magnet: see electromagnet; magnetism.

Magnets and their associated magnetic field lines. A permanent magnet (such as a bar or disk elipsis

Any material capable of attracting iron and producing a magnetic field outside itself. By the end of the 19th century, all known elements and many compounds had been tested for magnetism, and all were found to have some magnetic property. However, only three elements—iron, nickel, and cobalt—exhibit ferromagnetism. Seealso compass, electromagnet.

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A magnet (from Greek μαγνήτης λίθος, "Magnesian stone") is a material or object that produces a magnetic field. This magnetic field is invisible and causes the most notable property of a magnet: a force that pulls on nearby magnetic materials, or attracts or repels other magnets. The structure of the invisible magnetic field of a magnet is made visible by the pattern formed when iron filings are scattered around the magnet, as in the accompanying figure.



Background on the physics of magnetism and magnets

Magnetic field

The magnetic field (usually denoted B) is called a field (physics) because it has a value at every point in space. The magnetic field (at a given point) is specified by two properties: (1) its direction, which is along the orientation of a compass needle; and (2) its magnitude (also called strength), which is proportional to how strongly the compass needle orients along that direction. Direction and magnitude makes B a vector, so B is a vector field. (B can also depend on time.) In SI units the strength of the magnetic field is given in teslas.

Magnetic moment

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

A magnet both produces its own magnetic field and it responds to magnetic fields. The strength of the magnetic field it produces is at any given point proportional to the magnitude of its magnetic moment. In addition, when the magnet is put into an "external" magnetic field produced by a different source, it is subject to a torque tending to orient the magnetic moment parallel to the field. 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.



The magnetization of an object 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 the different sections of a bar magnet generally are magnetized with different directions and strengths (for example, due to 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 0.000001 m³, and therefore an average magnetization magnitude is 100,000 A/m. Iron can have a magnetization of around a million A/m. Such a large value explains why magnets are so effective at producing magnetic fields.

The Two Models for Magnets: Magnetic Poles and Atomic Currents

Magnetic pole model. 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. (No magnetic monopole has yet been observed.) If a bar magnet is broken in half, 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.

The magnetic pole approach is used by most professional magneticians, from those who design magnetic memory to those who design large-scale magnets. If the magnetic pole distribution is known, then outside the magnet the pole model gives the magnetic field exactly. By simply supplementing the pole model field with a term proportional to the magnetization (see Units and Calculations, below) the magnetic field within the magnet is given exactly. This pole model is also called the "Gilbert Model" of a magnetic dipole.

Ampère Model. Another model is the "Ampère Model", where all magnetization is due to the macroscopic effect of microscopic, or atomic, "bound currents", also called "Ampèrian currents". For a uniformly magnetized bar magnet in the shape of a cylinder, with poles uniformly distributed on its ends, the net effect of the microscopic bound currents is to make the magnet behave as if there is a macroscopic sheet of current around the cylinder, with local flow direction normal to the cylinder axis. (Since scraping off the outer layer of a magnet will not destroy its magnetic properties, there are subtleties associated with this model as well as with the pole model. What happens is that you have only scraped off a relatively small number of atoms, whose bound currents do not contribute much to the net magnetic moment.) A right-hand rule due to Ampère tells us how the currents flow, for a given magnetic moment. Align the thumb of your right hand along the magnetic moment, and with that hand grasp the cylinder. Your fingers will then point along the direction of flow. As noted above, the magnetic field given by the Amperian approach and the Gilbert approach are identical outside all magnets, and become identical within all magnets after the Gilbert "field" is supplemented. It is usually difficult to find the Amperian currents on the surface of a magnet, whereas it is often easier to find the effective poles for the same magnet. For one end (pole) of a permanent magnet outside a "soft" magnet, the pole picture of the "soft" magnet has it respond with an image pole of opposite sign to the applied pole; one also can find the Amperian currents on the surface of the "soft" magnet.

