Магнит

Object that has a magnetic field

Магнетитовый камень притягивается сверху неодимовым магнитом .

Магнит — это материал или объект, создающий магнитное поле . Это магнитное поле невидимо, но отвечает за наиболее заметное свойство магнита: силу, которая притягивает другие ферромагнитные материалы , такие как железо , сталь , никель , кобальт и т. д., и притягивает или отталкивает другие магниты.

Постоянный магнит — это объект, изготовленный из материала, который намагничивается и создает собственное постоянное магнитное поле. Повседневный пример — магнит на холодильнике, который используется для хранения заметок на дверце холодильника. Материалы, которые можно намагничивать, а также сильно притягиваться к магниту, называются ферромагнетиками (или ферримагнетиками ). К ним относятся элементы железо , никель и кобальт и их сплавы, некоторые сплавы редкоземельных металлов и некоторые природные минералы, такие как магнит . Хотя ферромагнитные (и ферримагнитные) материалы — единственные, которые притягиваются к магниту достаточно сильно, чтобы их можно было считать магнитными, все остальные вещества слабо реагируют на магнитное поле одним из нескольких других типов магнетизма .

Ферромагнитные материалы можно разделить на магнитно «мягкие» материалы, такие как отожженное железо , которое может намагничиваться, но не имеет тенденции оставаться намагниченным, и магнитно «твердые» материалы, которые это делают. Постоянные магниты изготавливаются из «твердых» ферромагнитных материалов, таких как алнико и феррит , которые во время производства подвергаются специальной обработке в сильном магнитном поле для выравнивания их внутренней микрокристаллической структуры, что делает их очень трудно размагничивать. Чтобы размагнитить насыщенный магнит, необходимо приложить определенное магнитное поле, и этот порог зависит от коэрцитивной силы соответствующего материала. «Твердые» материалы обладают высокой коэрцитивной силой, тогда как «мягкие» материалы имеют низкую коэрцитивную силу. Общая сила магнита измеряется его магнитным моментом или, альтернативно, общим магнитным потоком, который он производит. Локальная сила магнетизма в материале измеряется его намагниченностью .

Электромагнит состоит из катушки проволоки, которая действует как магнит, когда через нее проходит электрический ток , но перестает быть магнитом, когда ток прекращается. Часто катушку наматывают на сердечник из «мягкого» ферромагнитного материала, такого как мягкая сталь , что значительно усиливает магнитное поле, создаваемое катушкой.

Открытие и развитие

Древние люди узнали о магнетизме из магнитов (или магнетита ), которые естественным образом представляют собой намагниченные куски железной руды. Слово «магнит» было заимствовано в среднеанглийском языке от латинского « magnetum » «магнит», в конечном итоге от греческого μαγνῆτις [λίθος] ( magnetis [lithos] ) ^[1] , что означает «[камень] из Магнезии», ^[2] место в Анатолии , где магниты были найден (сегодня Маниса на территории современной Турции ). Магниты, подвешенные так, чтобы они могли вращаться, были первыми магнитными компасами . Самые ранние известные сохранившиеся описания магнитов и их свойств относятся к Анатолии, Индии и Китаю около 2500 лет назад. ^{[3] [4] [5]} Свойства магнитов и их сродство к железу были описаны Плинием Старшим в его энциклопедии Naturalis Historia в 1 веке нашей эры. ^[6]

В Китае XI века было обнаружено, что закалка раскаленного железа в магнитном поле Земли оставляет железо намагниченным навсегда. Это привело к разработке навигационного компаса , как описано в «Очерках бассейна снов» в 1088 году. ^{[7] [8]} К 12-13 векам нашей эры магнитные компасы использовались в навигации в Китае, Европе, на Аравийском полуострове и в других местах. ^[9]

Прямой железный магнит имеет тенденцию размагничиваться собственным магнитным полем. Чтобы преодолеть эту проблему, Даниэль Бернулли изобрел подковообразный магнит в 1743 году. ^{[7] [10]} Подковообразный магнит позволяет избежать размагничивания, возвращая линии магнитного поля к противоположному полюсу. ^[11]

В 1820 году Ганс Кристиан Эрстед обнаружил, что стрелка компаса отклоняется под действием электрического тока. В том же году Андре-Мари Ампер показал, что железо можно намагничивать, поместив его в соленоид с электрическим питанием. Это побудило Уильяма Стерджена разработать электромагнит с железным сердечником в 1824 году. ^[7] Джозеф Генри развил электромагнит до коммерческого продукта в 1830–1831 годах, впервые предоставив людям доступ к сильным магнитным полям. В 1831 году он построил сепаратор руды с электромагнитом, способным поднимать 750 фунтов (340 кг). ^[12]

Физика

Магнитное поле

Железные опилки, ориентированные в магнитном поле, создаваемом стержневым магнитом.

