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69-408: Many generator designs use electric current flowing through windings to produce the magnetic field on which the motor or generator operates. This is in contrast to designs that use permanent magnets to generate this field instead. Such devices may have a minimum working voltage, below which the device does not work correctly, or does so at greatly reduced efficiency. Some will disconnect themselves from

138-471: 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

207-401: A torque 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

276-420: A transgranular fracture . There is an ambiguity with powder grains: a powder grain can be made of several crystallites. Thus, the (powder) "grain size" found by laser granulometry can be different from the "grain size" (rather, crystallite size) found by X-ray diffraction (e.g. Scherrer method), by optical microscopy under polarised light , or by scanning electron microscopy (backscattered electrons). If

345-415: A combination of aluminium , nickel and cobalt with iron and small amounts of other elements added to enhance the properties of the magnet. Sintering offers superior mechanical characteristics, whereas casting delivers higher magnetic fields and allows for the design of intricate shapes. Alnico magnets resist corrosion and have physical properties more forgiving than ferrite, but not quite as desirable as

414-767: A common ground state in the manner of a Bose–Einstein condensate . The United States Department of Energy has identified a need to find substitutes for rare-earth metals in permanent-magnet technology, and has begun funding such research. The Advanced Research Projects Agency-Energy (ARPA-E) has sponsored a Rare Earth Alternatives in Critical Technologies (REACT) program to develop alternative materials. In 2011, ARPA-E awarded 31.6 million dollars to fund Rare-Earth Substitute projects. Iron nitrides are promising materials for rare-earth free magnets. The current cheapest permanent magnets, allowing for field strengths, are flexible and ceramic magnets, but these are also among

483-444: A critical extent, the material could fracture . During grain boundary migration, the rate determining step depends on the angle between two adjacent grains. In a small angle dislocation boundary, the migration rate depends on vacancy diffusion between dislocations. In a high angle dislocation boundary, this depends on the atom transport by single atom jumps from the shrinking to the growing grains. Grain boundaries are generally only

552-416: 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

621-404: A few nanometers wide. In common materials, crystallites are large enough that grain boundaries account for a small fraction of the material. However, very small grain sizes are achievable. In nanocrystalline solids, grain boundaries become a significant volume fraction of the material, with profound effects on such properties as diffusion and plasticity . In the limit of small crystallites, as

690-405: A high enough temperature. This is because grain boundaries are amorphous, and serve as nucleation points for the liquid phase . By contrast, if no solid nucleus is present as a liquid cools, it tends to become supercooled . Since this is undesirable for mechanical materials, alloy designers often take steps against it (by grain refinement ). Material fractures can be either intergranular or

759-427: A high- coercivity ferromagnetic compound (usually ferric oxide ) 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

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828-514: A large number crystallites held together by thin layers of amorphous solid. Most inorganic solids are polycrystalline, including all common metals, many ceramics , rocks, and ice. The areas where crystallites meet are known as grain boundaries . Crystallite size in monodisperse microstructures is usually approximated from X-ray diffraction patterns and grain size by other experimental techniques like transmission electron microscopy. Solid objects large enough to see and handle are rarely composed of

897-571: 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·m and a volume of 1 cm , or 1×10  m , 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

966-492: A metal. Trade names for alloys in this family include: Alni, Alcomax, Hycomax, Columax , and Ticonal . Injection-molded magnets are a composite of various types of resin and magnetic powders, allowing parts of complex shapes to be manufactured by injection molding. The physical and magnetic properties of the product depend on the raw materials, but are generally lower in magnetic strength and resemble plastics in their physical properties. Flexible magnets are composed of

1035-402: 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. The north pole of a magnet

1104-410: 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 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

1173-399: 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. In

1242-551: A permanent magnet has a large influence on its magnetic properties. When a magnet is magnetized , a demagnetizing field will be created inside it. As the name suggests, the demagnetizing field will work to demagnetize the magnet, decreasing its magnetic properties. The strength of the demagnetizing field H d {\displaystyle H_{d}} is proportional to the magnet's magnetization M {\displaystyle M} and shape, according to Here, N d {\displaystyle N_{d}}

1311-410: A similar mean crystallite size. Coarse grained rocks are formed very slowly, while fine grained rocks are formed quickly, on geological time scales. If a rock forms very quickly, such as from the solidification of lava ejected from a volcano , there may be no crystals at all. This is how obsidian forms. Grain boundaries are interfaces where crystals of different orientations meet. A grain boundary

