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A magnet is a material or object that produces a magnetic field. A "hard" or "permanent" magnet is one which stays magnetized for a long time, such as magnets often used in refrigerator doors. Permanent magnets occur naturally in some Rock (geology)s, particularly lodestone, but are now more commonly manufactured. A "soft" or "impermanent" magnet is one which loses its memory of previous magnetizations. "Soft" magnetic materials are often used in electromagnets to enhance (often hundreds or thousands of times) the magnetic field of a wire that carries an electrical current and is wrapped around the magnet; the field of the "soft" magnet increases with the current.

Two measures of a material's magnetic properties are its magnetic moment and its magnetization. A material without a permanent magnetic moment can, in the presence of magnetic fields, be attracted (paramagnetic), or repelled (diamagnetic). Liquid oxygen is paramagnetic; graphite is diamagnetic. Paramagnets tend to intensify the magnetic field in their vicinity, whereas diamagnets tend to weaken it. "Soft" magnets, which are strongly attracted to magnetic fields, can be thought of as strongly paramagnetic; superconductors, which are strongly repelled by magnetic fields, can be thought of as strongly diamagnetic.

Qualities The magnetic field, magnetic moment, and magnetization are Vector (spatial), meaning they have direction and magnitude. The magnetic moment and magnetization are properties only of the magnet, while the magnetic field it produces depends on the position relative to the magnet. The magnetic moment points from its south pole to its north pole. Also, its north pole points towards the Earth's geographic north pole, which is a magnetic south pole. A compass needle is approximately a bar magnet.

Magnetic field strength A magnetic field can be measured using a good magnetic compass (this is a small permanent magnet). The direction of the field at a point in space is the direction in which the compass needle points when it passes through that point and is in equilibrium. The magnitude (or strength, usually denoted by the symbol B) of a magnetic field can also be measured using a compass, if the field is, like the Earth's, nearly uniform over the volume occupied by the needle. The needle is rotated about its center, and this makes it oscillate about its equilibrium position. The period t of oscillation is measured. For small oscillation angles, the frequency of the oscillation, 1/t, is proportional to the square root of B. This is a result from the theory of rotational motion and the theory of the torque on a magnet, and can be tested by creating an electromagnet, which makes a magnetic field proportional to the electric current that it carries. The common unit of magnetic field is the tesla, denoted "T", equal to one N/(A·m) (Force/(Current·Distance)), or Weber (unit)/m² (magnetic flux per area), and about 20,000 times the Earth magnetic field. Technically, B should be called the magnetic induction field, because changing B induces an electric field, by Faraday's Law of electromagnetic induction.

Magnetic moment The magnetic moment μ of a magnet is the magnetic strength of the field at a distance r from the magnet. At large distances, the magnetic field B is proportional to μ and inversely proportional to r³. So, μ can be obtained by measuring B at a distance r. The common unit for magnetic moment is A·m². A wire in the shape of a circle with area A and carrying current I has a magnetic moment equal to IA.

Magnetization Magnetization of an object is its magnetic moment per unit volume. It is usually denoted M and has the units A/m. A good bar magnet may have a magnetic moment of 0.1 A·m² and a volume of 1 cm³, or 0.000001 m³, and therefore a magnetization of 100,000 A/m. Iron can have a magnetization of around a million A/m.

Magnetic Domains The magnetic moment of atoms in a Ferromagnetism material cause them to behave something like tiny permanent magnets. They stick together and align themselves into small regions of more or less uniform alignment called magnetic domains or Weiss domains. Magnetic domains can be observed with Magnetic Force Microscopy to reveal magnetic domain boundaries that resemble white lines in the sketch.There are many scientific experiments that can physically show magnetic fields.

When a domain contains too many molecules, it becomes unstable and divides into two domains aligned in opposite directions so that they stick together more stably as shown at the right.

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.

When magnetized strongly enough that the prevailing domain overruns all others to result in only one single domain, the material is magnetically saturated. When a magnetized ferromagnetic material is heated to the Curie point temperature, the molecules are agitated to the point that the magnetic domains lose the organization and the magnetic properties they cause cease. When the material is cooled, this domain alignment structure spontaneously returns as the material develops its crystalline structure.