Обнаружение магнитного поля с помощью компаса и железных опилок

Плотность магнитного потока (также называемая магнитным полем B или просто магнитным полем, обычно обозначаемым B ) представляет собой векторное поле . Вектор магнитного поля B в данной точке пространства задается двумя свойствами:

1. Его направление соответствует направлению стрелки компаса .
2. Его величина (также называемая силой ), которая пропорциональна тому, насколько сильно стрелка компаса ориентирована в этом направлении.

В единицах СИ напряженность магнитного поля B выражается в теслах . ^[13]

Магнитный момент

Магнитный момент магнита (также называемый магнитным дипольным моментом и обычно обозначаемый μ ) — это вектор , который характеризует общие магнитные свойства магнита. Для стержневого магнита направление магнитного момента указывает от южного полюса магнита к его северному полюсу ^[14] , а величина зависит от того, насколько сильны и насколько далеко друг от друга находятся эти полюса. В единицах СИ магнитный момент выражается в А·м ² (амперы, умноженные на метры в квадрате).

Магнит одновременно создает собственное магнитное поле и реагирует на магнитные поля. Сила создаваемого им магнитного поля в любой данной точке пропорциональна величине его магнитного момента. Кроме того, когда магнит помещается во внешнее магнитное поле, созданное другим источником, на него действует крутящий момент , стремящийся направить магнитный момент параллельно полю. ^[15] Величина этого крутящего момента пропорциональна как магнитному моменту, так и внешнему полю. На магнит также может действовать сила, движущая его в том или ином направлении, в зависимости от положения и ориентации магнита и источника. Если поле однородно в пространстве, на магнит не действует результирующая сила, хотя на него действует крутящий момент. ^[16]

Провод в форме круга площадью А с током I имеет магнитный момент, равный IA .

Намагниченность

Намагниченность намагниченного материала — это локальное значение его магнитного момента на единицу объема, обычно обозначаемое М , с единицами А / м . ^[17] Это векторное поле , а не просто вектор (как магнитный момент), потому что разные области магнита могут быть намагничены с разными направлениями и силой (например, из-за доменов, см. ниже). Хороший стержневой магнит может иметь магнитный момент величиной 0,1 А·м ² и объем 1 см ³ , или 1×10 ^-6  м ³ , и, следовательно, средняя величина намагничивания составляет 100 000 А/м. Железо может иметь намагниченность около миллиона ампер на метр. Столь большое значение объясняет, почему железные магниты так эффективно создают магнитные поля.

Моделирование магнитов

Поле цилиндрического стержневого магнита рассчитано точно

Для магнитов существуют две разные модели: магнитные полюса и атомные токи.

Хотя для многих целей удобно думать о магните как о наличии отдельных северного и южного магнитных полюсов, концепцию полюсов не следует понимать буквально: это просто способ обозначения двух разных концов магнита. Магнит не имеет четко выраженных северных или южных частиц на противоположных сторонах. Если стержневой магнит разбить на две части, пытаясь разделить северный и южный полюса, в результате получится два стержневых магнита, каждый из которых имеет северный и южный полюс. Однако версия подхода магнитного полюса используется профессиональными магнетиками для проектирования постоянных магнитов. ^{[ нужна цитата ]}

В этом подходе расходимость намагниченности ∇· M внутри магнетика трактуется как распределение магнитных монополей . Это математическое удобство, но оно не означает, что в магните действительно существуют монополи. Если распределение магнитных полюсов известно, то модель полюса дает магнитное поле H . Снаружи магнита поле B пропорционально H , а внутри намагниченность должна быть добавлена ​​к H. Расширение этого метода, учитывающее внутренние магнитные заряды, используется в теориях ферромагнетизма.

Другая модель — это модель Ампера , в которой вся намагниченность обусловлена ​​действием микроскопических или атомных круговых связанных токов , также называемых токами Ампера, проходящих по всему материалу. Для однородно намагниченного цилиндрического стержневого магнита конечный эффект микроскопических связанных токов заключается в том, что магнит ведет себя так, как будто вокруг поверхности течет макроскопический слой электрического тока с локальным направлением потока, перпендикулярным оси цилиндра. ^[18] Микроскопические токи в атомах внутри материала обычно нейтрализуются токами в соседних атомах, поэтому чистый вклад вносит только поверхность; сбривание внешнего слоя магнита не разрушит его магнитное поле, но оставит новую поверхность неуничтоженных токов круговых токов по всему материалу. ^[19] Правило правой руки показывает, в каком направлении течет положительно заряженный ток. Однако ток, возникающий из-за отрицательно заряженного электричества, на практике гораздо более распространен. ^{[ нужна цитата ]}

