This article is about objects and devices that produce magnetic fields. For a description of magnetic materials, seeMagnetism. For other uses, seeMagnet (disambiguation).
Amagnet is a material or object that produces amagnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on otherferromagnetic materials, such asiron,steel,nickel,cobalt, etc. and attracts or repels other magnets.
Apermanent magnet is an object made from a material that ismagnetized and creates its own persistent magnetic field. An everyday example is arefrigerator 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 calledferromagnetic (orferrimagnetic). These include the elements iron, nickel and cobalt and their alloys, some alloys ofrare-earth metals, and some naturally occurring minerals such aslodestone. 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 likeannealed 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 asalnico andferrite that are subjected to special processing in a strong magnetic field during manufacture to align their internalmicrocrystalline structure, making them very hard to demagnetize. To demagnetize a saturated magnet, a certain magnetic field must be applied, and this threshold depends oncoercivity of the respective material. "Hard" materials have high coercivity, whereas "soft" materials have low coercivity. The overall strength of a magnet is measured by itsmagnetic moment or, alternatively, the totalmagnetic flux it produces. The local strength of magnetism in a material is measured by itsmagnetization.
Anelectromagnet is made from a coil of wire that acts as a magnet when anelectric current passes through it but stops being a magnet when the current stops. Often, the coil is wrapped around acore of "soft" ferromagnetic material such asmild steel, which greatly enhances the magnetic field produced by the coil.
Ancient people learned about magnetism fromlodestones (ormagnetite) which are naturally magnetized pieces of iron ore. The wordmagnet was adopted inMiddle English fromLatinmagnetum "lodestone", ultimately fromGreekμαγνῆτις [λίθος] (magnētis [lithos])[1] meaning "[stone] fromMagnesia",[2] a place inAnatolia where lodestones were found (todayManisa in modern-dayTurkey). Lodestones, suspended so they could turn, were the firstmagnetic 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 byPliny the Elder in his encyclopediaNaturalis Historia in the 1st century AD.[6]
In 11th century China, it was discovered that quenching red hot iron that was aligned with the Earth's magnetic field would leave the iron permanently magnetized. This led to the development of the navigationalcompass, as described inDream 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, thehorseshoe magnet was invented byDaniel 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 yearAndré-Marie Ampère showed that iron can be magnetized by inserting it in an electrically fed solenoid.[12] This ledWilliam 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]
Themagnetic flux density (also called magneticB field or just magnetic field, usually denoted byB) is avector field. The magneticB fieldvector at a given point in space is specified by two properties:
Itsdirection, which is along the orientation of acompass needle.
Itsmagnitude (also calledstrength), which is proportional to how strongly the compass needle orients along that direction.
InSI units, the strength of the magneticB field is given inteslas.[14]
A magnet's magnetic moment (also called magnetic dipole moment and usually denotedμ) is avector 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. InSI 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 atorque 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 areaA and carryingcurrentI has a magnetic moment of magnitude equal toIA.
The magnetization of a magnetized material is the local value of its magnetic moment per unit volume, usually denotedM, with unitsA/m.[18] It is avector 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.
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, thedivergence of the magnetization ∇·M inside a magnet is treated as a distribution ofmagnetic 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 themagnetic fieldH. Outside the magnet, the fieldB is proportional toH, while inside the magnetization must be added toH. An extension of this method that allows for internal magnetic charges is used in theories of ferromagnetism.
Another model is theAmpère model, where all magnetization is due to the effect of microscopic, or atomic, circularbound 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 ofelectric 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 willnot destroy its magnetic field, but will leave a new surface of uncancelled currents from the circular currents throughout the material.[20] Theright-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]
The north pole of a magnet is defined as the pole that, when the magnet is freely suspended, points towards the Earth'sNorth Magnetic Pole in the Arctic (the magnetic andgeographic poles do not coincide, seemagnetic declination). Since opposite poles (north and south) attract, the North Magnetic Pole is actually thesouth pole of the Earth's magnetic field.[22][23][24][25] As a practical matter, to tell whichpole 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 anelectromagnet, whose poles can be identified by theright-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]
The termmagnet 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 itselectron configuration. Several forms of magnetic behavior have been observed in different materials, including:
Ferromagnetic andferrimagnetic 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 traditionalrefrigerator magnet. Ferrimagnetic materials, which includeferrites and the longest used and naturally occurring magnetic materialsmagnetite andlodestone, are similar to but weaker than ferromagnetics. The difference between ferro- and ferrimagnetic materials is related to their microscopic structure, as explained inMagnetism.