Physical origin of magnetism Magnetism, ultimately, is due to the motion of electric charge. For a macroscopic object, like a wire loop, an electric current flowing through it has a magnetic moment. Far from the loop there is a magnetic field proportional in strength to its magnetic moment.

For a microscopic object, the physical picture is more complex. An electron within an atom can have orbital angular momentum and a magnetic moment proportional to that orbital angular momentum; the electron also has intrinsic angular momentum, or spin, and a magnetic moment proportional to that spin angular momentum. The orbital and spin angular momentum of an electron are comparable in magnitude, as are their magnetic moments. Far from the electron there is a magnetic field proportional in strength to its magnetic moment.

In addition, within the atomic nucleus are both neutrons and protons, and these too have orbital and spin angular momentum, and associated magnetic moments. However, the nuclear magnetic moment typically is much smaller than the electron magnetic moment, because although the magnetic moment is proportional to its angular momentum (comparable to that of the electron) it is also inversely proportional to its mass. Nevertheless, it is the nucleus's relatively small nuclear magnetic moment that is responsible for nuclear magnetic resonance (NMR), which is the basis for magnetic resonance imaging (MRI).

Although most atoms and molecules have a net magnetic moment at temperatures well below room temperature, at room temperature they typically have no net magnetic moment. However, they can often be magnetized. If the orbital magnetic properties dominate, the response typically will be diamagnetic; if the intrinsic magnetic properties dominate, the response typically will be paramagnetic.

Solids are collections of atoms and molecules. At room temperature most solids are either diamagnetic or paramagnetic.

Although for many purposes it is convenient to think of a magnet as having magnetic poles, it must be remembered that no isolated magnetic pole has ever been observed. As indicated above, the proper description is ultimately one due to electrical currents. For a magnet, these currents should be thought of as circulating about its atoms, and flowing without any electrical resistance. This physical picture is due to André-Marie Ampère, and these atomic currents are known as Amperian currents. For a uniformly magnetized bar magnet in the shape of a cylinder, the net effect of the atomic currents is to make the magnet behave as if there is a sheet of current flowing around the cylinder, with local flow direction normal to the cylinder axis. 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 current flow. Permanent magnets A few elements -- especially iron, cobalt, and nickel -- are ferromagnetic at room temperature. When quantum mechanics and the Pauli Exclusion Principle are accounted for, the electrical energy within these atoms is found to be lower if the magnetic moments of the valence electrons are aligned. This makes them ferromagnetic. Every ferromagnet has its own individual temperature, called the Curie temperature, or Curie point, above which it loses its ferromagnetic properties. This is because the thermal tendency to disorder overwhelms the energy lowering due to ferromagnetic order. A perfectly aligned ferromagnet is said to have long-range order because all of its atoms have their magnetic moments pointing in the same direction. Real ferromagnets are not perfectly aligned, but rather contain perfectly aligned regions, called magnetic domains, which have their own magnetization directions.

A long bar magnet appears to have a north pole at one end and a south pole at the other. Near either end the magnetic field falls off inversely with the square of the distance from that pole.

For a magnet of any shape, at distances large compared to its size, the strength of the magnetic field falls off inversely with the cube of the distance from the magnet's center.

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 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.

If the coil of wire is wrapped around a material with no special magnetic properties (i.e., 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 magnets are used to focus particle beams.

Characteristics Permanent magnets and dipoles All magnets appear to have at least one north pole (reckoned positive) and at least one south pole (reckoned negative), and the net pole strength of every magnet is zero. Despite their apparent reality, as suggested by the image at the top of the page, where iron filings concentrate in regions of large magnetic field, poles are not physical objects on or in the magnet. They are simply a useful concept for describing magnets. Rather than poles being the fundamental unit, it is the magnetic dipole that is the fundamental unit. A magnetic dipole can be thought of as a combination of a positive and a negative pole that are microscopically close to one another and inseparable. This is not a bad description of the magnetic dipole of an electron in a magnetic material.