Полярность

Северный полюс магнита определяется как полюс, который, когда магнит свободно подвешен, направлен в сторону Северного магнитного полюса Земли в Арктике (магнитный и географический полюса не совпадают, см. магнитное склонение ). Поскольку противоположные полюса (северный и южный) притягиваются, Северный магнитный полюс фактически является южным полюсом магнитного поля Земли. ^{[20] [21] [22] [23]} На практике, чтобы определить, какой полюс магнита северный, а какой южный, вовсе не обязательно использовать магнитное поле Земли. Например, одним из методов было бы сравнить его с электромагнитом , полюса которого можно определить по правилу правой руки . По соглашению считается, что линии магнитного поля магнита выходят из северного полюса магнита и снова входят в южный полюс. ^[23]

Магнитные материалы

Термин «магнит» обычно применяется к объектам, которые создают собственное постоянное магнитное поле даже в отсутствие приложенного магнитного поля. Только определенные классы материалов могут это сделать. Однако большинство материалов создают магнитное поле в ответ на приложенное магнитное поле – явление, известное как магнетизм. Существует несколько типов магнетизма, и все материалы обладают хотя бы одним из них.

Общее магнитное поведение материала может сильно различаться в зависимости от структуры материала, особенно от его электронной конфигурации . В различных материалах наблюдалось несколько форм магнитного поведения, в том числе:

• Ферромагнитные и ферримагнитные материалы обычно считаются магнитными; они притягиваются к магниту настолько сильно, что это притяжение можно почувствовать. Эти материалы — единственные, которые могут сохранять намагниченность и становиться магнитами; Типичным примером является традиционный магнит на холодильник . Ферримагнитные материалы, которые включают в себя ферриты и самые старые и встречающиеся в природе магнитные материалы магнетит и магнит , похожи на ферромагнетики, но слабее их. Разница между ферро- и ферримагнитными материалами связана с их микроскопической структурой, как объяснено в книге «Магнетизм» .
• Парамагнитные вещества, такие как платина , алюминий и кислород , слабо притягиваются к любому полюсу магнита. Это притяжение в сотни тысяч раз слабее, чем у ферромагнитных материалов, поэтому его можно обнаружить только с помощью чувствительных приборов или с помощью чрезвычайно сильных магнитов. Магнитные феррожидкости , хотя они и состоят из крошечных ферромагнитных частиц, взвешенных в жидкости, иногда считаются парамагнитными, поскольку они не могут быть намагничены.
• Diamagnetic means repelled by both poles. Compared to paramagnetic and ferromagnetic substances, diamagnetic substances, such as carbon, copper, water, and plastic, are even more weakly repelled by a magnet. The permeability of diamagnetic materials is less than the permeability of a vacuum. All substances not possessing one of the other types of magnetism are diamagnetic; this includes most substances. Although force on a diamagnetic object from an ordinary magnet is far too weak to be felt, using extremely strong superconducting magnets, diamagnetic objects such as pieces of lead and even mice^[24] can be levitated, so they float in mid-air. Superconductors repel magnetic fields from their interior and are strongly diamagnetic.

There are various other types of magnetism, such as spin glass, superparamagnetism, superdiamagnetism, and metamagnetism.

