Magnetism

Magnetism is a class of physical phenomena that are mediated by magnetic fields. Electric currents and the magnetic moments of elementary particles give rise to a magnetic field, which acts on other currents and magnetic moments. The most familiar effects occur in ferromagnetic materials, which are strongly attracted by magnetic fields and can be magnetized to become permanent magnets, producing magnetic fields themselves. Only a few substances are ferromagnetic; the most common ones are iron, nickel and cobalt and their alloys. The prefix ferro- refers to iron, because permanent magnetism was first observed in lodestone, a form of natural iron ore called magnetite, Fe3O4.

Although ferromagnetism is responsible for most of the effects of magnetism encountered in everyday life, all other materials are influenced to some extent by a magnetic field, by several other types of magnetism. Paramagnetic substances such as aluminum and oxygen are weakly attracted to an applied magnetic field; diamagnetic substances such as copper and carbon are weakly repelled; while antiferromagnetic materials such as chromium and spin glasses have a more complex relationship with a magnetic field. The force of a magnet on paramagnetic, diamagnetic, and antiferromagnetic materials is usually too weak to be felt, and can be detected only by laboratory instruments, so in everyday life these substances are often described as non-magnetic.

The magnetic state (or magnetic phase) of a material depends on temperature and other variables such as pressure and the applied magnetic field. A material may exhibit more than one form of magnetism as these variables change.

Magnetic quadrupole moment
A magnetic quadrupole

History

Lodestone attracting nails
Lodestone, a natural magnet, attracting iron nails. Ancient humans discovered the property of magnetism from lodestone.
Blacksmith at the anvil. Wellcome L0005875
An illustration from Gilbert's 1600 De Magnete showing one of the earliest methods of making a magnet. A blacksmith holds a piece of red-hot iron in a north-south direction and hammers it as it cools. The magnetic field of the Earth aligns the domains, leaving the iron a weak magnet.
A man is violently rubbed with magnets. Coloured lithograph Wellcome V0011767
Drawing of a medical treatment using magnetic brushes. Charles Jacque 1843, France.

Magnetism was first discovered in the ancient world, when people noticed that lodestones, naturally magnetized pieces of the mineral magnetite, could attract iron.[1] The word magnet comes from the Greek term μαγνῆτις λίθος magnētis lithos,[2] "the Magnesian stone,[3] lodestone." In ancient Greece, Aristotle attributed the first of what could be called a scientific discussion of magnetism to the philosopher Thales of Miletus, who lived from about 625 BC to about 545 BC.[4] The ancient Indian medical text Sushruta Samhita describes using magnetite to remove arrows embedded in a person's body.[5]

In ancient China, the earliest literary reference to magnetism lies in a 4th-century BC book named after its author, The Sage of Ghost Valley.[6] The 2nd-century BC annals, Lüshi Chunqiu, also notes: "The lodestone makes iron approach, or it attracts it."[7] The earliest mention of the attraction of a needle is in a 1st-century work Lunheng (Balanced Inquiries): "A lodestone attracts a needle."[8] The 11th-century Chinese scientist Shen Kuo was the first person to write—in the Dream Pool Essays—of the magnetic needle compass and that it improved the accuracy of navigation by employing the astronomical concept of true north. By the 12th century the Chinese were known to use the lodestone compass for navigation. They sculpted a directional spoon from lodestone in such a way that the handle of the spoon always pointed south.

Alexander Neckam, by 1187, was the first in Europe to describe the compass and its use for navigation. In 1269, Peter Peregrinus de Maricourt wrote the Epistola de magnete, the first extant treatise describing the properties of magnets. In 1282, the properties of magnets and the dry compasses were discussed by Al-Ashraf, a Yemeni physicist, astronomer, and geographer.[9]

In 1600, William Gilbert published his De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure (On the Magnet and Magnetic Bodies, and on the Great Magnet the Earth). In this work he describes many of his experiments with his model earth called the terrella. From his experiments, he concluded that the Earth was itself magnetic and that this was the reason compasses pointed north (previously, some believed that it was the pole star (Polaris) or a large magnetic island on the north pole that attracted the compass).

An understanding of the relationship between electricity and magnetism began in 1819 with work by Hans Christian Ørsted, a professor at the University of Copenhagen, who discovered by the accidental twitching of a compass needle near a wire that an electric current could create a magnetic field. This landmark experiment is known as Ørsted's Experiment. Several other experiments followed, with André-Marie Ampère, who in 1820 discovered that the magnetic field circulating in a closed-path was related to the current flowing through the perimeter of the path; Carl Friedrich Gauss; Jean-Baptiste Biot and Félix Savart, both of whom in 1820 came up with the Biot–Savart law giving an equation for the magnetic field from a current-carrying wire; Michael Faraday, who in 1831 found that a time-varying magnetic flux through a loop of wire induced a voltage, and others finding further links between magnetism and electricity. James Clerk Maxwell synthesized and expanded these insights into Maxwell's equations, unifying electricity, magnetism, and optics into the field of electromagnetism. In 1905, Einstein used these laws in motivating his theory of special relativity,[10] requiring that the laws held true in all inertial reference frames.

Electromagnetism has continued to develop into the 21st century, being incorporated into the more fundamental theories of gauge theory, quantum electrodynamics, electroweak theory, and finally the standard model.

Sources of magnetism

Magnetism, at its root, arises from two sources:

  1. Electric current.
  2. Spin magnetic moments of elementary particles.

The magnetic properties of materials are mainly due to the magnetic moments of their atoms' orbiting electrons. The magnetic moments of the nuclei of atoms 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 nevertheless very important in other contexts, particularly in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI).

Ordinarily, the enormous number of 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), and combining into filled subshells with zero net orbital motion. In both cases, the electrons preferentially adopt arrangements in which the magnetic moment of each electron is cancelled by the opposite moment of another 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.

Sometimes, either spontaneously, or owing to an applied external magnetic field—each of the electron magnetic moments will be, on average, lined up. A suitable material can then produce a strong net magnetic field.