The effect of aligning many dipoles and placing them head-to-tail in a line is that there appears a north pole at one end and a south pole at the other, with all the intermediate north and south poles canceling out. The net effect is a very long dipole that appears to have poles only at its ends. Alternatively, aligning many dipoles and placing them on a sheet producing an object whose magnetic field is like that of a wire carrying current around the perimeter of the sheet.

North-south pole designation and the Earth's magnetic field A standard naming system for the poles of magnets is important. Historically, the terms north and south reflect awareness of the relationship between magnets and the earth's magnetic field. A freely suspended magnet will eventually orient itself north-to-south, because of its attraction to the north and south magnetic poles of the earth. The end of a magnet that points (approximately) toward the Earth's geographic North Pole is labeled as the north pole of the magnet; correspondingly, the end that points south is the south pole of the magnet. (The actual geographic north pole is in a slightly different location than the corresponding magnetic pole; see Magnetic North Pole.)

The Earth's present geographic north is thus actually its magnetic south. Confounding the situation further, magnetized rocks on the ocean floor show that the Earth's magnetic field has geomagnetic reversal in the past, so this system of naming is likely to be incorrect at some time in the future.

Fortunately, by using an electromagnet and the right hand rule relating the electromagnet's current and the magnetic field it produces, the orientation of the field of a magnet can be defined without reference to the Earth's geomagnetic field.

To avoid the confusion between geographic and magnetic north and south poles, the terms positive and negative are sometimes used for the poles of a magnet. The positive pole is that which seeks geographical north.

Common uses
































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 flow of 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 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"). Due to the way their regular crystalline atomic structure causes their spins to interact, some metals are (ferro)magnetic when found in their natural states, as ores. These include iron ore (magnetite or lodestone), cobalt and nickel, as well the rare earth metals gadolinium and dysprosium (when at a very low temperature). Such naturally occurring (ferro)magnets were used in the first experiments with magnetism. Technology has since expanded the availability of magnetic materials to include various manmade products, all based, however, on naturally magnetic elements.

Composites Ceramic or ferrite Ceramic, or ferrite, magnets are made of a sintered composite material 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.

Alnico 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.

Injection molded Injection molding 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 Flexible magnets are similar to injection molded magnets, using a flexible resin or binder such as vinyl, and produced in flat strips or sheets. These magnets are lower in magnetic strength but can be very flexible, depending on the binder used.

Rare earth magnets 'Rare earth' (lanthanoid) elements have a partially occupied f electron shell (which can accommodate up to 14 electrons.) The spin of these electrons can be aligned, resulting in very strong magnetic fields, and therefore these elements are used in compact high-strength magnets where their higher price is not a concern.

Samarium-cobalt Samarium-cobalt magnets are highly resistant to oxidation, with higher magnetic strength and temperature resistance than alnico or ceramic materials. Sintered samarium-cobalt magnets are brittle and prone to chipping and cracking and may fracture when subjected to thermal shock.

Neodymium-iron-boron (NIB) Neodymium magnets, more formally referred to as neodymium-iron-boron (NdFeB) magnets, have the highest magnetic field strength, but are inferior to samarium cobalt in resistance to oxidation and temperature. This type of magnet has traditionally been expensive, due to both the cost of raw materials and licensing of the patents involved. This high cost limited their use to applications where such high strengths from a compact magnet are critical. Use of protective surface treatments such as gold, nickel, zinc and tin plating and epoxy resin coating can provide corrosion protection where required. Beginning in the 1980s, NIB magnets have increasingly become less expensive and more popular in other applications such as children's magnetic building toys. Even tiny neodymium magnets are very powerful and have important safety considerations.Magnet Man, Magnet Basics - Safety Considerations accessed 6 October 2006.

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 "domain" level and theoretically could provide a far denser storage medium than conventional magnets. In this direction research on monolayers of SMMs is currently under way. Very briefly, the two main attributes of an SMM are:

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


    • Most 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.

    See results from NIST published April 2005, or

    Magnetic behaviors There are many forms of magnetic behavior, and all materials exhibit at least one of these behaviors. Magnets vary in the permanency of their magnetization and the strength of the magnetic field that is created.