Common uses

Hard disk drives record data on a thin magnetic coating

Magnetic hand separator for heavy minerals

• Magnetic recording media: VHS tapes contain a reel of magnetic tape. The information that makes up the video and sound is encoded on the magnetic coating on the tape. Common audio cassettes also rely on magnetic tape. Similarly, in computers, floppy disks and hard disks record data on a thin magnetic coating.^[25]
• Credit, debit, and automatic teller machine cards: All of these cards have a magnetic strip on one side. This strip encodes the information to contact an individual's financial institution and connect with their account(s).^[26]
• Older types of televisions (non flat screen) and older large computer monitors: TV and computer screens containing a cathode ray tube employ an electromagnet to guide electrons to the screen.^[27]
• Speakers and microphones: Most speakers employ a permanent magnet and a current-carrying coil to convert electric energy (the signal) into mechanical energy (movement that creates the sound). The coil is wrapped around a bobbin attached to the speaker cone and carries the signal as changing current that interacts with the field of the permanent magnet. The voice coil feels a magnetic force and in response, moves the cone and pressurizes the neighboring air, thus generating sound. Dynamic microphones employ the same concept, but in reverse. A microphone has a diaphragm or membrane attached to a coil of wire. The coil rests inside a specially shaped magnet. When sound vibrates the membrane, the coil is vibrated as well. As the coil moves through the magnetic field, a voltage is induced across the coil. This voltage drives a current in the wire that is characteristic of the original sound.
• Electric guitars use magnetic pickups to transduce the vibration of guitar strings into electric current that can then be amplified. This is different from the principle behind the speaker and dynamic microphone because the vibrations are sensed directly by the magnet, and a diaphragm is not employed. The Hammond organ used a similar principle, with rotating tonewheels instead of strings.
• Electric motors and generators: Some electric motors rely upon a combination of an electromagnet and a permanent magnet, and, much like loudspeakers, they convert electric energy into mechanical energy. A generator is the reverse: it converts mechanical energy into electric energy by moving a conductor through a magnetic field.
• Medicine: Hospitals use magnetic resonance imaging to spot problems in a patient's organs without invasive surgery.
• Chemistry: Chemists use nuclear magnetic resonance to characterize synthesized compounds.
• Chucks are used in the metalworking field to hold objects. Magnets are also used in other types of fastening devices, such as the magnetic base, the magnetic clamp and the refrigerator magnet.
• Compasses: A compass (or mariner's compass) is a magnetized pointer free to align itself with a magnetic field, most commonly Earth's magnetic field.
• Art: Vinyl magnet sheets may be attached to paintings, photographs, and other ornamental articles, allowing them to be attached to refrigerators and other metal surfaces. Objects and paint can be applied directly to the magnet surface to create collage pieces of art. Metal magnetic boards, strips, doors, microwave ovens, dishwashers, cars, metal I beams, and any metal surface can be used magnetic vinyl art.
• Science projects: Many topic questions are based on magnets, including the repulsion of current-carrying wires, the effect of temperature, and motors involving magnets.^[28]

Magnets have many uses in toys. M-tic uses magnetic rods connected to metal spheres for construction.

• Toys: Given their ability to counteract the force of gravity at close range, magnets are often employed in children's toys, such as the Magnet Space Wheel and Levitron, to amusing effect.
• Refrigerator magnets are used to adorn kitchens, as a souvenir, or simply to hold a note or photo to the refrigerator door.
• Magnets can be used to make jewelry. Necklaces and bracelets can have a magnetic clasp, or may be constructed entirely from a linked series of magnets and ferrous beads.
• Magnets can pick up magnetic items (iron nails, staples, tacks, paper clips) that are either too small, too hard to reach, or too thin for fingers to hold. Some screwdrivers are magnetized for this purpose.
• Magnets can be used in scrap and salvage operations to separate magnetic metals (iron, cobalt, and nickel) from non-magnetic metals (aluminum, non-ferrous alloys, etc.). The same idea can be used in the so-called "magnet test", in which a car chassis is inspected with a magnet to detect areas repaired using fiberglass or plastic putty.
• Magnets are found in process industries, food manufacturing especially, in order to remove metal foreign bodies from materials entering the process (raw materials) or to detect a possible contamination at the end of the process and prior to packaging. They constitute an important layer of protection for the process equipment and for the final consumer.^[29]
• Magnetic levitation transport, or maglev, is a form of transportation that suspends, guides and propels vehicles (especially trains) through electromagnetic force. Eliminating rolling resistance increases efficiency. The maximum recorded speed of a maglev train is 581 kilometers per hour (361 mph).
• Magnets may be used to serve as a fail-safe device for some cable connections. For example, the power cords of some laptops are magnetic to prevent accidental damage to the port when tripped over. The MagSafe power connection to the Apple MacBook is one such example.

Medical issues and safety

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.^[30]

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.^[31]

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 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).^[32]
• 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.^[33]

Demagnetizing ferromagnets

Magnetized ferromagnetic materials can be demagnetized (or degaussed) in the following ways:

• Heating a magnet past its Curie temperature; the molecular motion destroys the alignment of the magnetic domains. 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 disks, and degaussing coils used to demagnetize CRTs.
• Some demagnetization or reverse magnetization will occur if any part of the magnet is subjected to a reverse field above the magnetic material's coercivity.
• Demagnetization progressively occurs if the magnet is subjected to cyclic fields sufficient to move the magnet away from the linear part on the second quadrant of the B–H curve of the magnetic material (the demagnetization curve).
• Hammering or jarring: mechanical disturbance tends to randomize the magnetic domains and reduce magnetization of an object, but may cause unacceptable damage.

Types of permanent magnets

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 metals are ferromagnetic when found in their natural states, as ores. These include iron ore (magnetite or lodestone), cobalt and nickel, as well as the rare earth metals gadolinium and dysprosium (when at a very low temperature). Such naturally occurring ferromagnets were used in the first experiments with magnetism. Technology has since expanded the availability of magnetic materials to include various man-made products, all based, however, on naturally magnetic elements.