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.

Materials

Magnetism
Hierarchy of types of magnetism.[11]

Diamagnetism

Diamagnetism appears in all materials, and is the tendency of a material to oppose an applied magnetic field, and therefore, to be repelled by a magnetic field. However, in a material with paramagnetic properties (that is, with a tendency to enhance an external magnetic field), the paramagnetic behavior dominates.[12] Thus, despite its universal occurrence, diamagnetic behavior is observed only in a purely diamagnetic material. In a diamagnetic material, there are no unpaired electrons, so the intrinsic electron magnetic moments cannot produce any bulk effect. In these cases, the magnetization arises from the electrons' orbital motions, which can be understood classically as follows:

When a material is put in a magnetic field, the electrons circling the nucleus will experience, in addition to their Coulomb attraction to the nucleus, a Lorentz force from the magnetic field. Depending on which direction the electron is orbiting, this force may increase the centripetal force on the electrons, pulling them in towards the nucleus, or it may decrease the force, pulling them away from the nucleus. This effect systematically increases the orbital magnetic moments that were aligned opposite the field, and decreases the ones aligned parallel to the field (in accordance with Lenz's law). This results in a small bulk magnetic moment, with an opposite direction to the applied field.

Note that this description is meant only as a heuristic; the Bohr-van Leeuwen theorem shows that diamagnetism is impossible according to classical physics, and that a proper understanding requires a quantum-mechanical description.

Note that all materials undergo this orbital response. However, in paramagnetic and ferromagnetic substances, the diamagnetic effect is overwhelmed by the much stronger effects caused by the unpaired electrons.

Paramagnetism

In a paramagnetic material 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, causing their magnetic fields to cancel out, 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.

Ferromagnetism

Ferromagneses penzermek 1
Tip of permanent magnet with coins demonstrating ferromagnetism

A ferromagnet, like a paramagnetic substance, has unpaired electrons. However, in addition to the electrons' intrinsic magnetic moment's tendency to be parallel to an applied field, there is also in these materials a tendency for these magnetic moments to orient parallel to each other to maintain a lowered-energy state. Thus, even in the absence of an applied field, the magnetic moments of the electrons in the material spontaneously line up parallel to one another.

Every ferromagnetic substance 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.

Ferromagnetism only occurs in a few substances; common ones are iron, nickel, cobalt, their alloys, and some alloys of rare-earth metals.

Magnetic domains

Magnetic Domains 2
Magnetic domains boundaries (white lines) in ferromagnetic material (black rectangle)
Magnetic Domains 3
Effect of a magnet on the domains

The magnetic moments of atoms in a ferromagnetic 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 a magnetic force microscope 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 (dotted yellow area), as shown at the left. When the magnetizing field is removed, the domains may not return to an unmagnetized state. This results in the ferromagnetic material's 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, in a manner roughly analogous to how a liquid can freeze into a crystalline solid.

Antiferromagnetism

In an antiferromagnet, unlike a ferromagnet, there is a tendency for the intrinsic magnetic moments of neighboring valence electrons to point in opposite directions. When all atoms are arranged in a substance so that each neighbor is anti-parallel, the substance is antiferromagnetic. Antiferromagnets have a zero net magnetic moment, meaning that no field is produced 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 ferromagnetic properties.

In some materials, neighboring electrons prefer to point in opposite directions, but there is no geometrical arrangement in which each pair of neighbors is anti-aligned. This is called a spin glass and is an example of geometrical frustration.

Ferrimagnetism

Ferrimagnetic ordering
Ferrimagnetic ordering

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

Most ferrites are ferrimagnetic. The first discovered magnetic substance, magnetite, is a ferrite and was originally believed to be a ferromagnet; Louis Néel disproved this, however, after discovering ferrimagnetism.

Superparamagnetism

When a ferromagnet or ferrimagnet is sufficiently small, it acts like a single magnetic spin that is subject to Brownian motion. Its response to a magnetic field is qualitatively similar to the response of a paramagnet, but much larger.

Other types of magnetism

Electromagnet

Electromagnet
An electromagnet attracts paper clips when current is applied creating a magnetic field. The electromagnet loses them when current and magnetic field are removed.

An electromagnet is a type of magnet in which the magnetic field is produced by an electric current.[13] The magnetic field disappears when the current is turned off. Electromagnets usually consist of a large number of closely spaced turns of wire that create the magnetic field. The wire turns are often wound around a magnetic core made from a ferromagnetic or ferrimagnetic material such as iron; the magnetic core concentrates the magnetic flux and makes a more powerful magnet.

The main advantage of an electromagnet over a permanent magnet is that the magnetic field can be quickly changed by controlling the amount of electric current in the winding. However, unlike a permanent magnet that needs no power, an electromagnet requires a continuous supply of current to maintain the magnetic field.

Electromagnets are widely used as components of other electrical devices, such as motors, generators, relays, solenoids, loudspeakers, hard disks, MRI machines, scientific instruments, and magnetic separation equipment. Electromagnets are also employed in industry for picking up and moving heavy iron objects such as scrap iron and steel.[14] Electromagnetism was discovered in 1820.[15]

Magnetism, electricity, and special relativity

MagnetismFromLengthContraction
Magnetism from length-contraction.

As a consequence of Einstein's theory of special relativity, electricity and magnetism are fundamentally interlinked. Both magnetism lacking electricity, and electricity without magnetism, are inconsistent with special relativity, due to such effects as length contraction, time dilation, and the fact that the magnetic force is velocity-dependent. However, when both electricity and magnetism are taken into account, the resulting theory (electromagnetism) is fully consistent with special relativity.[10][16] In particular, a phenomenon that appears purely electric or purely magnetic to one observer may be a mix of both to another, or more generally the relative contributions of electricity and magnetism are dependent on the frame of reference. Thus, special relativity "mixes" electricity and magnetism into a single, inseparable phenomenon called electromagnetism, analogous to how relativity "mixes" space and time into spacetime.