    Paramagnetism Most popularly found in paper clips, paramagnetism is exhibited in substances which do not emit fields by themselves, but when exposed to a magnetic field, its electrons will begin to spin in such a manner that the substance emits a field of its own. A good analogy 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.

    Diamagnetism Unscientifically referred to as 'non-magnetic,' diamagnets actually exhibit some magnetic behavior - just to very small magnitudes. While paramagnetism is affected more by the direction of the spin of electrons, diamagnetism is affected by electrons' centripetal forces. Under the influence of a field, electrons of opposite spin will see opposite effects to their centripetal force: one will increase and one will decrease. This results in a very small magnetic force. All materials exhibit this type of magnetism, however, when diamagnetism pairs with a stronger type of magnetic behavior, the diamagnetic effect is severely overshadowed.

    Ferromagnetism This is the 'popular' perception of a magnet. Ferromagnetic materials have a high retainment for magnetization, and a common example is a traditional refrigerator magnet. By technicality, ferromagnetism exists when all of the atoms contribute to the magnetic force emitted. The mechanical explanation of this is similar to that of paramagnetism - the electrons' spins align such it creates a magnetic force. However, unlike paramagnetic substances, a ferromagnet will retain this spin alignment.

    Ferrimagnetism Like ferromagnetism, ferrimagnets retain their magnetization in the absence of a field. However, they are arranged such that some of its atoms oppose the magnetic moment. These atoms are said to be anti-aligned. The first discovered magnetic substance, magnetite, was originally believed to be a ferromagnet; Louis Néel disproved this, however, with the discovery of ferrimagnetism.

    Antiferromagnetism When all atoms are arranged in a substance so that they are anti-aligned, the substance is antiferromagnetic. Antiferromagnets have a zero net magnetic moment, meaning no field is emitted by them. Antiferromagnets are less common compared to the other types of behaviors, and are mostly observed at low temperatures. In varying temperatures, antiferromagnets can be seen to exhibit diamagnetic and ferrimagnetic properties.

    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.

    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 T (tesla). 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 G (gauss). One T equals 104 G.

    (2) The magnetic field H is given in SI units of ampere-turns/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 Oe (oersted). One A-turn/m equals 4\pi x 10-3 Oe.

    (3) The magnetization M is given in SI units of ampere/meter (A/m). In CGS the unit of M is the emu, or electromagnetic unit. One A/m equals10-3 emu. A good permanent magnet can have a magnetization as large as a million A/m. 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=\mu_0(H+M) holds, where \mu_0 is the permeability of space, which equals 4\pi x 10-7 tesla∙meter/ampere. In CGS it is written as B=H+4\piM.

    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's on the order of hundreds or thousands. For materials satisfying M=χH, we can also write B=\mu_0(1+χ)H=\mu_0\mu_rH=\muH, where \mu_r=1+χ is the (dimensionless) relative permeability and \mu=\mu_0\mu_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 \chi(SI)=4\pi\chi(CGS), 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 "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.

    Calculating the magnetic force Calculating the attractive or repulsive force between two magnets is, in the general case, an extremely complex operation, as it depends on the shape, magnetization, orientation and separation of the magnets.

    Force between two magnetic poles The force between two magnetic poles is given by:

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

    where F is force (SI unit: newton) qm1 and qm2 are the pole strengths (SI unit: ampere-meter) μ is the Permeability (electromagnetism) of the intervening medium (SI unit: tesla (unit) metre per ampere or henry per meter) r is the separation (SI unit: meter).

    The pole description is useful to practicing magneticians who design 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 attracting surfaces of area A and equal but opposite magnetizations M F=\frac{\mu_0}{2}AM^2 where A is the area of each surface, in m2 M is their magnetization, in ampere/m. \mu_0 is the permeability of space, which equals 4\pi x 10-7 tesla∙meter/ampere

    Force between two bar magnets The force between two identical cylindrical bar magnets placed end-to-end is given by: F=\left {B_0^2 A^2 \left( L^2+R^2 \right)} {\pi\mu_0L^2}\right \left 1 {x^2--> + {\frac 1 {(x+2L)^2--> - {\frac 2 {(x+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 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.