Composites

A stack of ferrite magnets

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

Alnico magnets are made by casting or sintering a combination of aluminium, nickel and cobalt with iron and small amounts of other elements added to enhance the properties of the magnet. Sintering offers superior mechanical characteristics, whereas casting delivers higher magnetic fields and allows for the design of intricate shapes. Alnico magnets resist corrosion and have physical properties more forgiving than ferrite, but not quite as desirable as a metal. Trade names for alloys in this family include: Alni, Alcomax, Hycomax, Columax, and Ticonal.^[34]

Injection-molded magnets are a composite of various types of resin and magnetic powders, allowing parts of complex shapes to be manufactured by injection molding. The physical and magnetic properties of the product depend on the raw materials, but are generally lower in magnetic strength and resemble plastics in their physical properties.

Flexible magnet

Flexible magnets are composed of a high-coercivity ferromagnetic compound (usually ferric oxide) mixed with a resinous polymer binder.^[35] 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.^[36]

For magnetic compounds (e.g. Nd₂Fe₁₄B) that are vulnerable to a grain boundary corrosion problem it gives additional protection.^[35]

Rare-earth magnets

Ovoid-shaped magnets (possibly hematine), one hanging from another

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:

1. a large ground state spin value (S), which is provided by ferromagnetic or ferrimagnetic coupling between the paramagnetic metal centres
2. a negative value of the anisotropy of the zero field splitting (D)

Most SMMs contain manganese but can also be found with vanadium, iron, nickel and cobalt clusters. More recently, it has been found that some chain systems can also display a magnetization that persists for long times at higher temperatures. These systems have been called single-chain magnets.

Nano-structured magnets

Some nano-structured materials exhibit energy waves, called magnons, that coalesce into a common ground state in the manner of a Bose–Einstein condensate.^[37][38]

Rare-earth-free permanent magnets

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.^[39] Iron nitrides are promising materials for rare-earth free magnets.^[40]

Costs

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,^{[35][non-primary source needed][41]} 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.^[42]

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 540 °C (1,000 °F), around 300 °C (570 °F) for ferrite and SmCo, about 140 °C (280 °F) for NIB and lower for flexible ceramics, but the exact numbers depend on the grade of material.

Electromagnets

An electromagnet, in its simplest form, is a wire that has been coiled into one or more loops, known as a solenoid. When electric current flows through the wire, a magnetic field is generated. It is concentrated near (and especially inside) the coil, and its field lines are very similar to those of a magnet. The orientation of this effective magnet is determined by the right hand rule. The magnetic moment and the magnetic field of the electromagnet are proportional to the number of loops of wire, to the cross-section of each loop, and to the current passing through the wire.^[43]

If the coil of wire is wrapped around a material with no special magnetic properties (e.g., cardboard), it will tend to generate a very weak field. However, if it is wrapped around a soft ferromagnetic material, such as an iron nail, then the net field produced can result in a several hundred- to thousandfold increase of field strength.

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

Units and calculations

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

In all units, it is convenient to employ two types of magnetic field, B and H, as well as the magnetization M, defined as the magnetic moment per unit volume.

1. The magnetic induction field B is given in SI units of teslas (T). B is the magnetic field whose time variation produces, by Faraday's Law, circulating electric fields (which the power companies sell). B also produces a deflection force on moving charged particles (as in TV tubes). The tesla is equivalent to the magnetic flux (in webers) per unit area (in meters squared), thus giving B the unit of a flux density. In CGS, the unit of B is the gauss (G). One tesla equals 10⁴ G.
2. The magnetic field H is given in SI units of ampere-turns per meter (A-turn/m). The turns appear because when H is produced by a current-carrying wire, its value is proportional to the number of turns of that wire. In CGS, the unit of H is the oersted (Oe). One A-turn/m equals 4π×10⁻³ Oe.
3. The magnetization M is given in SI units of amperes per meter (A/m). In CGS, the unit of M is the oersted (Oe). One A/m equals 10⁻³ emu/cm³. A good permanent magnet can have a magnetization as large as a million amperes per meter.
4. In SI units, the relation B = μ₀(H + M) holds, where μ₀ is the permeability of space, which equals 4π×10⁻⁷ T•m/A. In CGS, it is written as B = H + 4πM. (The pole approach gives μ₀H in SI units. A μ₀M term in SI must then supplement this μ₀H to give the correct field within B, the magnet. It will agree with the field B calculated using Ampèrian currents).

Materials that are not permanent magnets usually satisfy the relation M = χH in SI, where χ is the (dimensionless) magnetic susceptibility. Most non-magnetic materials have a relatively small χ (on the order of a millionth), but soft magnets can have χ on the order of hundreds or thousands. For materials satisfying M = χH, we can also write B = μ₀(1 + χ)H = μ₀μ_rH = μH, where μ_r = 1 + χ is the (dimensionless) relative permeability and μ =μ₀μ_r is the magnetic permeability. Both hard and soft magnets have a more complex, history-dependent, behavior described by what are called hysteresis loops, which give either B vs. H or M vs. H. In CGS, M = χH, but χ_SI = 4πχ_CGS, and μ = μ_r.

