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A magnet is a material or object that produces a
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
. 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 Iron () is a chemical element with symbol Fe (from la, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, right in ...
,
steel Steel is an alloy made up of iron with added carbon to improve its strength and fracture resistance compared to other forms of iron. Many other elements may be present or added. Stainless steels that are corrosion- and oxidation-resistan ...
,
nickel Nickel is a chemical element with symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel is a hard and ductile transition metal. Pure nickel is chemically reactive but large pieces are slow t ...
,
cobalt Cobalt is a chemical element with the symbol Co and atomic number 27. As with nickel, cobalt is found in the Earth's crust only in a chemically combined form, save for small deposits found in alloys of natural meteoric iron. The free element, p ...
, 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 Iron () is a chemical element with symbol Fe (from la, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, right in ...
,
nickel Nickel is a chemical element with symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel is a hard and ductile transition metal. Pure nickel is chemically reactive but large pieces are slow t ...
and
cobalt Cobalt is a chemical element with the symbol Co and atomic number 27. As with nickel, cobalt is found in the Earth's crust only in a chemically combined form, save for small deposits found in alloys of natural meteoric iron. The free element, p ...
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 Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomena in other entities. Electric currents and the magnetic moments of elementary particles ...
. Ferromagnetic materials can be divided into magnetically "soft" materials like annealed
iron Iron () is a chemical element with symbol Fe (from la, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, right in ...
, 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 A microcrystalline material is a crystallized substance or rock that contains small crystals visible only through microscopic examination. There is little agreement on the range of crystal sizes that should be regarded as microcrystalline, but the ...
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 In electromagnetism, the magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include loops of electric current (such as electroma ...
or, alternatively, the total
magnetic flux In physics, specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B over that surface. It is usually denoted or . The SI unit of magnetic flux is the weber ...
it produces. The local strength of magnetism in a material is measured by its
magnetization In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Movement within this field is described by direction and is either Axial or D ...
. An
electromagnet An electromagnet is a type of magnet in which the magnetic field is produced by an electric current. Electromagnets usually consist of wire wound into a coil. A current through the wire creates a magnetic field which is concentrated in ...
is made from a coil of wire that acts as a magnet when an
electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The movi ...
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 Carbon steel is a steel with carbon content from about 0.05 up to 2.1 percent by weight. The definition of carbon steel from the American Iron and Steel Institute (AISI) states: * no minimum content is specified or required for chromium, cobal ...
, which greatly enhances the magnetic field produced by the coil.


Discovery and development

Ancient people learned about magnetism from lodestones (or
magnetite Magnetite is a mineral and one of the main iron ores, with the chemical formula Fe2+Fe3+2O4. It is one of the oxides of iron, and is ferrimagnetic; it is attracted to a magnet and can be magnetized to become a permanent magnet itself. With ...
) which are naturally magnetized pieces of iron ore. The word ''
magnet 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, nicke ...
'' was adopted in
Middle English Middle English (abbreviated to ME) is a form of the English language that was spoken after the Norman conquest of 1066, until the late 15th century. The English language underwent distinct variations and developments following the Old Englis ...
from
Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through ...
''magnetum'' " lodestone", ultimately from Greek (''magnētis ithos') meaning " tonefrom Magnesia", a place in
Anatolia Anatolia, tr, Anadolu Yarımadası), and the Anatolian plateau, also known as Asia Minor, is a large peninsula in Western Asia and the westernmost protrusion of the Asian continent. It constitutes the major part of modern-day Turkey. The re ...
where lodestones were found (today Manisa in modern-day
Turkey Turkey ( tr, Türkiye ), officially the Republic of Türkiye ( tr, Türkiye Cumhuriyeti, links=no ), is a transcontinental country located mainly on the Anatolian Peninsula in Western Asia, with a small portion on the Balkan Peninsula ...
). 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 2500 years ago. The properties of lodestones and their affinity for iron were written of by
Pliny the Elder Gaius Plinius Secundus (AD 23/2479), called Pliny the Elder (), was a Roman author, naturalist and natural philosopher, and naval and army commander of the early Roman Empire, and a friend of the emperor Vespasian. He wrote the encyclopedic ' ...
in his encyclopedia '' Naturalis Historia''. By the 12th to 13th centuries AD, magnetic
compass A compass is a device that shows the cardinal directions used for navigation and geographic orientation. It commonly consists of a magnetized needle or other element, such as a compass card or compass rose, which can pivot to align itself with ...
es were used in navigation in China, Europe, the Arabian Peninsula and elsewhere.