    References External links



    A magnet is a material or object that produces a magnetic field. A "hard" or "permanent" magnet is one which stays magnetized for a long time, such as magnets often used in refrigerator doors. Permanent magnets occur naturally in some Rock (geology)s, particularly lodestone, but are now more commonly manufactured. A "soft" or "impermanent" magnet is one which loses its memory of previous magnetizations. "Soft" magnetic materials are often used in electromagnets to enhance (often hundreds or thousands of times) the magnetic field of a wire that carries an electrical current and is wrapped around the magnet; the field of the "soft" magnet increases with the current.

    Two measures of a material's magnetic properties are its magnetic moment and its magnetization. A material without a permanent magnetic moment can, in the presence of magnetic fields, be attracted (paramagnetic), or repelled (diamagnetic). Liquid oxygen is paramagnetic; graphite is diamagnetic. Paramagnets tend to intensify the magnetic field in their vicinity, whereas diamagnets tend to weaken it. "Soft" magnets, which are strongly attracted to magnetic fields, can be thought of as strongly paramagnetic; superconductors, which are strongly repelled by magnetic fields, can be thought of as strongly diamagnetic.

    Qualities The magnetic field, magnetic moment, and magnetization are Vector (spatial), meaning they have direction and magnitude. The magnetic moment and magnetization are properties only of the magnet, while the magnetic field it produces depends on the position relative to the magnet. The magnetic moment points from its south pole to its north pole. Also, its north pole points towards the Earth's geographic north pole, which is a magnetic south pole. A compass needle is approximately a bar magnet.

    Magnetic field strength A magnetic field can be measured using a good magnetic compass (this is a small permanent magnet). The direction of the field at a point in space is the direction in which the compass needle points when it passes through that point and is in equilibrium. The magnitude (or strength, usually denoted by the symbol B) of a magnetic field can also be measured using a compass, if the field is, like the Earth's, nearly uniform over the volume occupied by the needle. The needle is rotated about its center, and this makes it oscillate about its equilibrium position. The period t of oscillation is measured. For small oscillation angles, the frequency of the oscillation, 1/t, is proportional to the square root of B. This is a result from the theory of rotational motion and the theory of the torque on a magnet, and can be tested by creating an electromagnet, which makes a magnetic field proportional to the electric current that it carries. The common unit of magnetic field is the tesla, denoted "T", equal to one N/(A·m) (Force/(Current·Distance)), or Weber (unit)/m² (magnetic flux per area), and about 20,000 times the Earth magnetic field. Technically, B should be called the magnetic induction field, because changing B induces an electric field, by Faraday's Law of electromagnetic induction.

    Magnetic moment The magnetic moment μ of a magnet is the magnetic strength of the field at a distance r from the magnet. At large distances, the magnetic field B is proportional to μ and inversely proportional to r³. So, μ can be obtained by measuring B at a distance r. The common unit for magnetic moment is A·m². A wire in the shape of a circle with area A and carrying current I has a magnetic moment equal to IA.

    Magnetization Magnetization of an object is its magnetic moment per unit volume. It is usually denoted M and has the units A/m. A good bar magnet may have a magnetic moment of 0.1 A·m² and a volume of 1 cm³, or 0.000001 m³, and therefore a magnetization of 100,000 A/m. Iron can have a magnetization of around a million A/m.

    Magnetic Domains The magnetic moment of atoms in a Ferromagnetism material cause them to behave something like tiny permanent magnets. They stick together and align themselves into small regions of more or less uniform alignment called magnetic domains or Weiss domains. Magnetic domains can be observed with Magnetic Force Microscopy to reveal magnetic domain boundaries that resemble white lines in the sketch.There are many scientific experiments that can physically show magnetic fields.

    When a domain contains too many molecules, it becomes unstable and divides into two domains aligned in opposite directions so that they stick together more stably as shown at the right.

    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.

    When magnetized strongly enough that the prevailing domain overruns all others to result in only one single domain, the material is magnetically saturated. When a magnetized ferromagnetic material is heated to the Curie point temperature, the molecules are agitated to the point that the magnetic domains lose the organization and the magnetic properties they cause cease. When the material is cooled, this domain alignment structure spontaneously returns as the material develops its crystalline structure.