Pole naming conventions

The north pole of the magnet is the pole which, when the magnet is freely suspended, points towards the Earth's magnetic north pole in northern Canada. Since opposite poles (north and south) attract whereas like poles (north and north, or south and south) repel, the Earth's present geographic north is thus actually its magnetic south. Confounding the situation further, the Earth's magnetic field has reversed itself many times in the distant past.

In order to avoid this confusion, the terms positive and negative poles are sometimes used instead of north and south, respectively.

As a practical matter, in order to tell which pole of a magnet is north and which is south, it is not necessary to use the earth's magnetic field at all. For example, one calibration method would be to compare it to an electromagnet, whose poles can be identified via the right-hand rule.

Descriptions of magnetic behaviors

There are many forms of magnetic behavior, and all materials exhibit at least one of them. Magnets vary both in the permanency of their magnetization, and in the strength and orientation of the magnetic field they create. This section describes, qualitatively, the primary types of magnetic behavior that materials can show. The physics underlying each of these behaviors is described in the next section below, and can also be found in more detail in their respective articles.

  • Most popularly found in paper clips, paramagnetism is exhibited in substances which do not produce fields by themselves, but which, when exposed to a magnetic field, reinforce that field by becoming magnetized themselves, and thus get attracted to that field. A good example for this behavior can be found in a bucket of nails - if you pick up a single nail, you can expect that other nails will not follow. However, you can apply an intense magnetic field to the bucket, pick up one nail, and find that many will come with it.
  • Unscientifically referred to as 'non-magnetic,' diamagnets actually do exhibit some magnetic behavior - just to very small magnitudes. In fact, diamagnetic materials, when exposed to a magnetic field, will magnetize (slightly) in the opposite direction, getting (slightly) repelled from the applied field. Superconductors are strongly diamagnetic.
  • Ferromagnetic and ferrimagnetic materials are the 'popular' perception of a magnet. These materials can retain their own magnetization; a common example is a traditional refrigerator magnet. (The difference between ferro- and ferrimagnetic materials is related to their microscopic structure, as explained below.)

Physics of magnetic behaviors


Magnetism, at its root, arises from two sources:

In magnetic materials, the most important sources of magnetization are, more specifically, the electrons' orbital angular motion around the nucleus, and the electrons' intrinsic magnetic moment (see Electron magnetic dipole moment). The other potential sources of magnetism are much less important: For example, the nuclear magnetic moments of the nuclei in the material are typically thousands of times smaller than the electrons' magnetic moments, so they are negligible in the context of the magnetization of materials. (Nuclear magnetic moments are important in other contexts, particularly in Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI).)

Ordinarily, the countless electrons in a material are arranged such that their magnetic moments (both orbital and intrinsic) cancel out. This is due, to some extent, to electrons combining into pairs with opposite intrinsic magnetic moments (as a result of the Pauli exclusion principle; see Electron configuration), or combining into "filled subshells" with zero net orbital motion; in both cases, the electron arrangement is so as to exactly cancel the magnetic moments from each electron. Moreover, even when the electron configuration is such that there are unpaired electrons and/or non-filled subshells, it is often the case that the various electrons in the solid will contribute magnetic moments that point in different, random directions, so that the material will not be magnetic.

However, sometimes (either spontaneously, or due to an applied external magnetic field) each of the electron magnetic moments will be, on average, lined up. Then the material can produce a net total magnetic field, which can potentially be quite strong.

The magnetic behavior of a material depends on its structure (particularly its electron configuration, for the reasons mentioned above), and also on the temperature (at high temperatures, random thermal motion makes it more difficult for the electrons to maintain alignment).

Physics of paramagnetism

In a paramagnet there are unpaired electrons, i.e. atomic or molecular orbitals with exactly one electron in them. While paired electrons are required by the Pauli exclusion principle to have their intrinsic ('spin') magnetic moments pointing in opposite directions (summing to zero), an unpaired electron is free to align its magnetic moment in any direction. When an external magnetic field is applied, these magnetic moments will tend to align themselves in the same direction as the applied field, thus reinforcing it.