Paramagnetic substances, such asplatinum,aluminum, andoxygen, 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. Magneticferrofluids, 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 ascarbon,copper,water, andplastic, are even more weakly repelled by a magnet. The permeability of diamagnetic materials is less than thepermeability 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 strongsuperconducting magnets, diamagnetic objects such as pieces oflead and even mice[26] can belevitated, so they float in mid-air.Superconductors repel magnetic fields from their interior and are strongly diamagnetic.
The shape of a permanent magnet has a large influence on its magnetic properties. When a magnet ismagnetized, ademagnetizing 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 asphere, 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 longcylinder will yield two different demagnetizing factors, depending on if it's magnetizedparallel to orperpendicular to its length.[16]
Hard disk drives record data on a thin magnetic coatingMagnetic hand separator for heavy minerals
Magnetic recording media:VHS tapes contain a reel ofmagnetic tape. The information that makes up the video and sound is encoded on the magnetic coating on the tape. Commonaudio cassettes also rely on magnetic tape. Similarly, in computers,floppy disks andhard disks record data on a thin magnetic coating.[27]
Credit,debit, andautomatic 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 oftelevisions (non flat screen) and older largecomputer monitors: TV and computer screens containing acathode-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 andmicrophones: 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 abobbin attached to the speakercone and carries the signal as changing current that interacts with the field of the permanent magnet. Thevoice coil feels a magnetic force and in response, moves the cone and pressurizes the neighboring air, thus generatingsound. 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 isinduced across the coil. This voltage drives a current in the wire that is characteristic of the original sound.
Electric guitars use magneticpickups to transduce the vibration of guitar strings into electric current that can then beamplified. 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. TheHammond organ used a similar principle, with rotatingtonewheels instead of strings.
Electric motors andgenerators: 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.
Compasses: A compass (or mariner's compass) is a magnetized pointer free to align itself with a magnetic field, most commonlyEarth'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 intoys. M-tic uses magnetic rods connected to metal spheres forconstruction.
Toys: Given their ability to counteract the force of gravity at close range, magnets are often employed in children's toys, such as theMagnet Space Wheel andLevitron, to amusing effect.
Refrigerator magnets are used to adorn kitchens, as asouvenir, 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, ormaglev, is a form of transportation that suspends, guides and propels vehicles (especially trains) through electromagnetic force. Eliminatingrolling 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 afail-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. TheMagSafe power connection to the Apple MacBook is one such example.
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 (seeElectromagnetic 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 apacemaker has been embedded in a patient's chest (usually for the purpose of monitoring and regulating the heart for steady electrically inducedbeats), 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.
Ferromagnetic materials can be magnetized in the following ways:
Heating the object higher than itsCurie 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]
Magnetized ferromagnetic materials can be demagnetized (or degaussed) in the following ways:
Heating a magnet past itsCurie 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'scoercivity 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, anddegaussing coils used to demagnetizeCRTs.
Some demagnetization or reverse magnetization will occur if any part of the magnet is subjected to a reverse field above the magnetic material'scoercivity.
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.
Many materials have unpaired electron spins, and the majority of these materials areparamagnetic. When the spins interact with each other in such a way that the spins align spontaneously, the materials are calledferromagnetic (what is often loosely termed as magnetic). Because of the way their regularcrystallineatomic structure causes their spins to interact, somemetals are ferromagnetic when found in their natural states, asores. These includeiron ore (magnetite orlodestone),cobalt andnickel, as well as the rare earth metalsgadolinium anddysprosium (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.
Ceramic, orferrite, magnets are made of asinteredcomposite of powdered iron oxide andbarium/strontium carbonateceramic. Given the low cost of the materials and manufacturing methods, inexpensive magnets (or non-magnetized ferromagnetic cores, for use inelectronic components such asportable AM radio antennas) of various shapes can be easily mass-produced. The resulting magnets are non-corroding butbrittle and must be treated like other ceramics.
Alnico magnets are made bycasting orsintering a combination ofaluminium,nickel andcobalt withiron 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, andTiconal.[37]
Injection-molded magnets are acomposite of various types ofresin 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 resembleplastics in their physical properties.
Flexible magnets are composed of a high-coercivityferromagnetic compound (usuallyferric 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 agrain boundary corrosion problem it gives additional protection.[38]
Rare earth (lanthanoid) elements have a partially occupiedfelectron 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 aresamarium–cobalt andneodymium–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.
Advanced Research Projects Agency-Energy (ARPA-E) 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]
In 2026 researchers announced high entropy (5+-element alloys) permanent boride magnets using abundant 3dtransition metals and boron rather thanrare-earth elements. The magnets operate at ambient temperatures and pressures. They adopted a crystal structure with C16tetragonal symmetry. The magnets were formed by combinatorial sputtering.[44]
The current[update] 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][45][46] 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.[47]
Temperature sensitivity varies, but when a magnet is heated to a temperature known as theCurie 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.