    Physical origin of magnetism Magnetism, ultimately, is due to the motion of electric charge. For a macroscopic object, like a wire loop, an electric current flowing through it has a magnetic moment. Far from the loop there is a magnetic field proportional in strength to its magnetic moment.

    For a microscopic object, the physical picture is more complex. An electron within an atom can have orbital angular momentum and a magnetic moment proportional to that orbital angular momentum; the electron also has intrinsic angular momentum, or spin, and a magnetic moment proportional to that spin angular momentum. The orbital and spin angular momentum of an electron are comparable in magnitude, as are their magnetic moments. Far from the electron there is a magnetic field proportional in strength to its magnetic moment.

    In addition, within the atomic nucleus are both neutrons and protons, and these too have orbital and spin angular momentum, and associated magnetic moments. However, the nuclear magnetic moment typically is much smaller than the electron magnetic moment, because although the magnetic moment is proportional to its angular momentum (comparable to that of the electron) it is also inversely proportional to its mass. Nevertheless, it is the nucleus's relatively small nuclear magnetic moment that is responsible for nuclear magnetic resonance (NMR), which is the basis for magnetic resonance imaging (MRI).

    Although most atoms and molecules have a net magnetic moment at temperatures well below room temperature, at room temperature they typically have no net magnetic moment. However, they can often be magnetized. If the orbital magnetic properties dominate, the response typically will be diamagnetic; if the intrinsic magnetic properties dominate, the response typically will be paramagnetic.

    Solids are collections of atoms and molecules. At room temperature most solids are either diamagnetic or paramagnetic.

    Although for many purposes it is convenient to think of a magnet as having magnetic poles, it must be remembered that no isolated magnetic pole has ever been observed. As indicated above, the proper description is ultimately one due to electrical currents. For a magnet, these currents should be thought of as circulating about its atoms, and flowing without any electrical resistance. This physical picture is due to André-Marie Ampère, and these atomic currents are known as Amperian currents. For a uniformly magnetized bar magnet in the shape of a cylinder, the net effect of the atomic currents is to make the magnet behave as if there is a sheet of current flowing around the cylinder, with local flow direction normal to the cylinder axis. 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 current flow. Permanent magnets A few elements -- especially iron, cobalt, and nickel -- are ferromagnetic at room temperature. When quantum mechanics and the Pauli Exclusion Principle are accounted for, the electrical energy within these atoms is found to be lower if the magnetic moments of the valence electrons are aligned. This makes them ferromagnetic. Every ferromagnet has its own individual temperature, called the Curie temperature, or Curie point, above which it loses its ferromagnetic properties. This is because the thermal tendency to disorder overwhelms the energy lowering due to ferromagnetic order. A perfectly aligned ferromagnet is said to have long-range order because all of its atoms have their magnetic moments pointing in the same direction. Real ferromagnets are not perfectly aligned, but rather contain perfectly aligned regions, called magnetic domains, which have their own magnetization directions.

    A long bar magnet appears to have a north pole at one end and a south pole at the other. Near either end the magnetic field falls off inversely with the square of the distance from that pole.

    For a magnet of any shape, at distances large compared to its size, the strength of the magnetic field falls off inversely with the cube of the distance from the magnet's center.

    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 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.

    If the coil of wire is wrapped around a material with no special magnetic properties (i.e., 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 magnets are used to focus particle beams.

    Characteristics Permanent magnets and dipoles All magnets appear to have at least one north pole (reckoned positive) and at least one south pole (reckoned negative), and the net pole strength of every magnet is zero. Despite their apparent reality, as suggested by the image at the top of the page, where iron filings concentrate in regions of large magnetic field, poles are not physical objects on or in the magnet. They are simply a useful concept for describing magnets. Rather than poles being the fundamental unit, it is the magnetic dipole that is the fundamental unit. A magnetic dipole can be thought of as a combination of a positive and a negative pole that are microscopically close to one another and inseparable. This is not a bad description of the magnetic dipole of an electron in a magnetic material.