All observations on electromagnetism apply to what might be considered to be primarily magnetism, e.g. perturbations in the magnetic field are necessarily accompanied by a nonzero electric field, and propagate at the speed of light.

Magnetic fields in a material

In a vacuum,

where μ0 is the vacuum permeability.

In a material,

The quantity μ0M is called magnetic polarization.

If the field H is small, the response of the magnetization M in a diamagnet or paramagnet is approximately linear:

the constant of proportionality being called the magnetic susceptibility. If so,

In a hard magnet such as a ferromagnet, M is not proportional to the field and is generally nonzero even when H is zero (see Remanence).

Magnetic force

Magnet0873
Magnetic lines of force of a bar magnet shown by iron filings on paper
Detecting magnetic field with compass and with iron filings

The phenomenon of magnetism is "mediated" by the magnetic field. An electric current or magnetic dipole creates a magnetic field, and that field, in turn, imparts magnetic forces on other particles that are in the fields.

Maxwell's equations, which simplify to the Biot–Savart law in the case of steady currents, describe the origin and behavior of the fields that govern these forces. Therefore, magnetism is seen whenever electrically charged particles are in motion—for example, from movement of electrons in an electric current, or in certain cases from the orbital motion of electrons around an atom's nucleus. They also arise from "intrinsic" magnetic dipoles arising from quantum-mechanical spin.

The same situations that create magnetic fields—charge moving in a current or in an atom, and intrinsic magnetic dipoles—are also the situations in which a magnetic field has an effect, creating a force. Following is the formula for moving charge; for the forces on an intrinsic dipole, see magnetic dipole.

When a charged particle moves through a magnetic field B, it feels a Lorentz force F given by the cross product:[17]

where

is the electric charge of the particle, and
v is the velocity vector of the particle

Because this is a cross product, the force is perpendicular to both the motion of the particle and the magnetic field. It follows that the magnetic force does no work on the particle; it may change the direction of the particle's movement, but it cannot cause it to speed up or slow down. The magnitude of the force is

where is the angle between v and B.

One tool for determining the direction of the velocity vector of a moving charge, the magnetic field, and the force exerted is labeling the index finger "V", the middle finger "B", and the thumb "F" with your right hand. When making a gun-like configuration, with the middle finger crossing under the index finger, the fingers represent the velocity vector, magnetic field vector, and force vector, respectively. See also right-hand rule.

Magnetic dipoles

A very common source of magnetic field found in nature is a dipole, with a "South pole" and a "North pole", terms dating back to the use of magnets as compasses, interacting with the Earth's magnetic field to indicate North and South on the globe. Since opposite ends of magnets are attracted, the north pole of a magnet is attracted to the south pole of another magnet. The Earth's North Magnetic Pole (currently in the Arctic Ocean, north of Canada) is physically a south pole, as it attracts the north pole of a compass. A magnetic field contains energy, and physical systems move toward configurations with lower energy. When diamagnetic material is placed in a magnetic field, a magnetic dipole tends to align itself in opposed polarity to that field, thereby lowering the net field strength. When ferromagnetic material is placed within a magnetic field, the magnetic dipoles align to the applied field, thus expanding the domain walls of the magnetic domains.

Magnetic monopoles

Since a bar magnet gets its ferromagnetism from electrons distributed evenly throughout the bar, when a bar magnet is cut in half, each of the resulting pieces is a smaller bar magnet. Even though a magnet is said to have a north pole and a south pole, these two poles cannot be separated from each other. A monopole—if such a thing exists—would be a new and fundamentally different kind of magnetic object. It would act as an isolated north pole, not attached to a south pole, or vice versa. Monopoles would carry "magnetic charge" analogous to electric charge. Despite systematic searches since 1931, as of 2010, they have never been observed, and could very well not exist.[18]

Nevertheless, some theoretical physics models predict the existence of these magnetic monopoles. Paul Dirac observed in 1931 that, because electricity and magnetism show a certain symmetry, just as quantum theory predicts that individual positive or negative electric charges can be observed without the opposing charge, isolated South or North magnetic poles should be observable. Using quantum theory Dirac showed that if magnetic monopoles exist, then one could explain the quantization of electric charge—that is, why the observed elementary particles carry charges that are multiples of the charge of the electron.

Certain grand unified theories predict the existence of monopoles which, unlike elementary particles, are solitons (localized energy packets). The initial results of using these models to estimate the number of monopoles created in the big bang contradicted cosmological observations—the monopoles would have been so plentiful and massive that they would have long since halted the expansion of the universe. However, the idea of inflation (for which this problem served as a partial motivation) was successful in solving this problem, creating models in which monopoles existed but were rare enough to be consistent with current observations.[19]

Quantum-mechanical origin of magnetism

While heuristic explanations based on classical physics can be formulated, diamagnetism, paramagnetism and ferromagnetism can only be fully explained using quantum theory.[20][21] A successful model was developed already in 1927, by Walter Heitler and Fritz London, who derived, quantum-mechanically, how hydrogen molecules are formed from hydrogen atoms, i.e. from the atomic hydrogen orbitals and centered at the nuclei A and B, see below. That this leads to magnetism is not at all obvious, but will be explained in the following.

According to the Heitler–London theory, so-called two-body molecular -orbitals are formed, namely the resulting orbital is:

Here the last product means that a first electron, r1, is in an atomic hydrogen-orbital centered at the second nucleus, whereas the second electron runs around the first nucleus. This "exchange" phenomenon is an expression for the quantum-mechanical property that particles with identical properties cannot be distinguished. It is specific not only for the formation of chemical bonds, but as one will see, also for magnetism, i.e. in this connection the term exchange interaction arises, a term which is essential for the origin of magnetism, and which is stronger, roughly by factors 100 and even by 1000, than the energies arising from the electrodynamic dipole-dipole interaction.