Physics


Magnetic field

The magnetic flux density (also called magnetic B field or just magnetic field, usually denoted B) is a vector field. The magnetic B field vector at a given point in space is specified by two properties: # Its ''direction'', which is along the orientation of a
compass needle A compass is a device that shows the cardinal directions used for navigation and geographic orientation. It commonly consists of a magnetized needle or other element, such as a compass card or compass rose, which can pivot to align itself with ...
. # 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.


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, 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 In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment of force (also abbreviated to moment). It represents the capability of a force to produce change in the rotational motion of th ...
tending to orient the magnetic moment parallel to the field. 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. 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

The magnetization of a magnetized material is the local value of its magnetic moment per unit volume, usually denoted M, with units A/ m. 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

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. In this approach, the
divergence In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's source at each point. More technically, the divergence represents the volume density of ...
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 A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
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 An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The movi ...
flowing around the surface, with local flow direction normal to the cylinder axis. 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. The right-hand rule tells which direction positively-charged current flows. However, current due to negatively-charged electricity is far more prevalent in practice.


Polarity

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. 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 An electromagnet is a type of magnet in which the magnetic field is produced by an electric current. Electromagnets usually consist of wire wound into a coil. A current through the wire creates a magnetic field which is concentrated in ...
, 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.


Magnetic materials

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 In atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule (or other physical structure) in atomic or molecular orbitals. For example, the electron configuration of the neon ato ...
. 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 oldest magnetic materials
magnetite Magnetite is a mineral and one of the main iron ores, with the chemical formula Fe2+Fe3+2O4. It is one of the oxides of iron, and is ferrimagnetic; it is attracted to a magnet and can be magnetized to become a permanent magnet itself. With ...
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 Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomena in other entities. Electric currents and the magnetic moments of elementary particles ...
. * Paramagnetic substances, such as
platinum Platinum is a chemical element with the symbol Pt and atomic number 78. It is a dense, malleable, ductile, highly unreactive, precious, silverish-white transition metal. Its name originates from Spanish , a diminutive of "silver". Pla ...
,
aluminum Aluminium (aluminum in American and Canadian English) is a chemical element with the symbol Al and atomic number 13. Aluminium has a density lower than those of other common metals, at approximately one third that of steel. It ha ...
, and
oxygen Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements ...
, 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 Carbon () is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent—its atom making four electrons available to form covalent chemical bonds. It belongs to group 14 of the periodic table. Carbon ma ...
,
copper Copper is a chemical element with the symbol Cu (from la, cuprum) and atomic number 29. It is a soft, malleable, and ductile metal with very high thermal and electrical conductivity. A freshly exposed surface of pure copper has a pink ...
,
water Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as ...
, and
plastic Plastics are a wide range of synthetic or semi-synthetic materials that use polymers as a main ingredient. Their plasticity makes it possible for plastics to be moulded, extruded or pressed into solid objects of various shapes. This adapta ...
, 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 magnet A superconducting magnet is an electromagnet made from coils of superconducting wire. They must be cooled to cryogenic temperatures during operation. In its superconducting state the wire has no electrical resistance and therefore can conduct much ...
s, diamagnetic objects such as pieces of
lead Lead is a chemical element with the symbol Pb (from the Latin ) and atomic number 82. It is a heavy metal that is denser than most common materials. Lead is soft and malleable, and also has a relatively low melting point. When freshly cut, ...
and even mice 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 Superparamagnetism is a form of magnetism which appears in small ferromagnetic or ferrimagnetic nanoparticles. In sufficiently small nanoparticles, magnetization can randomly flip direction under the influence of temperature. The typical time be ...
, superdiamagnetism, and metamagnetism.