    The effect of aligning many dipoles and placing them head-to-tail in a line is that there appears a north pole at one end and a south pole at the other, with all the intermediate north and south poles canceling out. The net effect is a very long dipole that appears to have poles only at its ends. Alternatively, aligning many dipoles and placing them on a sheet producing an object whose magnetic field is like that of a wire carrying current around the perimeter of the sheet.

    North-south pole designation and the Earth's magnetic field A standard naming system for the poles of magnets is important. Historically, the terms north and south reflect awareness of the relationship between magnets and the earth's magnetic field. A freely suspended magnet will eventually orient itself north-to-south, because of its attraction to the north and south magnetic poles of the earth. The end of a magnet that points (approximately) toward the Earth's geographic North Pole is labeled as the north pole of the magnet; correspondingly, the end that points south is the south pole of the magnet. (The actual geographic north pole is in a slightly different location than the corresponding magnetic pole; see Magnetic North Pole.)

    The Earth's present geographic north is thus actually its magnetic south. Confounding the situation further, magnetized rocks on the ocean floor show that the Earth's magnetic field has geomagnetic reversal in the past, so this system of naming is likely to be incorrect at some time in the future.

    Fortunately, by using an electromagnet and the right hand rule relating the electromagnet's current and the magnetic field it produces, the orientation of the field of a magnet can be defined without reference to the Earth's geomagnetic field.

    To avoid the confusion between geographic and magnetic north and south poles, the terms positive and negative are sometimes used for the poles of a magnet. The positive pole is that which seeks geographical north.

    Common uses
































    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 flow of 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 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"). Due to the way their regular crystalline atomic structure causes their spins to interact, some metals are (ferro)magnetic when found in their natural states, as ores. These include iron ore (magnetite or lodestone), cobalt and nickel, as well the rare earth metals gadolinium and dysprosium (when at a very low temperature). Such naturally occurring (ferro)magnets were used in the first experiments with magnetism. Technology has since expanded the availability of magnetic materials to include various manmade products, all based, however, on naturally magnetic elements.

    Composites Ceramic or ferrite Ceramic, or ferrite, magnets are made of a sintered composite material 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.

    Alnico 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.

    Injection molded Injection molding 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 Flexible magnets are similar to injection molded magnets, using a flexible resin or binder such as vinyl, and produced in flat strips or sheets. These magnets are lower in magnetic strength but can be very flexible, depending on the binder used.

    Rare earth magnets 'Rare earth' (lanthanoid) elements have a partially occupied f electron shell (which can accommodate up to 14 electrons.) The spin of these electrons can be aligned, resulting in very strong magnetic fields, and therefore these elements are used in compact high-strength magnets where their higher price is not a concern.

    Samarium-cobalt Samarium-cobalt magnets are highly resistant to oxidation, with higher magnetic strength and temperature resistance than alnico or ceramic materials. Sintered samarium-cobalt magnets are brittle and prone to chipping and cracking and may fracture when subjected to thermal shock.

    Neodymium-iron-boron (NIB) Neodymium magnets, more formally referred to as neodymium-iron-boron (NdFeB) magnets, have the highest magnetic field strength, but are inferior to samarium cobalt in resistance to oxidation and temperature. This type of magnet has traditionally been expensive, due to both the cost of raw materials and licensing of the patents involved. This high cost limited their use to applications where such high strengths from a compact magnet are critical. Use of protective surface treatments such as gold, nickel, zinc and tin plating and epoxy resin coating can provide corrosion protection where required. Beginning in the 1980s, NIB magnets have increasingly become less expensive and more popular in other applications such as children's magnetic building toys. Even tiny neodymium magnets are very powerful and have important safety considerations.Magnet Man, Magnet Basics - Safety Considerations accessed 6 October 2006.

    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 "domain" level and theoretically could provide a far denser storage medium than conventional magnets. In this direction research on monolayers of SMMs is currently under way. Very briefly, the two main attributes of an SMM are:

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


    • Most 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.

    See results from NIST published April 2005, or

    Magnetic behaviors There are many forms of magnetic behavior, and all materials exhibit at least one of these behaviors. Magnets vary in the permanency of their magnetization and the strength of the magnetic field that is created.