As for the spin function , which is responsible for the magnetism, we have the already mentioned Pauli's principle, namely that a symmetric orbital (i.e. with the + sign as above) must be multiplied with an antisymmetric spin function (i.e. with a − sign), and vice versa. Thus:

,

I.e., not only and must be substituted by α and β, respectively (the first entity means "spin up", the second one "spin down"), but also the sign + by the − sign, and finally ri by the discrete values si (= ±½); thereby we have and . The "singlet state", i.e. the − sign, means: the spins are antiparallel, i.e. for the solid we have antiferromagnetism, and for two-atomic molecules one has diamagnetism. The tendency to form a (homoeopolar) chemical bond (this means: the formation of a symmetric molecular orbital, i.e. with the + sign) results through the Pauli principle automatically in an antisymmetric spin state (i.e. with the − sign). In contrast, the Coulomb repulsion of the electrons, i.e. the tendency that they try to avoid each other by this repulsion, would lead to an antisymmetric orbital function (i.e. with the − sign) of these two particles, and complementary to a symmetric spin function (i.e. with the + sign, one of the so-called "triplet functions"). Thus, now the spins would be parallel (ferromagnetism in a solid, paramagnetism in two-atomic gases).

The last-mentioned tendency dominates in the metals iron, cobalt and nickel, and in some rare earths, which are ferromagnetic. Most of the other metals, where the first-mentioned tendency dominates, are nonmagnetic (e.g. sodium, aluminium, and magnesium) or antiferromagnetic (e.g. manganese). Diatomic gases are also almost exclusively diamagnetic, and not paramagnetic. However, the oxygen molecule, because of the involvement of π-orbitals, is an exception important for the life-sciences.

The Heitler-London considerations can be generalized to the Heisenberg model of magnetism (Heisenberg 1928).

The explanation of the phenomena is thus essentially based on all subtleties of quantum mechanics, whereas the electrodynamics covers mainly the phenomenology.

Units

SI

Symbol[22] Name of quantity Unit name Symbol Base units
Q electric charge coulomb C A⋅s
I electric current ampere A A (= W/V = C/s)
J electric current density ampere per square metre A/m2 A⋅m−2
U, ΔV, Δφ; E potential difference; electromotive force volt V J/C = kg⋅m2⋅s−3⋅A−1
R; Z; X electric resistance; impedance; reactance ohm Ω V/A = kg⋅m2⋅s−3⋅A−2
ρ resistivity ohm metre Ω⋅m kg⋅m3⋅s−3⋅A−2
P electric power watt W V⋅A = kg⋅m2⋅s−3
C capacitance farad F C/V = kg−1⋅m−2⋅A2⋅s4
ΦE electric flux volt metre V⋅m kg⋅m3⋅s−3⋅A−1
E electric field strength volt per metre V/m N/C = kg⋅m⋅A−1⋅s−3
D electric displacement field coulomb per square metre C/m2 A⋅s⋅m−2
ε permittivity farad per metre F/m kg−1⋅m−3⋅A2⋅s4
χe electric susceptibility (dimensionless) 1 1
G; Y; B conductance; admittance; susceptance siemens S Ω−1 = kg−1⋅m−2⋅s3⋅A2
κ, γ, σ conductivity siemens per metre S/m kg−1⋅m−3⋅s3⋅A2
B magnetic flux density, magnetic induction tesla T Wb/m2 = kg⋅s−2⋅A−1 = N⋅A−1⋅m−1
Φ, ΦM, ΦB magnetic flux weber Wb V⋅s = kg⋅m2⋅s−2⋅A−1
H magnetic field strength ampere per metre A/m A⋅m−1
L, M inductance henry H Wb/A = V⋅s/A = kg⋅m2⋅s−2⋅A−2
μ permeability henry per metre H/m kg⋅m⋅s−2⋅A−2
χ magnetic susceptibility (dimensionless) 1 1

Other

Living things

Some organisms can detect magnetic fields, a phenomenon known as magnetoception. In addition to detection, biomagnetic phenomena are utilized by organisms in a number of ways. For instance, chitons, a type of marine mollusk, produce magnetite to harden their teeth, and even humans produce magnetite in bodily tissue.[23] Magnetobiology studies magnetic fields as a medical treatment; fields naturally produced by an organism are known as biomagnetism.