Common uses

* Magnetic recording media: VHS tapes contain a reel of
magnetic tape Magnetic tape is a medium for magnetic storage made of a thin, magnetizable coating on a long, narrow strip of plastic film. It was developed in Germany in 1928, based on the earlier magnetic wire recording from Denmark. Devices that use magnet ...
. The information that makes up the video and sound is encoded on the magnetic coating on the tape. Common
audio cassettes The Compact Cassette or Musicassette (MC), also commonly called the tape cassette, cassette tape, audio cassette, or simply tape or cassette, is an analog magnetic tape recording format for audio recording and playback. Invented by Lou Otten ...
also rely on magnetic tape. Similarly, in computers,
floppy disk A floppy disk or floppy diskette (casually referred to as a floppy, or a diskette) is an obsolescent type of disk storage composed of a thin and flexible disk of a magnetic storage medium in a square or nearly square plastic enclosure lined ...
s and
hard disk A hard disk drive (HDD), hard disk, hard drive, or fixed disk is an electro-mechanical data storage device that stores and retrieves digital data using magnetic storage with one or more rigid rapidly rotating platters coated with magn ...
s record data on a thin magnetic coating. * Credit,
debit Debits and credits in double-entry bookkeeping are entries made in account ledgers to record changes in value resulting from business transactions. A debit entry in an account represents a transfer of value ''to'' that account, and a credit e ...
, and
automatic teller machine An automated teller machine (ATM) or cash machine (in British English) is an electronic telecommunications device that enables customers of financial institutions to perform financial transactions, such as cash withdrawals, deposits, f ...
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). * Older types of
television Television, sometimes shortened to TV, is a telecommunication medium for transmitting moving images and sound. The term can refer to a television set, or the medium of television transmission. Television is a mass medium for advertising, ...
s (non flat screen) and older large
computer monitor A computer monitor is an output device that displays information in pictorial or textual form. A discrete monitor comprises a visual display, support electronics, power supply, housing, electrical connectors, and external user controls. The ...
s: TV and computer screens containing a
cathode ray tube A cathode-ray tube (CRT) is a vacuum tube containing one or more electron guns, which emit electron beams that are manipulated to display images on a phosphorescent screen. The images may represent electrical waveforms ( oscilloscope), ...
employ an electromagnet to guide electrons to the screen. * Speakers and
microphone A microphone, colloquially called a mic or mike (), is a transducer that converts sound into an electrical signal. Microphones are used in many applications such as telephones, hearing aids, public address systems for concert halls and publ ...
s: 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 A bobbin or spool is a spindle or cylinder, with or without flanges, on which yarn, thread, wire, tape or film is wound. Bobbins are typically found in industrial textile machinery, as well as in sewing machines, fishing reels, tape measu ...
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 In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by ...
. 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 The Hammond organ is an electric organ invented by Laurens Hammond and John M. Hanert and first manufactured in 1935. Multiple models have been produced, most of which use sliding drawbars to vary sounds. Until 1975, Hammond organs generated ...
used a similar principle, with rotating tonewheels instead of strings. *
Electric motor An electric motor is an electrical machine that converts electrical energy into mechanical energy. Most electric motors operate through the interaction between the motor's magnetic field and electric current in a wire winding to generate f ...
s 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 Medicine is the science and practice of caring for a patient, managing the diagnosis, prognosis, prevention, treatment, palliation of their injury or disease, and promoting their health. Medicine encompasses a variety of health care pr ...
: Hospitals use
magnetic resonance imaging Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology to form pictures of the anatomy and the physiological processes of the body. MRI scanners use strong magnetic fields, magnetic field gradients, and radio wave ...
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 Metalworking is the process of shaping and reshaping metals to create useful objects, parts, assemblies, and large scale structures. As a term it covers a wide and diverse range of processes, skills, and tools for producing objects on every scale ...
field to hold objects. Magnets are also used in other types of fastening devices, such as the
magnetic base A magnetic switchable device (often called a magnetic base) is a magnetic fixture that uses one or more permanent magnets in a configuration that allows the external field to be turned on or off. They are used in many applications including op ...
, the magnetic clamp and the refrigerator magnet. *
Compass A compass is a device that shows the cardinal directions used for navigation and geographic orientation. It commonly consists of a magnetized needle or other element, such as a compass card or compass rose, which can pivot to align itself with ...
es: A compass (or mariner's compass) is a magnetized pointer free to align itself with a magnetic field, most commonly
Earth's magnetic field Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from Earth's interior out into space, where it interacts with the solar wind, a stream of charged particles emanating from the Sun. The magneti ...
. * 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 project A science project is an educational activity for students involving experiments or construction of models in one of the science disciplines. Students may present their science project at a science fair, so they may also call it a science fair ...
s: Many topic questions are based on magnets, including the repulsion of current-carrying wires, the effect of temperature, and motors involving magnets. * 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 The Whee-lo or Magnet Space Wheel, is a toy that propels a plastic wheel along both sides of a metal track with magnets built into the wheel. As the track is tilted up and down, the wheel rolls the length of the track, top and bottom, and then ...
and Levitron, to amusing effect. * Refrigerator magnets are used to adorn kitchens, as a
souvenir A souvenir (), memento, keepsake, or token of remembrance is an object a person acquires for the memories the owner associates with it. A souvenir can be any object that can be collected or purchased and transported home by the traveler as a m ...
, 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. * Magnetic levitation transport, or maglev, is a form of transportation that suspends, guides and propels vehicles (especially trains) through electromagnetic force. Eliminating
rolling resistance Rolling resistance, sometimes called rolling friction or rolling drag, is the force resisting the motion when a body (such as a ball, tire, or wheel) rolls on a surface. It is mainly caused by non-elastic effects; that is, not all the energy ...
increases efficiency. The maximum recorded speed of a maglev train is . * 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 MagSafe is a series of proprietary magnetically attached power connectors developed by Apple Inc. for Mac laptops. MagSafe was introduced on January 10, 2006, in conjunction with the MacBook Pro, the first Intel-based Mac laptop, at the Mac ...
power connection to the Apple MacBook is one such example.