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 q_m = MA, so that M can be thought of as a pole strength per unit area.

Fields of a magnet

Field lines of cylindrical magnets with various aspect ratios

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

Closer to the magnet, the magnetic field becomes more complicated and more dependent on the detailed shape and magnetization of the magnet. Formally, the field can be expressed as a multipole expansion: A dipole field, plus a quadrupole field, plus an octupole field, etc.

At close range, many different fields are possible. For example, for a long, skinny bar magnet with its north pole at one end and south pole at the other, the magnetic field near either end falls off inversely with the square of the distance from that pole.

Calculating the magnetic force

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.^[44] 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^[45]) is given by the Maxwell equation:^[46]

${\displaystyle F={{B^{2}A} \over {2\mu _{0}}}}$,

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:

${\displaystyle m={{B^{2}A} \over {2\mu _{0}g}},}$

where g is the gravitational acceleration.

Force between two magnetic poles

Classically, the force between two magnetic poles is given by:^[47]

${\displaystyle F={{\mu q_{m1}q_{m2}} \over {4\pi r^{2}}}}$

where

F is force (SI unit: newton)

q_m1 and q_m2 are the magnitudes of magnetic poles (SI unit: ampere-meter)

μ is the permeability of the intervening medium (SI unit: tesla meter per ampere, henry per meter or newton per ampere squared)

r is the separation (SI unit: meter).

The pole description is useful to the engineers designing real-world magnets, but real magnets have a pole distribution more complex than a single north and south. Therefore, implementation of the pole idea is not simple. In some cases, one of the more complex formulae given below will be more useful.

Force between two nearby magnetized surfaces of area A

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:^[48][49]

${\displaystyle F={\frac {\mu _{0}H^{2}A}{2}}={\frac {B^{2}A}{2\mu _{0}}}}$

where:

A is the area of each surface, in m²

H is their magnetizing field, in A/m

μ₀ is the permeability of space, which equals 4π×10⁻⁷ T•m/A

B is the flux density, in T.

Force between two bar magnets

The force between two identical cylindrical bar magnets placed end to end at large distance ${\displaystyle z\gg R}$ is approximately:^{[dubious – discuss]},^[48]

${\displaystyle F\simeq \left[{\frac {B_{0}^{2}A^{2}\left(L^{2}+R^{2}\right)}{\pi \mu _{0}L^{2}}}\right]\left[{\frac {1}{z^{2}}}+{\frac {1}{(z+2L)^{2}}}-{\frac {2}{(z+L)^{2}}}\right]}$

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.

${\displaystyle B_{0}\,=\,{\frac {\mu _{0}}{2}}M}$ 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.

Force between two cylindrical magnets

For two cylindrical magnets with radius ${\displaystyle R}$ and length ${\displaystyle L}$, with their magnetic dipole aligned, the force can be asymptotically approximated at large distance ${\displaystyle z\gg R}$ by,^[50]

${\displaystyle F(z)\simeq {\frac {\pi \mu _{0}}{4}}M^{2}R^{4}\left[{\frac {1}{z^{2}}}+{\frac {1}{(z+2L)^{2}}}-{\frac {2}{(z+L)^{2}}}\right]}$

where ${\displaystyle M}$ is the magnetization of the magnets and ${\displaystyle z}$ is the gap between the magnets. A measurement of the magnetic flux density very close to the magnet ${\displaystyle B_{0}}$ is related to ${\displaystyle M}$ approximately by the formula

${\displaystyle B_{0}={\frac {\mu _{0}}{2}}M}$

The effective magnetic dipole can be written as

${\displaystyle m=MV}$

Where ${\displaystyle V}$ is the volume of the magnet. For a cylinder, this is ${\displaystyle V=\pi R^{2}L}$.

When ${\displaystyle z\gg L}$, the point dipole approximation is obtained,

${\displaystyle F(x)={\frac {3\pi \mu _{0}}{2}}M^{2}R^{4}L^{2}{\frac {1}{z^{4}}}={\frac {3\mu _{0}}{2\pi }}M^{2}V^{2}{\frac {1}{z^{4}}}={\frac {3\mu _{0}}{2\pi }}m_{1}m_{2}{\frac {1}{z^{4}}}}$

which matches the expression of the force between two magnetic dipoles.