1380-563: A simple magnetic dipole; for example, quadrupole and sextupole magnets are used to focus particle beams . Crystallite A crystallite is a small or even microscopic crystal which forms, for example, during the cooling of many materials. Crystallites are also referred to as grains . Bacillite is a type of crystallite. It is rodlike with parallel longulites . The orientation of crystallites can be random with no preferred direction, called random texture , or directed, possibly due to growth and processing conditions. While

1449-417: A single crystal cut into two parts, one of which is rotated, we see that there are five variables required to define a grain boundary. The first two numbers come from the unit vector that specifies a rotation axis. The third number designates the angle of rotation of the grain. The final two numbers specify the plane of the grain boundary (or a unit vector that is normal to this plane). Grain boundaries disrupt

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1518-833: A single crystal, except for a few cases ( gems , silicon single crystals for the electronics industry, certain types of fiber , single crystals of a nickel -based superalloy for turbojet engines, and some ice crystals which can exceed 0.5 meters in diameter). The crystallite size can vary from a few nanometers to several millimeters. The extent to which a solid is crystalline ( crystallinity ) has important effects on its physical properties. Sulfur , while usually polycrystalline, may also occur in other allotropic forms with completely different properties. Although crystallites are referred to as grains, powder grains are different, as they can be composed of smaller polycrystalline grains themselves. Generally, polycrystals cannot be superheated ; they will melt promptly once they are brought to

1587-400: A strong magnetic field during manufacture to align their internal microcrystalline structure, making them very hard to demagnetize. To demagnetize a saturated magnet, a certain magnetic field must be applied, and this threshold depends on coercivity of the respective material. "Hard" materials have high coercivity, whereas "soft" materials have low coercivity. The overall strength of a magnet

1656-700: A widespread disconnection of generating units. Depending on the application the device may, during and after the dip, be required to: A variety of standards exist and generally vary across jurisdictions. Examples of the such grid codes are the German BDEW grid code and its supplements 2, 3, and 4 as well as the National Grid Code in UK. For wind turbines, the FRT testing is described in the standard IEC 61400-21 (2nd edition August 2008). More detailed testing procedures are stated in

1725-425: Is a single-phase interface, with crystals on each side of the boundary being identical except in orientation. The term "crystallite boundary" is sometimes, though rarely, used. Grain boundary areas contain those atoms that have been perturbed from their original lattice sites, dislocations , and impurities that have migrated to the lower energy grain boundary. Treating a grain boundary geometrically as an interface of

1794-566: Is an object made from a material that is magnetized and creates its own persistent magnetic field. An everyday example is a refrigerator magnet used to hold notes on a refrigerator door. Materials that can be magnetized, which are also the ones that are strongly attracted to a magnet, are called ferromagnetic (or ferrimagnetic ). These include the elements iron , nickel and cobalt and their alloys, some alloys of rare-earth metals , and some naturally occurring minerals such as lodestone . Although ferromagnetic (and ferrimagnetic) materials are

1863-416: Is called the demagnetizing factor, and has a different value depending on the magnet's shape. For example, if the magnet is a sphere , then N d = 1 3 {\displaystyle N_{d}={\frac {1}{3}}} . 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,

1932-443: 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

2001-562: 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

2070-473: Is given by the Hall–Petch relationship . The high interfacial energy and relatively weak bonding in grain boundaries makes them preferred sites for the onset of corrosion and for the precipitation of new phases from the solid. Grain boundary migration plays an important role in many of the mechanisms of creep . Grain boundary migration occurs when a shear stress acts on the grain boundary plane and causes

2139-405: 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 a solenoid . When electric current flows through

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2208-509: Is known, then the pole model gives the magnetic field H . Outside the magnet, the field B is proportional to H , while inside the magnetization must be added to H . An extension of this method that allows for internal magnetic charges is used in theories of ferromagnetism. Another model is the Ampère model, where all magnetization is due to the effect of microscopic, or atomic, circular bound currents , also called Ampèrian currents, throughout

2277-462: Is measured by its magnetic moment or, alternatively, the total magnetic flux it produces. The local strength of magnetism in a material is measured by its magnetization . An electromagnet is made from a coil of wire that acts as a magnet when an electric current passes through it but stops being a magnet when the current stops. Often, the coil is wrapped around a core of "soft" ferromagnetic material such as mild steel , which greatly enhances

2346-464: Is north and which is south, it is not necessary to use the Earth's magnetic field at all. For example, one method would be to compare it to an electromagnet , whose poles can be identified by the right-hand rule . The magnetic field lines of a magnet are considered by convention to emerge from the magnet's north pole and reenter at the south pole. The term magnet is typically reserved for objects that produce their own persistent magnetic field even in