Medical issues and safety

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. 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. 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

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 Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin ''vibrationem'' ("shaking, brandishing"). The oscillations may be periodic, such as the motion of a pendulum—or random, su ...
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). * 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.


Demagnetizing ferromagnets

Magnetized ferromagnetic materials can be demagnetized (or degaussed) in the following ways: *
Heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is ...
ing a magnet past its Curie temperature; the molecular motion destroys the alignment of the magnetic domains. This always removes all magnetization. * 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 disk A hard disk drive (HDD), hard disk, hard drive, or fixed disk is an electro-mechanical data storage device that stores and retrieves digital data using magnetic storage with one or more rigid rapidly rotating platters coated with magn ...
s, 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


Magnetic metallic elements

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
metal A metal (from ancient Greek, Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electrical resistivity and conductivity, e ...
s are ferromagnetic when found in their natural states, as ores. These include
iron ore Iron ores are rocks and minerals from which metallic iron can be economically extracted. The ores are usually rich in iron oxides and vary in color from dark grey, bright yellow, or deep purple to rusty red. The iron is usually found in the ...
(
magnetite Magnetite is a mineral and one of the main iron ores, with the chemical formula Fe2+Fe3+2O4. It is one of the oxides of iron, and is ferrimagnetic; it is attracted to a magnet and can be magnetized to become a permanent magnet itself. With ...
or lodestone),
cobalt Cobalt is a chemical element with the symbol Co and atomic number 27. As with nickel, cobalt is found in the Earth's crust only in a chemically combined form, save for small deposits found in alloys of natural meteoric iron. The free element, p ...
and
nickel Nickel is a chemical element with symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel is a hard and ductile transition metal. Pure nickel is chemically reactive but large pieces are slow t ...
, as well as the rare earth metals gadolinium and
dysprosium Dysprosium is the chemical element with the symbol Dy and atomic number 66. It is a rare-earth element in the lanthanide series with a metallic silver luster. Dysprosium is never found in nature as a free element, though, like other lanthanide ...
(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