An electromagnet, in its simplest form, is a wire that has been coiled into one or more loops, known as asolenoid. 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 theright 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.[48]
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.
For most engineering applications, MKS (rationalized) orSI (Système International) units are commonly used. Two other sets of units,Gaussian andCGS-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 andH, as well as themagnetizationM, defined as the magnetic moment per unit volume.
The magnetic induction fieldB 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 givingB the unit of a flux density. In CGS, the unit ofB is the gauss (G). One tesla equals 104 G.
The magnetic fieldH is given in SI units of ampere-turns per meter (A-turn/m). Theturns appear because whenH is produced by a current-carrying wire, its value is proportional to the number of turns of that wire. In CGS, the unit ofH is the oersted (Oe). One A-turn/m equals 4π×10−3 Oe.
The magnetizationM is given in SI units of amperes per meter (A/m). In CGS, the unit ofM 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 relationB =μ0(H + M) holds, whereμ0 is the permeability of space, which equals 4π×10−7 T•m/A. In CGS, it is written asB =H + 4πM. (The pole approach givesμ0H in SI units. Aμ0M term in SI must then supplement thisμ0H to give the correct field withinB, the magnet. It will agree with the fieldB calculated using Ampèrian currents).
Materials that are not permanent magnets usually satisfy the relationM =χH in SI, whereχ is the (dimensionless) magnetic susceptibility. Most non-magnetic materials have a relatively smallχ (on the order of a millionth), but soft magnets can haveχ on the order of hundreds or thousands. For materials satisfyingM =χH, we can also writeB =μ0(1 + χ)H =μ0μrH =μH, whereμr = 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 calledhysteresis loops, which give eitherB vs.H orM vs.H. In CGS,M =χH, butχSI = 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 symbolm 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 symbolμ has been used in some texts for magnetic permeability and in other texts for magnetic moment. We will useμ for magnetic permeability andm for magnetic moment. For pole strength, we will employqm. For a bar magnet of cross-sectionA with uniform magnetizationM along its axis, the pole strength is given byqm =MA, so thatM can be thought of as a pole strength per unit area.
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 adipole 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 amultipole expansion: A dipole field, plus aquadrupole 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 withthe square of the distance from that pole.
The strength of a given magnet is sometimes given in terms of itspull force — its ability to pullferromagnetic objects.[49] 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[50]) is given by theMaxwell equation:[51]
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 usingGilbert model, which assumes that the pole of magnet is charged withmagnetic monopoles that induces the same in the ferromagnetic object.
If a magnet is acting vertically, it can lift a massm in kilograms given by the simple equation:
qm1 andqm2 are the magnitudes of magnetic poles (SI unit:ampere-meter)
μ is thepermeability of the intervening medium (SI unit:teslameter perampere, 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 areaA
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 offringing is negligible and the volume of the air gap is much smaller than that of the magnetized material:[53][54]
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
The force between two identical cylindrical bar magnets placed end to end at large distance is approximately:[dubious –discuss],[53]
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,numerical methods must be used.
For two cylindrical magnets with radius and length, with their magnetic dipole aligned, the force can be asymptotically approximated at large distance by,[55]
where is the magnetization of the magnets and is the gap between the magnets.A measurement of the magnetic flux density very close to the magnet is related to approximately by the formula
The effective magnetic dipole can be written as
Where is the volume of the magnet. For a cylinder, this is.
When, the point dipole approximation is obtained,
which matches the expression of the force between two magnetic dipoles.
^Müller, Karl-Hartmut; Sawatzki, Simon; Gauß, Roland; Gutfleisch, Oliver (2021), Coey, J. M. D.; Parkin, Stuart S.P. (eds.), "Permanent Magnet Materials and Applications",Handbook of Magnetism and Magnetic Materials, Cham: Springer International Publishing, p. 1391,doi:10.1007/978-3-030-63210-6_29,ISBN978-3-030-63210-6,S2CID244736617{{citation}}: CS1 maint: work parameter with ISBN (link)
^Delaunay, Jean (2008).Ampère, André-Marie. Vol. 1. Charles Scribner's Sons. pp. 142–149.{{cite book}}:|work= ignored (help)
^abNave, Carl R. (2010)."Bar Magnet".Hyperphysics. Dept. of Physics and Astronomy, Georgia State Univ.Archived from the original on 2011-04-08. Retrieved2011-04-10.
"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.
Wayne M. Saslow,Electricity, Magnetism, and Light, Academic (2002).ISBN0-12-619455-6. 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).ISBN0-12-269951-3.