2415-429: Is possible to cause a chain reaction that takes other generators offline as well. This can occur in the event of a voltage dip that causes one of the generators to disconnect from the grid. As voltage dips are often caused by too little generation for the load in a distribution grid, removing generation can cause the voltage to drop further. This may bring the voltage down enough to cause another generator to trip, lower

2484-476: Is specified by two properties: In SI units, the strength of the magnetic B field is given in teslas . 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,

2553-400: 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 . 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

2622-410: 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. Nd 2 Fe 14 B ) that are vulnerable to a grain boundary corrosion problem it gives additional protection. Rare earth ( lanthanoid ) elements have

2691-515: The horseshoe magnet was invented by Daniel Bernoulli in 1743. A horseshoe magnet avoids demagnetization by returning the magnetic field lines to the opposite pole. In 1820, Hans Christian Ørsted discovered that a compass needle is deflected by a nearby electric current. In the same year André-Marie Ampère showed that iron can be magnetized by inserting it in an electrically fed solenoid. This led William Sturgeon to develop an iron-cored electromagnet in 1824. Joseph Henry further developed

2760-429: 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,

2829-575: The Earth's magnetic field would leave the iron permanently magnetized. This led to the development of the navigational compass , as described in Dream Pool Essays in 1088. By the 12th to 13th centuries AD, magnetic compasses were used in navigation in China, Europe, the Arabian Peninsula and elsewhere. A straight iron magnet tends to demagnetize itself by its own magnetic field. To overcome this,

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2898-693: The German guideline FGW TR3 (Rev. 22). Testing of devices with less than 16 Amp rated current is described in the EMC standard IEC 61000-4-11 and for higher current devices in IEC 61000-4-34. Permanent 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 , nickel , cobalt , etc. and attracts or repels other magnets. A permanent magnet

2967-689: The absence of an applied magnetic field. Only certain classes of materials can do this. Most materials, however, produce a magnetic field in response to an applied magnetic field – a phenomenon known as magnetism. There are several types of magnetism, and all materials exhibit at least one of them. The overall magnetic behavior of a material can vary widely, depending on the structure of the material, particularly on its electron configuration . Several forms of magnetic behavior have been observed in different materials, including: There are various other types of magnetism, such as spin glass , superparamagnetism , superdiamagnetism , and metamagnetism . The shape of

3036-660: The availability of magnetic materials to include various man-made products, all based, however, on naturally magnetic elements. Ceramic, or ferrite , magnets are made of a sintered composite of powdered iron oxide and barium / strontium carbonate ceramic . Given the low cost of the materials and manufacturing methods, inexpensive magnets (or non-magnetized ferromagnetic cores, for use in electronic components such as portable AM radio antennas ) of various shapes can be easily mass-produced. The resulting magnets are non-corroding but brittle and must be treated like other ceramics. Alnico magnets are made by casting or sintering

3105-452: The circuit when these conditions apply. The effect is more pronounced in doubly-fed induction generators (DFIG), which have two sets of powered magnetic windings, than in squirrel-cage induction generators which have only one. Synchronous generators may slip and become unstable, if the voltage of the stator winding goes below a certain threshold. In a grid containing many distributed generators subject to disconnection at under voltage, it

3174-421: The crystallites are mostly ordered with a random spread of orientations, one has a mosaic crystal . Abnormal grain growth , where a small number of crystallites are significantly larger than the mean crystallite size, is commonly observed in diverse polycrystalline materials, and results in mechanical and optical properties that diverge from similar materials having a monodisperse crystallite size distribution with

3243-404: The dangers of grain boundaries in certain materials such as superalloy turbine blades, great technological leaps were made to minimize as much as possible the effect of grain boundaries in the blades. The result was directional solidification processing in which grain boundaries were eliminated by producing columnar grain structures aligned parallel to the axis of the blade, since this is usually

3312-461: The demagnetizing factor only has one value. But a magnet that is shaped like a long cylinder will yield two different demagnetizing factors, depending on if it's magnetized parallel to or perpendicular to its length. 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

3381-416: 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). The magnetic flux density (also called magnetic B field or just magnetic field, usually denoted by B ) is a vector field . The magnetic B field vector at a given point in space

3450-451: The first magnetic compasses . The earliest known surviving descriptions of magnets and their properties are from Anatolia, India, and China around 2,500 years ago. The properties of lodestones and their affinity for iron were written of by Pliny the Elder in his encyclopedia Naturalis Historia in the 1st century AD. In 11th century China, it was discovered that quenching red hot iron in

3519-403: The following ways: Magnetized ferromagnetic materials can be demagnetized (or degaussed) in the following ways: 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