Ceramic, or ferrite, magnets are made of a
sintered Clinker nodules produced by sintering Sintering or frittage is the process of compacting and forming a solid mass of material by pressure or heat without melting it to the point of liquefaction. Sintering happens as part of a manufacturing ...
composite Composite or compositing may refer to: Materials * Composite material, a material that is made from several different substances ** Metal matrix composite, composed of metal and other parts ** Cermet, a composite of ceramic and metallic materials ...
of powdered iron oxide and
barium Barium is a chemical element with the symbol Ba and atomic number 56. It is the fifth element in group 2 and is a soft, silvery alkaline earth metal. Because of its high chemical reactivity, barium is never found in nature as a free element. Th ...
/ strontium carbonate
ceramic A ceramic is any of the various hard, brittle, heat-resistant and corrosion-resistant materials made by shaping and then firing an inorganic, nonmetallic material, such as clay, at a high temperature. Common examples are earthenware, porcelain, ...
. Given the low cost of the materials and manufacturing methods, inexpensive magnets (or non-magnetized ferromagnetic cores, for use in
electronic component An electronic component is any basic discrete device or physical entity in an electronic system used to affect electrons or their associated fields. Electronic components are mostly industrial products, available in a singular form and are no ...
s 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 Casting is a manufacturing process in which a liquid material is usually poured into a mold, which contains a hollow cavity of the desired shape, and then allowed to solidify. The solidified part is also known as a ''casting'', which is ejecte ...
or
sintering Clinker nodules produced by sintering Sintering or frittage is the process of compacting and forming a solid mass of material by pressure or heat without melting it to the point of liquefaction. Sintering happens as part of a manufacturing ...
a combination of
aluminium Aluminium (aluminum in American and Canadian English) is a chemical element with the symbol Al and atomic number 13. Aluminium has a density lower than those of other common metals, at approximately one third that of steel. It ha ...
,
nickel Nickel is a chemical element with symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel is a hard and ductile transition metal. Pure nickel is chemically reactive but large pieces are slow t ...
and
cobalt Cobalt is a chemical element with the symbol Co and atomic number 27. As with nickel, cobalt is found in the Earth's crust only in a chemically combined form, save for small deposits found in alloys of natural meteoric iron. The free element, p ...
with
iron Iron () is a chemical element with symbol Fe (from la, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, right in ...
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''. Injection-molded magnets are a
composite Composite or compositing may refer to: Materials * Composite material, a material that is made from several different substances ** Metal matrix composite, composed of metal and other parts ** Cermet, a composite of ceramic and metallic materials ...
of various types of
resin In polymer chemistry and materials science, resin is a solid or highly viscous substance of plant or synthetic origin that is typically convertible into polymers. Resins are usually mixtures of organic compounds. This article focuses on nat ...
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
plastic Plastics are a wide range of synthetic or semi-synthetic materials that use polymers as a main ingredient. Their plasticity makes it possible for plastics to be moulded, extruded or pressed into solid objects of various shapes. This adapta ...
s in their physical properties.


Flexible magnet

Flexible magnets are composed of a high- coercivity ferromagnetic compound (usually
ferric oxide Iron(III) oxide or ferric oxide is the inorganic compound with the formula Fe2O3. It is one of the three main oxides of iron, the other two being iron(II) oxide (FeO), which is rare; and iron(II,III) oxide (Fe3O4), which also occurs naturall ...
) mixed with a resinous polymer binder. 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. For magnetic compounds (e.g. Nd2 Fe14 B) that are vulnerable to a
grain boundary In materials science, a grain boundary is the interface between two grains, or crystallites, in a polycrystalline material. Grain boundaries are two-dimensional defects in the crystal structure, and tend to decrease the electrical and therma ...
corrosion problem it gives additional protection.