See also

  • Magnetic quadrupole moment.svg Magnetism portal

References

  1. ^ Du Trémolet de Lacheisserie, Étienne; Damien Gignoux; Michel Schlenker (2005). Magnetism: Fundamentals. Springer. pp. 3–6. ISBN 978-0-387-22967-6.
  2. ^ Platonis Opera, Meyer and Zeller, 1839, p. 989.
  3. ^ 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. Retrieved 22 March 2013.
  4. ^ Fowler, Michael (1997). "Historical Beginnings of Theories of Electricity and Magnetism". Retrieved 2008-04-02.
  5. ^ Kumar Goyal, Rajendra (2017). Nanomaterials and Nanocomposites: Synthesis, Properties, Characterization Techniques, and Applications. CRC Press. p. 171. ISBN 9781498761673.
  6. ^ The section "Fanying 2" (反應第二) of The Guiguzi: "其察言也,不失若磁石之取鍼,舌之取燔骨".
  7. ^ Li, Shu-hua (1954). "Origine de la Boussole II. Aimant et Boussole". Isis (in French). 45 (2): 175–196. doi:10.1086/348315. JSTOR 227361. un passage dans le Liu-che-tch'ouen-ts'ieou [...]: “La pierre d'aimant fait venir le fer ou elle l'attire.”
    From the section "Jingtong" (精通) of the "Almanac of the Last Autumn Month" (季秋紀): "慈石召鐵,或引之也]"
  8. ^ In the section "A Last Word on Dragons" (亂龍篇 Luanlong) of the Lunheng: "Amber takes up straws, and a load-stone attracts needles" (頓牟掇芥,磁石引針).
  9. ^ Schmidl, Petra G. (1996–1997). "Two Early Arabic Sources On The Magnetic Compass". Journal of Arabic and Islamic Studies. 1: 81–132.
  10. ^ a b A. Einstein: "On the Electrodynamics of Moving Bodies", June 30, 1905.
  11. ^ HP Meyers (1997). Introductory solid state physics (2 ed.). CRC Press. p. 362; Figure 11.1. ISBN 9781420075021.
  12. ^ Catherine Westbrook; Carolyn Kaut; Carolyn Kaut-Roth (1998). MRI (Magnetic Resonance Imaging) in practice (2 ed.). Wiley-Blackwell. p. 217. ISBN 978-0-632-04205-0.
  13. ^ Purcell 2013, p. 320,584
  14. ^ Merzouki, Rochdi; Samantaray, Arun Kumar; Pathak, Pushparaj Mani (2012). Intelligent Mechatronic Systems: Modeling, Control and Diagnosis. Springer Science & Business Media. pp. 403–405. ISBN 978-1447146285.
  15. ^ Sturgeon, W. (1825). "Improved Electro Magnetic Apparatus". Trans. Royal Society of Arts, Manufactures, & Commerce. 43: 37–52. cited in Miller, T.J.E (2001). Electronic Control of Switched Reluctance Machines. Newnes. p. 7. ISBN 978-0-7506-5073-1.
  16. ^ Griffiths 1998, chapter 12
  17. ^ Jackson, John David (1999). Classical electrodynamics (3rd ed.). New York: Wiley. ISBN 978-0-471-30932-1.
  18. ^ Milton mentions some inconclusive events (p. 60) and still concludes that "no evidence at all of magnetic monopoles has survived" (p.3). Milton, Kimball A. (June 2006). "Theoretical and experimental status of magnetic monopoles". Reports on Progress in Physics. 69 (6): 1637–1711. arXiv:hep-ex/0602040. Bibcode:2006RPPh...69.1637M. doi:10.1088/0034-4885/69/6/R02..
  19. ^ Guth, Alan (1997). The Inflationary Universe: The Quest for a New Theory of Cosmic Origins. Perseus. ISBN 978-0-201-32840-0. OCLC 38941224..
  20. ^ The magnetism of matter, Feynman Lectures in Physics Ch 34
  21. ^ Ferromagnetism, Feynman Lectures in Physics Ch 36
  22. ^ International Union of Pure and Applied Chemistry (1993). Quantities, Units and Symbols in Physical Chemistry, 2nd edition, Oxford: Blackwell Science. ISBN 0-632-03583-8. pp. 14–15. Electronic version.
  23. ^ Kirschvink, Joseph L.; Kobayashi-Kirshvink, Atsuko; Diaz-Ricci, Juan C.; Kirschvink, Steven J. (1992). "Magnetite in Human Tissues: A Mechanism for the Biological Effects of Weak ELF Magnetic Fields" (PDF). Bioelectromagnetics Supplement. 1: 101–113. Retrieved 29 March 2016.

Further reading

  • David K. Cheng (1992). Field and Wave Electromagnetics. Addison-Wesley Publishing Company, Inc. ISBN 978-0-201-12819-2.
  • Furlani, Edward P. (2001). Permanent Magnet and Electromechanical Devices: Materials, Analysis and Applications. Academic Press. ISBN 978-0-12-269951-1. OCLC 162129430.
  • Griffiths, David J. (1998). Introduction to Electrodynamics (3rd ed.). Prentice Hall. ISBN 978-0-13-805326-0. OCLC 40251748.
  • Kronmüller, Helmut. (2007). Handbook of Magnetism and Advanced Magnetic Materials, 5 Volume Set. John Wiley & Sons. ISBN 978-0-470-02217-7. OCLC 124165851.
  • Purcell, Edward M. (2012). Electricity and magnetism (3rd ed.). Cambridge: Cambridge Univ. Press. ISBN 9781-10701-4022.
  • Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W.H. Freeman. ISBN 978-0-7167-0810-0. OCLC 51095685.

External links

Animal Magnetism (Merzbow album)

Animal Magnetism is an album by the Japanese noise musician Merzbow. The cover depicts Masami Akita's pet silkie chickens. Pier 39 is a pier in San Francisco taken over by sea lions.

Animal magnetism

Animal magnetism, also known as mesmerism, was the name given by German doctor Franz Mesmer in the 18th century to what he believed to be an invisible natural force (Lebensmagnetismus) possessed by all living things, including humans, animals, and vegetables. He believed that the force could have physical effects, including healing, and he tried persistently but without success to achieve scientific recognition of his ideas.The vitalist theory attracted numerous followers in Europe and the United States and was popular into the 19th century. Practitioners were often known as magnetizers rather than mesmerists. It was an important specialty in medicine for about 75 years from its beginnings in 1779, and continued to have some influence for another 50 years. Hundreds of books were written on the subject between 1766 and 1925, but it is almost entirely forgotten today. Mesmerism is still practised as a form of alternative medicine in some countries, but magnetic practices are not recognized as part of medical science.

Charisma

The term charisma () has two senses:

compelling attractiveness or charm that can inspire devotion in others

a divinely conferred power or talentIn discussing sense 1, scholars in sociology, political science, psychology, and management reserve the term for a type of leadership seen as extraordinary; in these fields, the term "charisma" is used to describe a particular type of leader who uses "values-based, symbolic, and emotion-laden leader signaling".In some theological usages, the term appears as charism, with a meaning the same as sense 2.Since the advent of Dungeons & Dragons in 1974, the word charisma has also been used as an "mental attribute" within the context of tabletop and video gaming, alongside intelligence and wisdom, where it designates actual strength of personality, persuasiveness, personal magnetism, and their leadership ability.

Curie temperature

In physics and materials science, the Curie temperature (TC), or Curie point, is the temperature above which certain materials lose their permanent magnetic properties, to be replaced by induced magnetism. The Curie temperature is named after Pierre Curie, who showed that magnetism was lost at a critical temperature.The force of magnetism is determined by the magnetic moment, a dipole moment within an atom which originates from the angular momentum and spin of electrons. Materials have different structures of intrinsic magnetic moments that depend on temperature; the Curie temperature is the critical point at which a material's intrinsic magnetic moments change direction.