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3588-400: The grains to slide. This means that fine-grained materials actually have a poor resistance to creep relative to coarser grains, especially at high temperatures, because smaller grains contain more atoms in grain boundary sites. Grain boundaries also cause deformation in that they are sources and sinks of point defects. Voids in a material tend to gather in a grain boundary, and if this happens to

3657-457: The individual crystallites are oriented completely at random, a large enough volume of polycrystalline material will be approximately isotropic . This property helps the simplifying assumptions of continuum mechanics to apply to real-world solids. However, most manufactured materials have some alignment to their crystallites, resulting in texture that must be taken into account for accurate predictions of their behavior and characteristics. When

3726-601: The magnetic field produced by the coil. Ancient people learned about magnetism from lodestones (or magnetite ) which are naturally magnetized pieces of iron ore. The word magnet was adopted in Middle English from Latin magnetum "lodestone", ultimately from Greek μαγνῆτις [λίθος] ( magnētis [lithos] ) meaning "[stone] from Magnesia", a place in Anatolia where lodestones were found (today Manisa in modern-day Turkey ). Lodestones, suspended so they could turn, were

3795-403: The magnetic moment is specified in terms of A·m (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

3864-437: 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. Ferromagnetic materials can be magnetized in

3933-416: The material. For a uniformly magnetized cylindrical bar magnet, the net effect of the microscopic bound currents is to make the magnet behave as if there is a macroscopic sheet of electric current flowing around the surface, with local flow direction normal to the cylinder axis. Microscopic currents in atoms inside the material are generally canceled by currents in neighboring atoms, so only the surface makes

4002-437: The misalignment between these regions forms boundaries that are key to data storage. The inductive head measures the orientation of the magnetic moments of these domain regions and reads out either a “1” or “0”. These bits are the data being read. Grain size is important in this technology because it limits the number of bits that can fit on one hard disk. The smaller the grain sizes, the more data that can be stored. Because of

4071-472: The motion of dislocations through a material. Dislocation propagation is impeded because of the stress field of the grain boundary defect region and the lack of slip planes and slip directions and overall alignment across the boundaries. Reducing grain size is therefore a common way to improve strength , often without any sacrifice in toughness because the smaller grains create more obstacles per unit area of slip plane. This crystallite size-strength relationship

4140-533: The only ones attracted to a magnet strongly enough to be commonly considered magnetic, all other substances respond weakly to a magnetic field, by one of several other types of magnetism . Ferromagnetic materials can be divided into magnetically "soft" materials like annealed iron , which can be magnetized but do not tend to stay magnetized, and magnetically "hard" materials, which do. Permanent magnets are made from "hard" ferromagnetic materials such as alnico and ferrite that are subjected to special processing in

4209-549: 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 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

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4278-533: The structure of a single crystal is highly ordered and its lattice is continuous and unbroken, amorphous materials, such as glass and many polymers, are non-crystalline and do not display any structures, as their constituents are not arranged in an ordered manner. Polycrystalline structures and paracrystalline phases are in between these two extremes. Polycrystalline materials, or polycrystals, are solids that are composed of many crystallites of varying size and orientation. Most materials are polycrystalline, made of

4347-429: The two main attributes of an SMM are: 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. Some nano-structured materials exhibit energy waves , called magnons , that coalesce into

4416-401: The voltage even further, and may cause a cascading failure . Modern large-scale wind turbines, typically 1 MW and larger, are normally required to include systems that allow them to operate through such an event, and thereby “ride through” the voltage dip. Similar requirements are now becoming common on large solar power installations that likewise might cause instability in the event of

4485-454: The volume fraction of grain boundaries approaches 100%, the material ceases to have any crystalline character, and thus becomes an amorphous solid . Grain boundaries are also present in magnetic domains in magnetic materials. A computer hard disk, for example, is made of a hard ferromagnetic material that contains regions of atoms whose magnetic moments can be realigned by an inductive head. The magnetization varies from region to region, and

4554-459: The way their regular crystalline atomic structure causes their spins to interact, some metals are ferromagnetic when found in their natural states, as ores . These include iron ore ( magnetite or lodestone ), cobalt and nickel , as well as the rare earth metals gadolinium and dysprosium (when at a very low temperature). Such naturally occurring ferromagnets were used in the first experiments with magnetism. Technology has since expanded

4623-473: 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, 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

4692-421: The wire, a magnetic field is generated. It is concentrated near (and especially inside) the coil, and its field lines are very similar to those of a magnet. The orientation of this effective magnet is determined by the right hand rule . The magnetic moment and the magnetic field of the electromagnet are proportional to the number of loops of wire, to the cross-section of each loop, and to the current passing through

4761-540: 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 motors , junkyard cranes, and magnetic resonance imaging machines. Some applications involve configurations more than

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