Rare-earth magnets

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)

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: # a large ground state spin value (''S''), which is provided by ferromagnetic or ferrimagnetic coupling between the paramagnetic metal centres # 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

Some nano-structured materials exhibit energy
wave In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (re ...
s, called
magnon A magnon is a quasiparticle, a collective excitation of the electrons' spin structure in a crystal lattice. In the equivalent wave picture of quantum mechanics, a magnon can be viewed as a quantized spin wave. Magnons carry a fixed amount of en ...
s, that coalesce into a common ground state in the manner of a Bose–Einstein condensate.


Rare-earth-free permanent magnets

The
United States Department of Energy The United States Department of Energy (DOE) is an executive department of the U.S. federal government that oversees U.S. national energy policy and manages the research and development of nuclear power and nuclear weapons in the United States ...
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.


Costs

The 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, ''An Overview of MnAl Permanent Magnets with a Study on Their Potential in Electrical Machines''
/ref> has been developed and is now dominating the low-cost magnets field. 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.


Temperature

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 , around for ferrite and SmCo, about for NIB and lower for flexible ceramics, but the exact numbers depend on the grade of material.


Electromagnets

An electromagnet, in its simplest form, is a wire that has been coiled into one or more loops, known as a
solenoid upright=1.20, An illustration of a solenoid upright=1.20, Magnetic field created by a seven-loop solenoid (cross-sectional view) described using field lines A solenoid () is a type of electromagnet formed by a helix, helical coil of wire whose ...
. 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 In mathematics and physics, the right-hand rule is a common mnemonic for understanding orientation of axes in three-dimensional space. It is also a convenient method for quickly finding the direction of a cross-product of 2 vectors. Most of ...
. 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. 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 motor An electric motor is an electrical machine that converts electrical energy into mechanical energy. Most electric motors operate through the interaction between the motor's magnetic field and electric current in a wire winding to generate f ...
s, junkyard cranes, and
magnetic resonance imaging Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology to form pictures of the anatomy and the physiological processes of the body. MRI scanners use strong magnetic fields, magnetic field gradients, and radio wave ...
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

For most engineering applications, MKS (rationalized) or SI (Système International) units are commonly used. Two other sets of units,
Gaussian Carl Friedrich Gauss (1777–1855) is the eponym of all of the topics listed below. There are over 100 topics all named after this German mathematician and scientist, all in the fields of mathematics, physics, and astronomy. The English eponym ...
and CGS-EMU, are the same for magnetic properties and are commonly used in physics. In all units, it is convenient to employ two types of magnetic field, B and H, as well as the
magnetization In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Movement within this field is described by direction and is either Axial or D ...
M, defined as the magnetic moment per unit volume. # 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. # 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. # 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. # In SI units, the relation B = ''μ''0(H + M) holds, where ''μ''0 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 ''μ''0H in SI units. A ''μ''0M term in SI must then supplement this ''μ''0H 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 = ''χ''H 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 = ''χ''H, we can also write B = ''μ''0(1 + ''χ'')H = ''μ''0''μ''rH = ''μ''H, where ''μ''r = 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 = ''χ''H, but ''χ''SI = 4''πχ''CGS, 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 ''q''''m''. 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

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 multipole expansion is a mathematical series representing a function that depends on angles—usually the two angles used in the spherical coordinate system (the polar and azimuthal angles) for three-dimensional Euclidean space, \R^3. Similar ...
: 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


Pull force of a single magnet

The strength of a given magnet is sometimes given in terms of its ''pull force'' — its ability to pull ferromagnetic objects. 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) is given by the
Maxwell equation Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. Th ...
: :F=, 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: :m=, where g is the
gravitational acceleration In physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing drag). This is the steady gain in speed caused exclusively by the force of gravitational attraction. All bodie ...
.


Force between two magnetic poles

Classically, the force between two magnetic poles is given by: :F= where :''F'' is force (SI unit: newton) :''q''''m''1 and ''q''''m''2 are the magnitudes of magnetic poles (SI unit: ampere-meter) :''μ'' is the permeability of the intervening medium (SI unit: tesla meter per
ampere The ampere (, ; symbol: A), often shortened to amp,SI supports only the use of symbols and deprecates the use of abbreviations for units. is the unit of electric current in the International System of Units (SI). One ampere is equal to elect ...
, 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''

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: :F=\frac = \frac where: :''A'' is the area of each surface, in m2 :''H'' is their magnetizing field, in A/m :''μ''0 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

The force between two identical cylindrical bar magnets placed end to end at large distance z\gg R is approximately:, :F \simeq \left frac \right\left + - \right/math> 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. :B_0 \,=\, \fracM 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, numerical methods must be used.