Permanent magnetism is caused by the alignment of magnetic moments and induced magnetism is created when disordered magnetic moments are forced to align in an applied magnetic field. For example, the ordered magnetic moments (ferromagnetic, Figure 1) change and become disordered (paramagnetic, Figure 2) at the Curie temperature. Higher temperatures make magnets weaker, as spontaneous magnetism only occurs below the Curie temperature. Magnetic susceptibility above the Curie temperature can be calculated from the Curie–Weiss law, which is derived from Curie's law.

In analogy to ferromagnetic and paramagnetic materials, the Curie temperature can also be used to describe the phase transition between ferroelectricity and paraelectricity. In this context, the order parameter is the electric polarization that goes from a finite value to zero when the temperature is increased above the Curie temperature.

Diamagnetism

Diamagnetic materials are repelled by a magnetic field; an applied magnetic field creates an induced magnetic field in them in the opposite direction, causing a repulsive force. In contrast, paramagnetic and ferromagnetic materials are attracted by a magnetic field. Diamagnetism is a quantum mechanical effect that occurs in all materials; when it is the only contribution to the magnetism, the material is called diamagnetic. In paramagnetic and ferromagnetic substances the weak diamagnetic force is overcome by the attractive force of magnetic dipoles in the material. The magnetic permeability of diamagnetic materials is less than μ0, the permeability of vacuum. In most materials diamagnetism is a weak effect which can only be detected by sensitive laboratory instruments, but a superconductor acts as a strong diamagnet because it repels a magnetic field entirely from its interior.

Diamagnetism was first discovered when Sebald Justinus Brugmans observed in 1778 that bismuth and antimony were repelled by magnetic fields. In 1845, Michael Faraday demonstrated that it was a property of matter and concluded that every material responded (in either a diamagnetic or paramagnetic way) to an applied magnetic field. On a suggestion by William Whewell, Faraday first referred to the phenomenon as diamagnetic (the prefix dia- meaning through or across), then later changed it to diamagnetism.

Earth's magnetic field

Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from the Earth's interior out into space, where it interacts with the solar wind, a stream of charged particles emanating from the Sun. The magnetic field is generated by electric currents due to the motion of convection currents of molten iron in the Earth's outer core: these convection currents are caused by heat escaping from the core, a natural process called a geodynamo. The magnitude of the Earth's magnetic field at its surface ranges from 25 to 65 microteslas (0.25 to 0.65 gauss). As an approximation, it is represented by a field of a magnetic dipole currently tilted at an angle of about 11 degrees with respect to Earth's rotational axis, as if there were a bar magnet placed at that angle at the center of the Earth. The North geomagnetic pole, currently located near Greenland in the northern hemisphere, is actually the south pole of the Earth's magnetic field, and conversely.

While the North and South magnetic poles are usually located near the geographic poles, they slowly and continuously move over geological time scales, but sufficiently slowly for ordinary compasses to remain useful for navigation. However, at irregular intervals averaging several hundred thousand years, the Earth's field reverses and the North and South Magnetic Poles respectively, abruptly switch places. These reversals of the geomagnetic poles leave a record in rocks that are of value to paleomagnetists in calculating geomagnetic fields in the past. Such information in turn is helpful in studying the motions of continents and ocean floors in the process of plate tectonics.

The magnetosphere is the region above the ionosphere that is defined by the extent of the Earth's magnetic field in space. It extends several tens of thousands of kilometers into space, protecting the Earth from the charged particles of the solar wind and cosmic rays that would otherwise strip away the upper atmosphere, including the ozone layer that protects the Earth from harmful ultraviolet radiation.

Eddy current

Eddy currents (also called Foucault currents) are loops of electrical current induced within conductors by a changing magnetic field in the conductor according to Faraday's law of induction. Eddy currents flow in closed loops within conductors, in planes perpendicular to the magnetic field. They can be induced within nearby stationary conductors by a time-varying magnetic field created by an AC electromagnet or transformer, for example, or by relative motion between a magnet and a nearby conductor. The magnitude of the current in a given loop is proportional to the strength of the magnetic field, the area of the loop, and the rate of change of flux, and inversely proportional to the resistivity of the material.

By Lenz's law, an eddy current creates a magnetic field that opposes the change in the magnetic field that created it, and thus eddy currents react back on the source of the magnetic field. For example, a nearby conductive surface will exert a drag force on a moving magnet that opposes its motion, due to eddy currents induced in the surface by the moving magnetic field. This effect is employed in eddy current brakes which are used to stop rotating power tools quickly when they are turned off. The current flowing through the resistance of the conductor also dissipates energy as heat in the material. Thus eddy currents are a cause of energy loss in alternating current (AC) inductors, transformers, electric motors and generators, and other AC machinery, requiring special construction such as laminated magnetic cores or ferrite cores to minimize them. Eddy currents are also used to heat objects in induction heating furnaces and equipment, and to detect cracks and flaws in metal parts using eddy-current testing instruments.

Electromagnetic induction

Electromagnetic or magnetic induction is the production of an electromotive force (i.e., voltage) across an electrical conductor in a changing magnetic field.

Michael Faraday is generally credited with the discovery of induction in 1831, and James Clerk Maxwell mathematically described it as Faraday's law of induction. Lenz's law describes the direction of the induced field. Faraday's law was later generalized to become the Maxwell–Faraday equation, one of the four Maxwell equations in his theory of electromagnetism.

Electromagnetic induction has found many applications, including electrical components such as inductors and transformers, and devices such as electric motors and generators.

Electromagnetism

Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force usually exhibits electromagnetic fields such as electric fields, magnetic fields, and light, and is one of the four fundamental interactions (commonly called forces) in nature. The other three fundamental interactions are the strong interaction, the weak interaction, and gravitation. At high energy the weak force and electromagnetic force are unified as a single electroweak force.