Physics of diamagnetism




Note that all materials, including paramagnets, undergo this orbital response. However, in a paramagnet, this response is overwhelmed by the much stronger opposing response described above (i.e., alignment of the electrons' intrinsic magnetic moments).

Physics of ferromagnetism

A ferromagnet, like a paramagnet, has unpaired electrons. However, in addition to the electrons' intrinsic magnetic moments wanting to be parallel to an applied field, there is also in these materials a tendency for these magnetic moments to want to be parallel to each other. Thus, even when the applied field is removed, the electrons in the material can keep each other continually pointed in the same direction.


Magnetic Domains



When exposed to a magnetic field, the domain boundaries move so that the domains aligned with the magnetic field grow and dominate the structure as shown at the left. When the magnetizing field is removed, the domains may not return to a unmagnetized state. This results in the ferromagnetic material being magnetized, forming a permanent magnet.


Physics of antiferromagnetism



Physics of ferrimagnetism

Like ferromagnetism, ferrimagnets retain their magnetization in the absence of a field. However, like antiferromagnets, neighboring pairs of electron spins like to point in opposite directions. These two properties are not contradictory, due to the fact that in the optimal geometrical arrangement, there is more magnetic moment from the sublattice of electrons which point in one direction, than from the sublattice which points in the opposite direction.

The first discovered magnetic substance, magnetite, was originally believed to be a ferromagnet; Louis Néel disproved this, however, with the discovery of ferrimagnetism.

Other types of magnetism

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

Common uses of magnets

  • Common televisions and computer monitors: TV and computer screens using vacuum tube technology employ an electromagnet to guide electrons to the screen, in order to produce an image -- see the article on cathode ray tubes. Plasma screens and LCDs use different technologies.
  • Speakers and Microphones: Most speakers employ a permanent magnet and a current-carrying coil to convert electric energy (the signal) into mechanical energy (movement which creates the sound). The coil is wrapped around a bobbin attached to the speaker cone, and carries the signal as changing current which 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 generated across the coil (see Lenz's Law). This voltage drives current in the wire that is characteristic of the original sound.
  • Compasses: A compass (or mariner's compass) is a navigational instrument for finding directions on the Earth. It consists of a magnetized pointer free to align itself accurately with Earth's magnetic field, which is of great assistance in navigation. The cardinal points are north, south, east and west. A compass can be used in conjunction with a marine chronometer and a sextant to provide a very accurate navigation capability. This device greatly improved maritime trade by making travel safer and more efficient. An early form of the compass was invented in China in the 11th century. The familiar mariner's compass was invented in Europe around 1300, as was later the liquid compass and the gyrocompass which does not work with a magnetic field.
  • Art: 1 mm or thicker vinyl magnet sheets may be attached to paintings, photographs, and other ornamental articles, allowing them to be stuck to refrigerators and other metal surfaces.
  • Science Projects: Many topic questions are often based on magnets. For example; how is the strength of a magnet affected by glass, plastic, and cardboard?
  • Toys: Due to their ability to counteract the force of gravity at very close range, magnets are often employed in children's toys such as the Magnet Space Wheel to amusing effect.
  • Magnets can be used to make jewelry. Necklaces and bracelets can have a magnetic clasp. Necklaces and bracelets can be made from small but strong, cylindrical magnets and slightly larger iron or steel balls connected in a pattern that is repeated until it is long enough to fit on the wrist or neck. These accessories may be fragile enough to accidentally come apart, but they also can be disassembled and reassembled with a different design. When connected as a necklace or a bracelet, magnets lose their attraction to other pieces of iron steel because they are already attached to their own iron and steel balls.
  • Magnetic levitation transport, or maglev, is a form of transportation that suspends, guides and propels vehicles (especially trains) via electromagnetic force. This method can be faster than wheeled mass transit systems, potentially reaching velocities comparable to turboprop and jet aircraft (900 km/h, 559 mph). The maximum recorded speed of a maglev train is 581 km/h (361 mph), achieved in Japan in 2003.
  • A recently developed use of magnetism is to connect portable computer power cables. This prevents any damage to the power connector and stops the computer from being pulled off a table should the power lead be stepped on.