Force between two cylindrical magnets

For two cylindrical magnets with radius R and length L, with their magnetic dipole aligned, the force can be asymptotically approximated at large distance z\gg R by, : F(z) \simeq \frac M^2 R^4 \left frac + \frac - \frac\right where M is the magnetization of the magnets and z is the gap between the magnets. A measurement of the magnetic flux density very close to the magnet B_0 is related to M approximately by the formula : B_0 = \frac M The effective magnetic dipole can be written as : m = M V Where V is the volume of the magnet. For a cylinder, this is V = \pi R^2 L. When z\gg L, the point dipole approximation is obtained, : F(x) = \frac M^2 R^4 L^2\frac = \frac M^2 V^2\frac = \frac m_1 m_2\frac which matches the expression of the force between two magnetic dipoles.


See also

* Dipole magnet * Earnshaw's theorem * Electret *
Electromagnetic field An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical ...
*
Electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions o ...
* Halbach array * Magnetic nanoparticles * Magnetic switch * Magneto *
Magnetochemistry Magnetochemistry is concerned with the magnetic properties of chemical compounds. Magnetic properties arise from the spin and orbital angular momentum of the electrons contained in a compound. Compounds are diamagnetic when they contain no unpair ...
* Molecule-based magnets *
Single-molecule magnet A single-molecule magnet (SMM) is a metal-organic compound that has superparamagnetic behavior below a certain blocking temperature at the molecular scale. In this temperature range, a SMM exhibits magnetic hysteresis of purely molecular origin ...
*
Supermagnet A hard_disk_drive.html"_;"title="Nickel-plated_neodymium_magnet_on_a_bracket_from_a_hard_disk_drive">Nickel-plated_neodymium_magnet_on_a_bracket_from_a_hard_disk_drive_ file:Nd-magnet.jpg.html" ;"title="hard_disk_drive_.html" ;"title="hard_disk_d ...


Notes


References

* "The Early History of the Permanent Magnet". Edward Neville Da Costa Andrade, Endeavour, Volume 17, Number 65, January 1958. Contains an excellent description of early methods of producing permanent magnets. * "positive pole n". ''The Concise
Oxford English Dictionary The ''Oxford English Dictionary'' (''OED'') is the first and foundational historical dictionary of the English language, published by Oxford University Press (OUP). It traces the historical development of the English language, providing a c ...
''. Catherine Soanes and Angus Stevenson.
Oxford University Press Oxford University Press (OUP) is the university press of the University of Oxford. It is the largest university press in the world, and its printing history dates back to the 1480s. Having been officially granted the legal right to print book ...
, 2004. Oxford Reference Online. Oxford University Press. * Wayne M. Saslow, ''Electricity, Magnetism, and Light'', Academic (2002). . Chapter 9 discusses magnets and their magnetic fields using the concept of magnetic poles, but it also gives evidence that magnetic poles do not really exist in ordinary matter. Chapters 10 and 11, following what appears to be a 19th-century approach, use the pole concept to obtain the laws describing the magnetism of electric currents. * Edward P. Furlani, ''Permanent Magnet and Electromechanical Devices:Materials, Analysis and Applications,'' Academic Press Series in Electromagnetism (2001). .


External links


How magnets are made
(video)
Floating Ring Magnets
Bulletin of the IAPT, Volume 4, No. 6, 145 (June 2012). (Publication of the
Indian Association of Physics Teachers The Indian Association of Physics Teachers or IAPT is a body that coordinates the Physics Olympiad for India along with HBCSE. It was established in the year 1984 by D. P. Khandelwal, with active support from some Physics teachers. Its aim was ...
).
A brief history of electricity and magnetism
{{Authority control Types of magnets Magnetism