    Paramagnetism Most popularly found in paper clips, paramagnetism is exhibited in substances which do not emit fields by themselves, but when exposed to a magnetic field, its electrons will begin to spin in such a manner that the substance emits a field of its own. A good analogy 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.

    Diamagnetism Unscientifically referred to as 'non-magnetic,' diamagnets actually exhibit some magnetic behavior - just to very small magnitudes. While paramagnetism is affected more by the direction of the spin of electrons, diamagnetism is affected by electrons' centripetal forces. Under the influence of a field, electrons of opposite spin will see opposite effects to their centripetal force: one will increase and one will decrease. This results in a very small magnetic force. All materials exhibit this type of magnetism, however, when diamagnetism pairs with a stronger type of magnetic behavior, the diamagnetic effect is severely overshadowed.

    Ferromagnetism This is the 'popular' perception of a magnet. Ferromagnetic materials have a high retainment for magnetization, and a common example is a traditional refrigerator magnet. By technicality, ferromagnetism exists when all of the atoms contribute to the magnetic force emitted. The mechanical explanation of this is similar to that of paramagnetism - the electrons' spins align such it creates a magnetic force. However, unlike paramagnetic substances, a ferromagnet will retain this spin alignment.

    Ferrimagnetism Like ferromagnetism, ferrimagnets retain their magnetization in the absence of a field. However, they are arranged such that some of its atoms oppose the magnetic moment. These atoms are said to be anti-aligned. The first discovered magnetic substance, magnetite, was originally believed to be a ferromagnet; Louis Néel disproved this, however, with the discovery of ferrimagnetism.

    Antiferromagnetism When all atoms are arranged in a substance so that they are anti-aligned, the substance is antiferromagnetic. Antiferromagnets have a zero net magnetic moment, meaning no field is emitted by them. Antiferromagnets are less common compared to the other types of behaviors, and are mostly observed at low temperatures. In varying temperatures, antiferromagnets can be seen to exhibit diamagnetic and ferrimagnetic properties.

    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.

    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 T (tesla). 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 G (gauss). One T equals 104 G.

    (2) The magnetic field H is given in SI units of ampere-turns/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 Oe (oersted). One A-turn/m equals 4\pi x 10-3 Oe.

    (3) The magnetization M is given in SI units of ampere/meter (A/m). In CGS the unit of M is the emu, or electromagnetic unit. One A/m equals10-3 emu. A good permanent magnet can have a magnetization as large as a million A/m. 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=\mu_0(H+M) holds, where \mu_0 is the permeability of space, which equals 4\pi x 10-7 tesla∙meter/ampere. In CGS it is written as B=H+4\piM.

    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's on the order of hundreds or thousands. For materials satisfying M=χH, we can also write B=\mu_0(1+χ)H=\mu_0\mu_rH=\muH, where \mu_r=1+χ is the (dimensionless) relative permeability and \mu=\mu_0\mu_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 \chi(SI)=4\pi\chi(CGS), 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 "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.

    Calculating the magnetic force Calculating the attractive or repulsive force between two magnets is, in the general case, an extremely complex operation, as it depends on the shape, magnetization, orientation and separation of the magnets.

    Force between two magnetic poles The force between two magnetic poles is given by:

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

    where F is force (SI unit: newton) qm1 and qm2 are the pole strengths (SI unit: ampere-meter) μ is the Permeability (electromagnetism) of the intervening medium (SI unit: tesla (unit) metre per ampere or henry per meter) r is the separation (SI unit: meter).

    The pole description is useful to practicing magneticians who design 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 attracting surfaces of area A and equal but opposite magnetizations M F=\frac{\mu_0}{2}AM^2 where A is the area of each surface, in m2 M is their magnetization, in ampere/m. \mu_0 is the permeability of space, which equals 4\pi x 10-7 tesla∙meter/ampere

    Force between two bar magnets The force between two identical cylindrical bar magnets placed end-to-end is given by: F=\left {B_0^2 A^2 \left( L^2+R^2 \right)} {\pi\mu_0L^2}\right \left 1 {x^2--> + {\frac 1 {(x+2L)^2--> - {\frac 2 {(x+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 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.

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