Magnetism

Lodestone, a natural magnet, attracting iron nails. Ancient humans discovered the property of magnetism from lodestone.

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.

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.[3] The word magnet comes from the Greek term μαγνῆτις λίθος magnētis lithos,[4] "the Magnesian stone, lodestone".[5] 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.[6] The ancient Indian medical text Sushruta Samhita describes using magnetite to remove arrows embedded in a person's body.[7]

In ancient China, the earliest literary reference to magnetism lies in a 4th-century BC book named after its author, Guiguzi.[8] The 2nd-century BC annals, Lüshi Chunqiu, also notes: "The lodestone makes iron approach; some (force) is attracting it."[9] The earliest mention of the attraction of a needle is in a 1st-century work Lunheng (Balanced Inquiries): "A lodestone attracts a needle."[10] 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 Yemeni physicist, astronomer, and geographer.[11]

Leonardo Garzoni's only extant work, the Due trattati sopra la natura, e le qualità della calamita, 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, 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 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. Following this were several other scientists' experiments: André-Marie Ampère who in 1820 discovered that the magnetic field circulating in a closed-path was related to the current flowing through a surface enclosed by 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, Albert Einstein used these laws in motivating his theory of special relativity,[12] 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.

Magnetism, at its root, arises from three sources:

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

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 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.

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.

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.[15] 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.[16] Electromagnetism was discovered in 1820.[17]

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.[12][18] 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 general 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.[19]

In a vacuum,

${\displaystyle \mathbf {B} \ =\ \mu _{0}\mathbf {H} ,}$

where μ₀ is the vacuum permeability.

In a material,

${\displaystyle \mathbf {B} \ =\ \mu _{0}(\mathbf {H} +\mathbf {M} ).\ }$

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:

${\displaystyle \mathbf {M} =\chi \mathbf {H} ,}$

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

${\displaystyle \mu _{0}(\mathbf {H} +\mathbf {M} )\ =\ \mu _{0}(1+\chi )\mathbf {H} \ =\ \mu _{r}\mu _{0}\mathbf {H} \ =\ \mu \mathbf {H} .}$

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 lines of force of a bar magnet shown by iron filings on paper

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:[20]

${\displaystyle \mathbf {F} =q(\mathbf {v} \times \mathbf {B} )}$

where

${\displaystyle q}$ 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. 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

${\displaystyle F=qvB\sin \theta \,}$

where ${\displaystyle \theta }$ 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.

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.

A live frog levitates inside a 32 mm diameter vertical bore of a Bitter solenoid in a very strong magnetic field—about 16 teslas

Some organisms can detect magnetic fields, a phenomenon known as magnetoception. Some materials in living things are ferromagnetic, though it is unclear if the magnetic properties serve a special function or are merely a byproduct of containing iron. For instance, chitons, a type of marine mollusk, produce magnetite to harden their teeth, and even humans produce magnetite in bodily tissue.[24] 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.

While heuristic explanations based on classical physics can be formulated, diamagnetism, paramagnetism and ferromagnetism can be fully explained only using quantum theory.[25][26] 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 ${\displaystyle u_{A}}$ and ${\displaystyle u_{B}}$ 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 ${\displaystyle \sigma }$-orbitals are formed, namely the resulting orbital is:

${\displaystyle \psi (\mathbf {r} _{1},\,\,\mathbf {r} _{2})={\frac {1}{\sqrt {2}}}\,\,\left(u_{A}(\mathbf {r} _{1})u_{B}(\mathbf {r} _{2})+u_{B}(\mathbf {r} _{1})u_{A}(\mathbf {r} _{2})\right)}$

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 chemical bonds, 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 ${\displaystyle \chi (s_{1},s_{2})}$, 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:

${\displaystyle \chi (s_{1},\,\,s_{2})={\frac {1}{\sqrt {2}}}\,\,\left(\alpha (s_{1})\beta (s_{2})-\beta (s_{1})\alpha (s_{2})\right)}$,

I.e., not only ${\displaystyle u_{A}}$ and ${\displaystyle u_{B}}$ 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 (= ±1⁄2); thereby we have ${\displaystyle \alpha (+1/2)=\beta (-1/2)=1}$ and ${\displaystyle \alpha (-1/2)=\beta (+1/2)=0}$. 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 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.

Optically induced magnetism is essentially the combination of optics and induced magnetism. Optics is the study of the behavior of light and induced magnetism is when an object is kept near a magnet and the object itself becomes magnetic .

Optically induced magnetism works when an electric current passes through a magnetic layer and the electric current becomes spin-polarized. The spin-polarized current will exert a spin-transfer torque (STT) on the magnetization. This phenomenon can also be generated inside a non-magnetic metal due to the spin–orbit coupling (SOC) Spin–orbit interaction, and the corresponding torque (spin–orbit torque (SOT).

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