Electromagnetic phenomena are defined in terms of the electromagnetic force, sometimes called the Lorentz force, which includes both electricity and magnetism as different manifestations of the same phenomenon. The electromagnetic force plays a major role in determining the internal properties of most objects encountered in daily life. Ordinary matter takes its form as a result of intermolecular forces between individual atoms and molecules in matter, and is a manifestation of the electromagnetic force. Electrons are bound by the electromagnetic force to atomic nuclei, and their orbital shapes and their influence on nearby atoms with their electrons is described by quantum mechanics. The electromagnetic force governs all chemical processes, which arise from interactions between the electrons of neighboring atoms.

There are numerous mathematical descriptions of the electromagnetic field. In classical electrodynamics, electric fields are described as electric potential and electric current. In Faraday's law, magnetic fields are associated with electromagnetic induction and magnetism, and Maxwell's equations describe how electric and magnetic fields are generated and altered by each other and by charges and currents.

The theoretical implications of electromagnetism, particularly the establishment of the speed of light based on properties of the "medium" of propagation (permeability and permittivity), led to the development of special relativity by Albert Einstein in 1905.

Ferromagnetism

Ferromagnetism is the basic mechanism by which certain materials (such as iron) form permanent magnets, or are attracted to magnets. In physics, several different types of magnetism are distinguished. Ferromagnetism (along with the similar effect ferrimagnetism) is the strongest type and is responsible for the common phenomena of magnetism in magnets encountered in everyday life. Substances respond weakly to magnetic fields with three other types of magnetism, paramagnetism, diamagnetism, and antiferromagnetism, but the forces are usually so weak that they can only be detected by sensitive instruments in a laboratory. An everyday example of ferromagnetism is a refrigerator magnet used to hold notes on a refrigerator door. The attraction between a magnet and ferromagnetic material is "the quality of magnetism first apparent to the ancient world, and to us today".Permanent magnets (materials that can be magnetized by an external magnetic field and remain magnetized after the external field is removed) are either ferromagnetic or ferrimagnetic, as are the materials that are noticeably attracted to them. Only a few substances are ferromagnetic. The common ones are iron, nickel, cobalt and most of their alloys, and some compounds of rare earth metals.

Ferromagnetism is very important in industry and modern technology, and is the basis for many electrical and electromechanical devices such as electromagnets, electric motors, generators, transformers, and magnetic storage such as tape recorders, and hard disks, and nondestructive testing of ferrous materials.

Gauss's law for magnetism

In physics, Gauss's law for magnetism is one of the four Maxwell's equations that underlie classical electrodynamics. It states that the magnetic field B has divergence equal to zero, in other words, that it is a solenoidal vector field. It is equivalent to the statement that magnetic monopoles do not exist. Rather than "magnetic charges", the basic entity for magnetism is the magnetic dipole. (If monopoles were ever found, the law would have to be modified, as elaborated below.)

Gauss's law for magnetism can be written in two forms, a differential form and an integral form. These forms are equivalent due to the divergence theorem.

The name "Gauss's law for magnetism" is not universally used. The law is also called "Absence of free magnetic poles"; one reference even explicitly says the law has "no name". It is also referred to as the "transversality requirement" because for plane waves it requires that the polarization be transverse to the direction of propagation.

Gravity and Extreme Magnetism

The Gravity and Extreme Magnetism SMEX (GEMS) mission was a cancelled space observatory mission. The main scientific goal of GEMS was to be the first mission to systematically measure the polarization of cosmic X-Ray sources. GEMS would have provided data to help scientists study the shape of space that has been distorted by a spinning black hole's gravity and the structure and effects of the magnetic fields around Neutron stars. It was cancelled by NASA in June 2012 for potential cost overruns due to delays in developing the technology.

GEMS was managed by the National Aeronautics and Space Administration NASA, the United States space agency, at the Goddard Space Flight Center. The project was an astrophysics program reporting to NASA's Science Mission Directorate (SMD) in Washington, D.C..The spacecraft would have been launched on in July 2014 on a nine-month mission with a possible 15-month extension for a guest observer phase; but the mission was terminated at the Confirmation Review stage on May 10, 2012 due to expected cost overruns.

Cancelled missions can be reinstated—for example NuSTAR was cancelled in 2006, but reinstated a year later and launched in June 2012. However, NuSTAR was not cancelled due to project overruns, but rather due to changes in the overall NASA budget, so the circumstances for cancellation were very different. Small missions of the Explorer program offer a lot of flexibility and launch opportunities, and the lessons learned can be applied to the same missions goals, but on a different mission (Compare Vanguard 1 to Explorer 1). Several years later two new X-ray polarimetry mission won a NASA award to develop a X-ray polarimetry missions.

Live Magnetism

Live Magnetism is a live album by the Japanese noise musician Merzbow.

Magnet

A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, and attracts or repels other magnets.

A permanent magnet is an object made from a material that is magnetized and creates its own persistent magnetic field. An everyday example is a refrigerator magnet used to hold notes on a refrigerator door. Materials that can be magnetized, which are also the ones that are strongly attracted to a magnet, are called ferromagnetic (or ferrimagnetic). These include the elements iron, nickel and cobalt, some alloys of rare-earth metals, and some naturally occurring minerals such as lodestone. Although ferromagnetic (and ferrimagnetic) materials are the only ones attracted to a magnet strongly enough to be commonly considered magnetic, all other substances respond weakly to a magnetic field, by one of several other types of magnetism.

Ferromagnetic materials can be divided into magnetically "soft" materials like annealed iron, which can be magnetized but do not tend to stay magnetized, and magnetically "hard" materials, which do. Permanent magnets are made from "hard" ferromagnetic materials such as alnico and ferrite that are subjected to special processing in a strong magnetic field during manufacture to align their internal microcrystalline structure, making them very hard to demagnetize. To demagnetize a saturated magnet, a certain magnetic field must be applied, and this threshold depends on coercivity of the respective material. "Hard" materials have high coercivity, whereas "soft" materials have low coercivity. The overall strength of a magnet is measured by its magnetic moment or, alternatively, the total magnetic flux it produces. The local strength of magnetism in a material is measured by its magnetization.