See also

• Dipole magnet
• Earnshaw's theorem
• Electret
• Electromagnetic field
• Electromagnetism
• Halbach array
• Magnetic nanoparticles
• Magnetic switch
• Magneto
• Magnetochemistry
• Molecule-based magnets
• Single-molecule magnet
• Supermagnet

Notes

1. Platonis Opera Archived 2018-01-14 at the Wayback Machine, Meyer and Zeller, 1839, p. 989.
2. The location of Magnesia is debated; it could be the region in mainland Greece or Magnesia ad Sipylum. See, for example, "Magnet". Language Hat blog. 28 May 2005. Archived from the original on 19 May 2012. Retrieved 22 March 2013.
3. Fowler, Michael (1997). "Historical Beginnings of Theories of Electricity and Magnetism". Archived from the original on 2008-03-15. Retrieved 2008-04-02.
4. Vowles, Hugh P. (1932). "Early Evolution of Power Engineering". Isis. 17 (2): 412–420 [419–20]. doi:10.1086/346662. S2CID 143949193.
5. Li Shu-hua (1954). "Origine de la Boussole II. Aimant et Boussole". Isis. 45 (2): 175–196. doi:10.1086/348315. JSTOR 227361. S2CID 143585290.
6. Pliny the Elder, The Natural History, BOOK XXXIV. THE NATURAL HISTORY OF METALS., CHAP. 42.—THE METAL CALLED LIVE IRON Archived 2011-06-29 at the Wayback Machine. Perseus.tufts.edu. Retrieved on 2011-05-17.
7. Coey, J. M. D. (2009). Magnetism and magnetic materials. Cambridge: Cambridge University Press. pp. 1–3. ISBN 978-0-511-68515-6. OCLC 664016090.
8. "Four Great Inventions of Ancient China". Embassy of the People's Republic of China in the Republic of South Africa. 2004-12-13. Retrieved January 8, 2023.
9. Schmidl, Petra G. (1996–1997). "Two Early Arabic Sources On The Magnetic Compass" (PDF). Journal of Arabic and Islamic Studies. 1: 81–132. doi:10.5617/jais.4547. Archived (PDF) from the original on 2012-05-24.
10. "The Seven Magnetic Moments - Modern Magnets". Trinity College Dublin. Retrieved January 8, 2023.
11. 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, ISBN 978-3-030-63210-6, S2CID 244736617, retrieved 2023-01-08
12. "Joseph Henry – Engineering Hall of Fame". Edison Tech Center. Retrieved January 8, 2023.
13. Griffiths, David J. (1999). Introduction to Electrodynamics (3rd ed.). Prentice Hall. pp. 255–8. ISBN 0-13-805326-X. OCLC 40251748.
14. Knight, Jones, & Field, "College Physics" (2007) p. 815.
15. Cullity, B. D. & Graham, C. D. (2008). Introduction to Magnetic Materials (2 ed.). Wiley-IEEE Press. p. 103. ISBN 978-0-471-47741-9.
16. Boyer, Timothy H. (1988). "The Force on a Magnetic Dipole". American Journal of Physics. 56 (8): 688–692. Bibcode:1988AmJPh..56..688B. doi:10.1119/1.15501.
17. "Units for Magnetic Properties" (PDF). Lake Shore Cryotronics, Inc. Archived from the original (PDF) on 2011-07-14. Retrieved 2012-11-05.
18. Allen, Zachariah (1852). Philosophy of the Mechanics of Nature, and the Source and Modes of Action of Natural Motive-Power. D. Appleton and Company. p. 252.
19. Saslow, Wayne M. (2002). Electricity, Magnetism, and Light (3rd ed.). Academic Press. p. 426. ISBN 978-0-12-619455-5. Archived from the original on 2014-06-27.
20. Serway, Raymond A.; Chris Vuille (2006). Essentials of college physics. USA: Cengage Learning. p. 493. ISBN 0-495-10619-4. Archived from the original on 2013-06-04.
21. Emiliani, Cesare (1992). Planet Earth: Cosmology, Geology, and the Evolution of Life and Environment. UK: Cambridge University Press. p. 228. ISBN 0-521-40949-7. Archived from the original on 2016-12-24.
22. Manners, Joy (2000). Static Fields and Potentials. USA: CRC Press. p. 148. ISBN 0-7503-0718-8. Archived from the original on 2016-12-24.
23. Nave, Carl R. (2010). "Bar Magnet". Hyperphysics. Dept. of Physics and Astronomy, Georgia State Univ. Archived from the original on 2011-04-08. Retrieved 2011-04-10.
24. Mice levitated in NASA lab Archived 2011-02-09 at the Wayback Machine. Livescience.com (2009-09-09). Retrieved on 2011-10-08.
25. Mallinson, John C. (1987). The foundations of magnetic recording (2nd ed.). Academic Press. ISBN 0-12-466626-4.
26. "The stripe on a credit card". How Stuff Works. Archived from the original on 2011-06-24. Retrieved 19 July 2011.
