet[49]) is given by the Maxwell
equation:[50]

,
where:

 F is force (SI unit: newton)

 A is the cross section of the area of the pole (in square meters)
 B is the magnetic induction exerted by the magnet.
This result can be easily derived using Gilbert model, which assumes that the
pole of magnet is charged with magnetic monopoles that induces the same in
the ferromagnetic object.

If a magnet is acting vertically, it can lift a mass m in kilograms given by the

simple equation:

where g is the gravitational acceleration.

Force between two magnetic poles

[edit]
Further information: Magnetic moment § Forces between two magnetic
dipoles
Classically, the force between two magnetic poles is given by:[51]

where

F is force (SI unit: newton)

qm1 and qm2 are the magnitudes of magnetic poles (SI unit: ampere-meter)
μ is the permeability of the intervening medium (SI
unit: tesla meter per ampere, henry per meter or newton per ampere squared)
r is the separation (SI unit: meter).
The pole description is useful to the engineers
designing real-world magnets, but real magnets have a
pole distribution more complex than a single north and
 south. Therefore, implementation of the pole idea is not
simple. In some cases, one of the more complex
formulae given below will be more useful.

Force between two nearby magnetized

surfaces of area A
[edit]
The mechanical force between two nearby magnetized
surfaces can be calculated with the following equation.
The equation is valid only for cases in which the effect
of fringing is negligible and the volume of the air gap is
much smaller than that of the magnetized material:[52][53]

where:

A is the area of each surface, in m2

H is their magnetizing field, in A/m
μ0 is the permeability of space, which equals 4π×10−7 T•m/A
B is the flux density, in T.
Force between two bar
magnets
[edit]
The force between two identical
cylindrical bar magnets placed end to
end at large distance is
approximately:[dubious – discuss],[52]

where:

B0 is the magnetic flux density very close to each pole, in T,

A is the area of each pole, in m2,
L is the length of each magnet, in m,
R is the radius of each magnet, in m, and
z is the separation between the two magnets, in m.
relates the flux density at the pole to the magnetization of the magnet.
Note that all
these
formulations
are based
on Gilbert's
model,
which is
usable in
relatively
great
distances.
In other
models
(e.g.,
Ampère's
model), a
more
complicated
formulation
is used that
sometimes
cannot be
solved
analytically.
In these
cases, num
erical
methods mu
st be used.

Force
between
two
cylindrica
l magnets
[edit]
For two
cylindrical
magnets
with
radius and
length , with
their
magnetic
dipole
aligned, the
force can be
asymptotical
ly
approximate
d at large
distance by
,[54]

where is
the
magneti
zation of
the
magnets
and is
the gap
between
the
magnets
.A
measure
ment of
the
magneti
c flux
density
very
close to
the
magnet
is
related
to appro
ximately
by the
formula

The
effec
tive
mag
netic
dipol
e
can
be
writte
n as

W
h
e
r
e
i
s
t
h
e
v
ol
u
m
e
o
f
t
h
e
m
a
g
n
e
t.
F
o
r
a
c
yl
in
d
e
r,
t
hi
s
is
.

W
h
e
n
,
t
h
e
p
oi
n
t
di
p
ol
e
a
p
p
r
o
xi
m
a
ti
o
n
is
o
b
t
ai
n
e
d
,

w
hi
c
h
m
at
c
h
e
s
th
e
e
x
pr
e
s
si
o
n
of
th
e
fo
rc
e
b
et
w
e
e
n
t
w
o
m
a
g
n
et
ic
di
p
ol
e
s.

S
e
e
a
l
s
o
[e
di
t]

 Dipol
e
magn
et
 Earn
shaw'
s
theor
em
 Electr
et
 Electr
omag
netic
field
 Electr
omag
netis
m
 Halb
ach
array
 Magn
etic
nano
 partic
les
 Magn
etic
switc
h
 Magn
eto
 Magn
etoch
emist
ry
 Mole
cule-
base
d
magn
ets
 Singl
e-
mole
cule
magn
et
 Supe
rmag
net
N
o
t
e
s
[e
di
t]

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03-17.
Retrieved
2010-03-
09.
54. ^ David
Vokoun;
Marco
Beleggia;
Ludek
Heller;
Petr
Sittner
(2009). "
Magnetos
tatic
interactio
ns and
forces
between
cylindrical
permane
nt
magnets"
. Journal
of
Magnetis
m and
Magnetic
Materials.
321 (22):
3758–
3763. Bib
code:200
9JMMM..
321.3758
V. doi:10.
1016/
j.jmmm.2
009.07.03
0.