Magnetization and demagnetization

Ferromagnetic materials can be magnetized in the following ways:


Permanent magnets can be demagnetized in the following ways:


In an electromagnet which uses a soft iron core, ceasing the current will eliminate the magnetic field. However, a slight field may remain in the core material as a result of hysteresis.

Types of permanent magnets

Magnetic metallic elements



Ceramic or ferrite

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




Ticonal magnets are an alloy of titanium, cobalt, nickel, and aluminum, with iron and small amounts of other elements. It was developed by Philips for loudspeakers.

Injection molded




Rare earth magnets



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 "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:


Most SMM's 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 which persists for long times at relatively 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.


The current cheapest permanent magnets, allowing for field strengths, are flexible and ceramic magnets, but these are also among the weakest types. Neodymium-iron-boron (NIB) magnets are among the strongest. These cost more per kilogram than most other magnetic materials, but due 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 remagnetised however. Additionally some magnets are brittle and can fracture at high temperatures.


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 for a magnet. The orientation of this effective magnet is determined via 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.


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 in magnetism

How we write the laws of magnetism depends on which set of units we employ. For most engineering applications, MKS or SI (Système International) is common. Two other sets, Gaussian and CGS-emu, are the same for magnetic properties, and are commonly used in physics.


  1. The magnetic induction field B is given in SI units of teslas (T). B is the true 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" appears 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 4pi x 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 emu, or electromagnetic unit. One A/m equals 10-3 emu. A good permanent magnet can have a magnetization as large as a million amperes per meter. Magnetic fields produced by current-carrying wires would require comparably huge currents per unit length, one reason we employ permanent magnets and electromagnets.
  4. In SI units, the relation B = μ0(H + M) holds, where μ0 is the permeability of space, which equals 4pi x 10-7 tesla meters per ampere. 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 Amperian currents.]

Materials that are not permanent magnets usually satisfy the relation M = χH in SI, where χ is the (dimensionless) magnetic susceptibility. Most non-magnetic materials have a relatively small χ (on the order of a millionth), but soft magnets can have χ on the order of hundreds or thousands. For materials satisfying M = χH, we can also write B = μ0(1 + χ)H = μ0μrH = μH, where μr = 1 + χ is the (dimensionless) relative permeability and mu=mu_0mu_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 χSI = 4πχCGS, and mu=mu_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 qm. For a bar magnet of cross-section A with uniform magnetization M along its axis, the pole strength is given by qm = MA, so that M can be thought of as a pole strength per unit area.

Fields of a magnet




Calculating the magnetic force


Force between two magnetic poles

The force between two magnetic poles is given by:

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


F is force (SI unit: newton)
qm1 and qm2 are the magnitudes of magnetic poles (SI unit: ampere meter)
r is the separation (SI unit: meter).


Force between two nearby attracting surfaces of area A and equal but opposite magnetizations M

A is the area of each surface, in m²
M is their magnetization, in A/m.
mu_0 is the permeability of space, which equals 4pi x 10-7 tesla-meters per ampere

Force between two bar magnets

F=left[frac {B_0^2 A^2 left(L^2+R^2 right)} {pimu_0L^2}right] left[{frac 1 {x^2}} + {frac 1 {(x+2L)^2}} - {frac 2 {(x+L)^2}} right]
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
x is the separation between the two magnets, in m
B0 =frac{mu_0}{2}M relates the flux density at the pole to the magnetization of the magnet.

See also

Online references

Printed references

1. "positive pole n." The Concise Oxford English Dictionary. Ed. Catherine Soanes and Angus Stevenson. Oxford University Press, 2004. Oxford Reference Online. Oxford University Press.

2. 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 don't 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.

3. Edward P. Furlani, "Permanent Magnet and Electromechanical Devices: Materials, Analysis and Applications", Academic Press Series in Electromagnetism (2001). ISBN 0-12-269951-3.

Footnotes and References

External links

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