27. "Electromagnetic deflection in a cathode ray tube, I". National High Magnetic Field Laboratory. Archived from the original on 3 April 2012. Retrieved 20 July 2011.
28. "Snacks about magnetism". The Exploratorium Science Snacks. Exploratorium. Archived from the original on 7 April 2013. Retrieved 17 April 2013.
29. "Neodymium Magnets : Strength, design for tramp metal removal". Archived from the original on 2017-05-10. Retrieved 2016-12-05. Source on magnets in process industries
30. Schenck JF (2000). "Safety of strong, static magnetic fields". J Magn Reson Imaging. 12 (1): 2–19. doi:10.1002/1522-2586(200007)12:1<2::AID-JMRI2>3.0.CO;2-V. PMID 10931560. S2CID 19976829.
31. Oestreich AE (2008). "Worldwide survey of damage from swallowing multiple magnets". Pediatr Radiol. 39 (2): 142–7. doi:10.1007/s00247-008-1059-7. PMID 19020871. S2CID 21306900.
32. McKenzie, A. E. E. (1961). Magnetism and electricity. Cambridge. pp. 3–4.
33. "Ferromagnetic Materials". Phares Electronics. Archived from the original on 27 June 2015. Retrieved 26 June 2015.
34. Brady, George Stuart; Henry R. Clauser; John A. Vaccari (2002). Materials Handbook: An Encyclopedia for Managers. McGraw-Hill Professional. p. 577. ISBN 0-07-136076-X. Archived from the original on 2016-12-24.
35. "Nanostructured Mn-Al Permanent Magnets (patent)". Retrieved 18 Feb 2017.
36. "Press release: Fridge magnet transformed". Riken. March 11, 2011. Archived from the original on August 7, 2017.
37. "Nanomagnets Bend The Rules". Archived from the original on December 7, 2005. Retrieved November 14, 2005.
38. Della Torre, E.; Bennett, L.; Watson, R. (2005). "Extension of the Bloch T^3/2 Law to Magnetic Nanostructures: Bose-Einstein Condensation". Physical Review Letters. 94 (14): 147210. Bibcode:2005PhRvL..94n7210D. doi:10.1103/PhysRevLett.94.147210. PMID 15904108.
39. "Research Funding for Rare Earth Free Permanent Magnets". ARPA-E. Archived from the original on 10 October 2013. Retrieved 23 April 2013.
40. By (2022-09-01). "Iron Nitrides: Powerful Magnets Without The Rare Earth Elements". Hackaday. Retrieved 2023-11-08.
41. An Overview of MnAl Permanent Magnets with a Study on Their Potential in Electrical Machines
42. Frequently Asked Questions Archived 2008-03-12 at the Wayback Machine. Magnet sales & Mfct Co Inc. Retrieved on 2011-10-08.
43. Ruskell, Todd; Tipler, Paul A.; Mosca, Gene (2007). Physics for Scientists and Engineers (6 ed.). Palgrave Macmillan. ISBN 978-1-4292-0410-1.
44. "How Much Will a Magnet Hold?". www.kjmagnetics.com. Retrieved 2020-01-20.
45. "Magnetic Pull Force Explained - What is Magnet Pull Force? | Dura Magnetics USA". 19 October 2016. Retrieved 2020-01-20.
46. Cardarelli, François (2008). Materials Handbook: A Concise Desktop Reference (Second ed.). Springer. p. 493. ISBN 9781846286681. Archived from the original on 2016-12-24.
47. "Basic Relationships". Geophysics.ou.edu. Archived from the original on 2010-07-09. Retrieved 2009-10-19.
48. "Magnetic Fields and Forces". Archived from the original on 2012-02-20. Retrieved 2009-12-24.
49. "The force produced by a magnetic field". Archived from the original on 2010-03-17. Retrieved 2010-03-09.
50. David Vokoun; Marco Beleggia; Ludek Heller; Petr Sittner (2009). "Magnetostatic interactions and forces between cylindrical permanent magnets". Journal of Magnetism and Magnetic Materials. 321 (22): 3758–3763. Bibcode:2009JMMM..321.3758V. doi:10.1016/j.jmmm.2009.07.030.

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. Catherine Soanes and Angus Stevenson. Oxford University Press, 2004. Oxford Reference Online. Oxford University Press.
• Wayne M. Saslow, Electricity, Magnetism, and Light, Academic (2002). ISBN 0-12-619455-6. 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). ISBN 0-12-269951-3.

External links

• How magnets are made Archived 2013-03-16 at the Wayback Machine (video)
• Floating Ring Magnets, Bulletin of the IAPT, Volume 4, No. 6, 145 (June 2012). (Publication of the Indian Association of Physics Teachers).
• A brief history of electricity and magnetism