Magnetism

Magnetism is the class of physical attributes that occur through a magnetic field, which allows objects to attract or repel each other. Because both and of elementary particles give rise to a magnetic field, magnetism is one of two aspects of electromagnetism.

The most familiar effects occur in ferromagnetic materials, which are strongly attracted by magnetic fields and can be magnetization to become permanent , producing magnetic fields themselves. Demagnetizing a magnet is also possible. Only a few substances are ferromagnetic; the most common ones are iron, cobalt, nickel, and their alloys.

All substances exhibit some type of magnetism. Magnetic materials are classified according to their bulk susceptibility.

The strength of a magnetic field always decreases with distance from the magnetic source, though the exact mathematical relationship between strength and distance varies. Many factors can influence the magnetic field of an object including the magnetic moment of the material, the physical shape of the object, both the magnitude and direction of any electric current present within the object, and the temperature of the object.

In ancient China, the earliest literary reference to magnetism lies in a 4th-century BCE book named after its author, Guiguzi.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". The 2nd-century BCE annals, Lüshi Chunqiu, also notes: "The lodestone makes iron approach; some (force) is attracting it."
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]" The earliest mention of the attraction of a needle is in a 1st-century work Lunheng ( Balanced Inquiries): "A lodestone attracts a needle."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). 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 Umar II, a Islamic physics, astronomer, and geographer.

Leonardo Garzoni's only extant work, the Due trattati sopra la natura, e le qualità della calamita ( Two treatises on the nature and qualities of the magnet), is the first known example of a modern treatment of magnetic phenomena. Written in years near 1580 and never published, the treatise had a wide diffusion. In particular, Garzoni is referred to as an expert in magnetism by Niccolò Cabeo, whose Philosophia Magnetica (1629) is just a re-adjustment of Garzoni's work. Garzoni's treatise was known also to Giovanni Battista Della Porta.

In 1600, William Gilbert published his De Magnete ( 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 whereas, 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. 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. Around the same time, André-Marie Ampère carried out numerous systematic experiments and discovered that the magnetic force between two DC current loops of any shape is equal to the sum of the individual forces that each current element of one circuit exerts on each other current element of the other circuit.

In 1831, Michael Faraday discovered that a time-varying magnetic flux induces a voltage through a wire loop. In 1835, Carl Friedrich Gauss hypothesized, based on Ampère's force law in its original form, that all forms of magnetism arise as a result of elementary point charges moving relative to each other. Wilhelm Eduard Weber advanced Gauss's theory to Weber electrodynamics.

From around 1861, James Clerk Maxwell synthesized and expanded many of these insights into Maxwell's equations, unifying electricity, magnetism, and optics into the field of electromagnetism. However, Gauss's interpretation of magnetism is not fully compatible with Maxwell's electrodynamics. In 1905, Albert Einstein used Maxwell's equations in motivating his theory of special relativity, A. Einstein: "On the Electrodynamics of Moving Bodies", June 30, 1905. requiring that the laws hold true in all inertial reference frames. Gauss's approach of interpreting the magnetic force as a mere effect of relative velocities thus found its way back into electrodynamics to some extent.

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.

1. Electric current
2. Spin magnetic moments of elementary particles
3. Changing electric fields

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 canceled 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.

Sometimeseither spontaneously, or owing to an applied external magnetic fieldeach 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.

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$$q\backslash mathbf\{F\}\; =\; q\; (\backslash mathbf\{v\}\; \backslash times\; \backslash mathbf\{B\})\; ,$$

where $q$ 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. The magnitude of the force is

$$qF=qvB\backslash sin\backslash theta\backslash \; ,$$

where $\backslash theta$ 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.

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 charge or negative charge 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 Cosmic 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.

• gauss – the centimeter-gram-second (CGS) unit of magnetic field (denoted B).
• oersted – the CGS unit of magnetizing field (denoted H)
• maxwell – the CGS unit for magnetic flux
• gamma – a unit of magnetic flux density that was commonly used before the tesla came into use (1.0 gamma = 1.0 nanotesla)
• μ₀ – common symbol for the permeability of free space ( newton/(ampere-turn)²)

Magnetobiology studies the effects of magnetic fields on living organisms; fields naturally produced by an organism are known as biomagnetism. Many biological organisms are mostly made of water, and because water is diamagnetic, extremely strong magnetic fields can repel these living things.