R
e
f
e
r
e
n
c
e
s
[e
di
t]

 "The
Early
Histor
y of
the
Perm
anent
Magn
et".
Edwa
rd
Nevill
e Da
Costa
Andra
de,
Ende
avour,
Volu
me
17,
Numb
er 65,
Janua
ry
1958.
Conta
ins an
excell
ent
descri
ption
of
early
metho
ds of
produ
 cing
perm
anent
magn
ets.
 "positi
ve
pole
n". Th
e
Conci
se Ox
ford
Englis
h
Dictio
nary.
Cathe
rine
Soan
es
and
Angu
s
Steve
nson.
Oxfor
d
Unive
rsity
Press
,
2004.
Oxfor
d
Refer
ence
Onlin
e.
Oxfor
d
Unive
rsity
Press
.
 Wayn
e M.
Saslo
w, Ele
ctricit
y,
Magn
etism,
and
Light,
Acad
emic
(2002
). ISB
N 0-
12-
61945
5-6.
Chapt
er 9
discu
sses
magn
ets
and
their
magn
etic
fields
using
the
conce
pt of
magn
etic
poles,
but it
also
gives
evide
nce
that
magn
etic
poles
do not
really
exist
in
ordina
ry
matte
r.
Chapt
ers 10
and
11,
followi
ng
what
appea
rs to
be a
19th-
 centur
y
appro
ach,
use
the
pole
conce
pt to
obtain
the
laws
descri
bing
the
magn
etism
of
electri
c
curre
nts.
 Edwa
rd P.
Furla
ni, Pe
rman
ent
Magn
et
and
Electr
omec
hanic
al
Devic
es:M
ateria
ls,
Analy
sis
and
Applic
ations
, Aca
demic
Press
Serie
s in
Electr
omag
netis
m
(2001
). ISB
 N 0-
12-
26995
1-3.

E
x
t
e
r
n
a
l
l
i
n
k
s
[e
di
t]

Look
up
mag
net i
n
Wikti
onar
y,
the
free
dicti
onar
y.

Wiki
medi
a
Com
mon
s
has
medi
a
relat
ed
to M
agn
et.

 How
magn
ets
are
made
Archi
ved 2
013-
03-16
at
the
Wayb
ack
Mach
ine (v
ideo)
 Floati
ng
Ring
Magn
ets,
Bullet
in of
the
IAPT,
Volu
me 4,
No.
6,
145
(June
2012)
.
(Publi
catio
n of
the In
dian
 Asso
ciatio
n of
Physi
cs
Teac
hers).
 A
brief
histor
y of
electr
icity
and
magn
etism
show

Magnetism

show

Electric machines

 Germany
 United States
 France
y control databases: National  BnF data
 Japan
 Czech Republic
 Israel
C
at
e
g
or
ie
s:
 T
y
p
 e
s
of
m
a
g
n
et
s
 M
a
g
n
et
is
m
 M
et
al
lic
o
bj
e
ct
s
 Th
is
pa
ge
wa
s
las
t
ed
ite
d
on
26
M
ar
ch
20
25
,
at
19
:5
5(
U
T
C)
.
 Te
xt
is
av
ail
ab
le
un
de
r
th
e
Cr
ea
tiv
e
Co
m
m
on
s
Att
rib
uti
on
-
Sh
ar
eA
lik
e
4.
0
Lic
en
se
;
ad
diti
on
al
ter
m
s
m
ay
ap
ply
.
By
usi
ng
thi
s
sit
e,
yo
u
ag
re
e
to
th
e
Te
rm
s
of
Us
e
 an
d
Pri
va
cy
Po
lic
y.
Wi
kip
ed
ia
®
is
a
re
gis
ter
ed
tra
de
m
ar
k
of
th
e
Wi
ki
m
ed
ia
Fo
un
da
tio
n,
In
c.,
a
no
n-
pr
ofi
t
or
ga
niz
ati
on
.
 Pri

va

cy

po

lic

 Ab

ou
 t

Wi

kip

ed

ia

 Di

scl

ai

er

 Co

nt

ac

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kip

ed

ia

 Co

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uc

 De

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 St

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cs

 Co

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 M

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vie

S
e
a
r
c
h
Ma
gne
t
13
0
la
ng
ua
ge
s
A
d
d
t
o
p
ic