An electromagnet is made from a coil of wire that acts as a magnet when an electric current passes through it but stops being a magnet when the current stops. Often, the coil is wrapped around a core of "soft" ferromagnetic material such as mild steel, which greatly enhances the magnetic field produced by the coil.

Magnetic field

A magnetic field is a vector field that describes the magnetic influence of electrical currents and magnetized materials. In everyday life, the effects of magnetic fields are often seen in permanent magnets, which pull on magnetic materials (such as iron) and attract or repel other magnets. Magnetic fields surround and are created by magnetized material and by moving electric charges (electric currents) such as those used in electromagnets. Magnetic fields exert forces on nearby moving electrical charges and torques on nearby magnets. In addition, a magnetic field that varies with location exerts a force on magnetic materials. Both the strength and direction of a magnetic field varies with location. As such, it is an example of a vector field.

The term 'magnetic field' is used for two distinct but closely related fields denoted by the symbols B and H. In the International System of Units, H is measured in units of amperes per meter and B is measured in teslas, which are equivalent to newtons per meter per ampere. H and B differ in how they account for magnetization. In a vacuum, B and H are the same aside from units; but in a magnetized material, B/ and H differ by the magnetization M of the material at that point in the material.

Magnetic fields are produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin. Magnetic fields and electric fields are interrelated, and are both components of the electromagnetic force, one of the four fundamental forces of nature.

Magnetic fields are widely used throughout modern technology, particularly in electrical engineering and electromechanics. Rotating magnetic fields are used in both electric motors and generators. The interaction of magnetic fields in electric devices such as transformers is studied in the discipline of magnetic circuits. Magnetic forces give information about the charge carriers in a material through the Hall effect. The Earth produces its own magnetic field, which shields the Earth's ozone layer from the solar wind and is important in navigation using a compass.

Magnetic flux

In physics, specifically electromagnetism, the magnetic flux (often denoted Φ or ΦB) through a surface is the surface integral of the normal component of the magnetic field B passing through that surface. The SI unit of magnetic flux is the weber (Wb) (in derived units: volt seconds), and the CGS unit is the maxwell. Magnetic flux is usually measured with a fluxmeter, which contains measuring coils and electronics, that evaluates the change of voltage in the measuring coils to calculate the magnetic flux.

Magnetic susceptibility

In electromagnetism, the magnetic susceptibility (Latin: susceptibilis, "receptive"; denoted χ) is a measure of how much a material will become magnetized in an applied magnetic field. Mathematically, it is the ratio of magnetization M (magnetic moment per unit volume) to the applied magnetizing field intensity H. This allows a simple classification of most materials' response to an applied magnetic field into two categories: an alignment with the magnetic field, χ>0, called paramagnetism, or an alignment against the field, χ<0, called diamagnetism.

This alignment has several effects. First, the magnetic susceptibility indicates whether a material is attracted into or repelled out of a magnetic field. Paramagnetic materials align with the field, so are attracted to the magnetic field. Diamagnetic materials are anti-aligned, so are pushed away from magnetic fields. Second, on top of the applied field, the magnetic moment of the material adds its own magnetic field, causing the field lines to concentrate in paramagnetism, or be excluded in diamagnetism. Quantitative measures of the magnetic susceptibility also provide insights into the structure of materials, providing insight into bonding and energy levels.

Fundamentally, the magnetic moment of materials comes from the magnetism of the particles they are made of. Usually, this is dominated by the magnetic moments of electrons. Electrons are present in all materials, but without any external magnetic field, the magnetic moments of the electrons are usually in some way either paired up or randomized so the overall magnetism is zero.(the exception to this usual case is ferromagnetism) The fundamental reasons why the magnetic moments of the electrons line up or don't can be very complex, and can not be explained with classical physics. However, it is a useful simplification to simply measure the magnetic susceptibility of a material, and apply the macroscopic form of Maxwell's equations. This allows classical physics to make useful predictions without getting into the underlying quantum mechanical details.

Magnetostatics

Magnetostatics is the study of magnetic fields in systems where the currents are steady (not changing with time). It is the magnetic analogue of electrostatics, where the charges are stationary. The magnetization need not be static; the equations of magnetostatics can be used to predict fast magnetic switching events that occur on time scales of nanoseconds or less. Magnetostatics is even a good approximation when the currents are not static — as long as the currents do not alternate rapidly. Magnetostatics is widely used in applications of micromagnetics such as models of magnetic recording devices. Magnetostatic focussing can be achieved either by a permanent magnet or by passing current through a coil of wire whose axis coincides with the beam axis.

Paleomagnetism

This term is also sometimes used for natural remanent magnetization.

Paleomagnetism (or palaeomagnetism in the United Kingdom) is the study of the record of the Earth's magnetic field in rocks, sediment, or archeological materials. Certain minerals in rocks lock-in a record of the direction and intensity of the magnetic field when they form. This record provides information on the past behavior of Earth's magnetic field and the past location of tectonic plates. The record of geomagnetic reversals preserved in volcanic and sedimentary rock sequences (magnetostratigraphy) provides a time-scale that is used as a geochronologic tool. Geophysicists who specialize in paleomagnetism are called paleomagnetists.

Paleomagnetists led the revival of the continental drift hypothesis and its transformation into plate tectonics. Apparent polar wander paths provided the first clear geophysical evidence for continental drift, while marine magnetic anomalies did the same for seafloor spreading. Paleomagnetism continues to extend the history of plate tectonics back in time and are applied to the movement of continental fragments, or terranes.

Paleomagnetism relied heavily on new developments in rock magnetism, which in turn has provided the foundation for new applications of magnetism. These include biomagnetism, magnetic fabrics (used as strain indicators in rocks and soils), and environmental magnetism.

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