Gauss's force law states that the electromagnetic force $\backslash mathbf\{F\}\_1$ experienced by a point charge, $q\_1$ with trajectory $\backslash mathbf\{r\}\_1(t)$, in the vicinity of another point charge, $q\_2$ with trajectory $\backslash mathbf\{r\}\_2(t)$, in a vacuum is equal to the central force

$$\backslash mathbf\{F\}\_1\; =\; \backslash frac\{q\_1\backslash ,q\_2\}\{4\backslash ,\backslash pi\backslash ,\backslash epsilon\_0\}\backslash ,\backslash frac\{\backslash mathbf\{r\}\}$$

where $\backslash mathbf\{r\}\; =\; \backslash mathbf\{r\}\_1(t)\; -\; \backslash mathbf\{r\}\_2(t)$ is the distance between the charges and $\backslash mathbf\{v\}\; =\; \backslash dot\{\backslash mathbf\{r\}\}\_1(t)\; -\; \backslash dot\{\backslash mathbf\{r\}\}\_2(t)$ is the relative velocity. Wilhelm Eduard Weber confirmed Gauss's hypothesis in numerous experiments. By means of Weber electrodynamics it is possible to explain the static and quasi-static effects in the non-relativistic regime of classical electrodynamics without magnetic field and Lorentz force.

Since 1870, Maxwell electrodynamics has been developed, which postulates that electric and magnetic fields exist. In Maxwell's electrodynamics, the actual electromagnetic force can be calculated using the Lorentz force, which, like the Weber force, is speed-dependent. However, Maxwell's electrodynamics is not fully compatible with the work of Ampère, Gauss and Weber in the quasi-static regime. In particular, Ampère's original force law and the Biot-Savart law are only equivalent if the field-generating conductor loop is closed. Maxwell's electrodynamics therefore represents a break with the interpretation of magnetism by Gauss and Weber, since in Maxwell's electrodynamics it is no longer possible to deduce the magnetic force from a central force.

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

$$\backslash psi(\backslash mathbf\; r\_1,\backslash ,\backslash ,\backslash mathbf\; r\_2)=\backslash frac\{1\}\{\backslash sqrt\{2\}\}\backslash ,\backslash ,\backslash left\; (u\_A(\backslash mathbf\; r\_1)u\_B(\backslash mathbf\; r\_2)+u\_B(\backslash mathbf\; r\_1)u\_A(\backslash mathbf\; r\_2)\backslash right\; )$$

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 , but also for magnetism. That is, 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 $\backslash chi\; (s\_1,s\_2)$, 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:

$$\backslash chi\; (s\_1,\backslash ,\backslash ,s\_2)=\backslash frac\{1\}\{\backslash sqrt\{2\}\}\backslash ,\backslash ,\backslash left\; (\backslash alpha\; (s\_1)\backslash beta\; (s\_2)-\backslash beta\; (s\_1)\backslash alpha\; (s\_2)\backslash right\; )$$,

I.e., not only $u\_A$ and $u\_B$ 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 r_i by the discrete values s_i (= ±); thereby we have $\backslash alpha(+1/2)=\backslash beta(-1/2)=1$ and $\backslash alpha(-1/2)=\backslash beta(+1/2)=0$. 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 state"). 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.

• Coercivity
• Gravitomagnetism
• Magnetic hysteresis
• Magnetar
• Magnetic bearing
• Magnetic circuit
• Magnetic cooling
• Magnetic field viewing film
• Magnetic stirrer
• Switched-mode power supply
• Magnetic structure
• Micromagnetism
• Neodymium magnet
• Plastic magnet
• Rare-earth magnet
• Spin wave
• Spontaneous magnetization
• Vibrating-sample magnetometer
• Textbooks in electromagnetism

• David K. Cheng (1992). 9780201128192, Addison-Wesley Publishing Company, Inc.. ISBN 9780201128192
• Furlani, Edward P. (2025). 9780122699511, Academic Press. ISBN 9780122699511
• (1998). 9780138053260, Prentice Hall. . ISBN 9780138053260
• Kronmüller, Helmut. (2025). 9780470022177, John Wiley & Sons. ISBN 9780470022177
• (2025). 9781107014022, Cambridge Univ. Press. ISBN 9781107014022
• Tipler, Paul (2025). 9780716708100, W.H. Freeman. ISBN 9780716708100
• J. M. D. Coey (2025). 9781108717519, Cambridge University Press. ISBN 9781108717519

• The Exploratorium Science Snacks – Subject:Physics/Electricity & Magnetism
• A collection of magnetic structures – MAGNDATA