Intuitive statistics

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Intuitive_statistics 

Intuitive statistics, or folk statistics, refers to the cognitive phenomenon where organisms use data to make generalizations and predictions about the world. This can be a small amount of sample data or training instances, which in turn contribute to inductive inferences about either population-level properties, future data, or both. Inferences can involve revising hypotheses, or beliefs, in light of probabilistic data that inform and motivate future predictions. The informal tendency for cognitive animals to intuitively generate statistical inferences, when formalized with certain axioms of probability theory, constitutes statistics as an academic discipline.

Because this capacity can accommodate a broad range of informational domains, the subject matter is similarly broad and overlaps substantially with other cognitive phenomena. Indeed, some have argued that "cognition as an intuitive statistician" is an apt companion metaphor to the computer metaphor of cognition. Others appeal to a variety of statistical and probabilistic mechanisms behind theory construction and category structuring. Research in this domain commonly focuses on generalizations relating to number, relative frequency, risk, and any systematic signatures in inferential capacity that an organism (e.g., humans, or non-human primates) might have.

Background and theory

Intuitive inferences can involve generating hypotheses from incoming sense data, such as categorization and concept structuring. Data are typically probabilistic and uncertainty is the rule, rather than the exception, in learning, perception, language, and thought. Recently, researchers have drawn from ideas in probability theory, philosophy of mind, computer science, and psychology to model cognition as a predictive and generative system of probabilistic representations, allowing information structures to support multiple inferences in a variety of contexts and combinations. This approach has been called a probabilistic language of thought because it constructs representations probabilistically, from pre-existing concepts to predict a possible and likely state of the world.

Probability

Statisticians and probability theorists have long debated about the use of various tools, assumptions, and problems relating to inductive inference in particular. David Hume famously considered the problem of induction, questioning the logical foundations of how and why people can arrive at conclusions that extend beyond past experiences - both spatiotemporally and epistemologically. More recently, theorists have considered the problem by emphasizing techniques for arriving from data to hypothesis using formal content-independent procedures, or in contrast, by considering informal, content-dependent tools for inductive inference. Searches for formal procedures have led to different developments in statistical inference and probability theory with different assumptions, including Fisherian frequentist statistics, Bayesian inference, and Neyman-Pearson statistics.

Gerd Gigerenzer and David Murray argue that twentieth century psychology as a discipline adopted probabilistic inference as a unified set of ideas and ignored the controversies among probability theorists. They claim that a normative but incorrect view of how humans "ought to think rationally" follows from this acceptance. They also maintain, however, that the intuitive statistician metaphor of cognition is promising, and should consider different formal tools or heuristics as specialized for different problem domains, rather than a content- or context-free toolkit. Signal detection theorists and object detection models, for example, often use a Neyman-Pearson approach, whereas Fisherian frequentist statistics might aid cause-effect inferences.

Frequentist inference

Frequentist inference focuses on the relative proportions or frequencies of occurrences to draw probabilistic conclusions. It is defined by its closely related concept, frequentist probability. This entails a view that "probability" is nonsensical in the absence of pre-existing data, because it is understood as a relative frequency that long-run samples would approach given large amounts of data. Leda Cosmides and John Tooby have argued that it is not possible to derive a probability without reference to some frequency of previous outcomes, and this likely has evolutionary origins: Single-event probabilities, they claim, are not observable because organisms evolved to intuitively understand and make statistical inferences from frequencies of prior events, rather than to "see" probability as an intrinsic property of an event.

Bayesian inference

Bayesian inference generally emphasizes the subjective probability of a hypothesis, which is computed as a posterior probability using Bayes' Theorem. It requires a "starting point" called a prior probability, which has been contentious for some frequentists who claim that frequency data are required to develop a prior probability, in contrast to taking a probability as an a priori assumption.

Bayesian models have been quite popular among psychologists, particularly learning theorists, because they appear to emulate the iterative, predictive process by which people learn and develop expectations from new observations, while giving appropriate weight to previous observations. Andy Clark, a cognitive scientist and philosopher, recently wrote a detailed argument in support of understanding the brain as a constructive Bayesian engine that is fundamentally action-oriented and predictive, rather than passive or reactive. More classic lines of evidence cited among supporters of Bayesian inference include conservatism, or the phenomenon where people modify previous beliefs toward, but not all the way to, a conclusion implied by previous observations. This pattern of behavior is similar to the pattern of posterior probability distributions when a Bayesian model is conditioned on data, though critics argued that this evidence had been overstated and lacked mathematical rigor.

Alison Gopnik more recently tackled the problem by advocating the use of Bayesian networks, or directed graph representations of conditional dependencies. In a Bayesian network, edge weights are conditional dependency strengths that are updated in light of new data, and nodes are observed variables. The graphical representation itself constitutes a model, or hypothesis, about the world and is subject to change, given new data.

Error management theory

Error management theory (EMT) is an application of Neyman-Pearson statistics to cognitive and evolutionary psychology. It maintains that the possible fitness costs and benefits of type I (false positive) and type II (false negative) errors are relevant to adaptively rational inferences, toward which an organism is expected to be biased due to natural selection. EMT was originally developed by Martie Haselton and David Buss, with initial research focusing on its possible role in sexual overperception bias in men and sexual underperception bias in women.

This is closely related to a concept called the "smoke detector principle" in evolutionary theory. It is defined by the tendency for immune, affective, and behavioral defenses to be hypersensitive and overreactive, rather than insensitive or weakly expressed. Randolph Nesse maintains that this is a consequence of a typical payoff structure in signal detection: In a system that is invariantly structured with a relatively low cost of false positives and high cost of false negatives, naturally selected defenses are expected to err on the side of hyperactivity in response to potential threat cues. This general idea has been applied to hypotheses about the apparent tendency for humans to apply agency to non-agents based on uncertain or agent-like cues. In particular, some claim that it is adaptive for potential prey to assume agency by default if it is even slightly suspected, because potential predator threats typically involve cheap false positives and lethal false negatives.

Heuristics and biases

Heuristics are efficient rules, or computational shortcuts, for producing a judgment or decision. The intuitive statistician metaphor of cognition led to a shift in focus for many psychologists, away from emotional or motivational principles and toward computational or inferential principles. Empirical studies investigating these principles have led some to conclude that human cognition, for example, has built-in and systematic errors in inference, or cognitive biases. As a result, cognitive psychologists have largely adopted the view that intuitive judgments, generalizations, and numerical or probabilistic calculations are systematically biased. The result is commonly an error in judgment, including (but not limited to) recurrent logical fallacies (e.g., the conjunction fallacy), innumeracy, and emotionally motivated shortcuts in reasoning. Social and cognitive psychologists have thus considered it "paradoxical" that humans can outperform powerful computers at complex tasks, yet be deeply flawed and error-prone in simple, everyday judgments.

Much of this research was carried out by Amos Tversky and Daniel Kahneman as an expansion of work by Herbert Simon on bounded rationality and satisficing. Tversky and Kahneman argue that people are regularly biased in their judgments under uncertainty, because in a speed-accuracy tradeoff they often rely on fast and intuitive heuristics with wide margins of error rather than slow calculations from statistical principles. These errors are called "cognitive illusions" because they involve systematic divergences between judgments and accepted, normative rules in statistical prediction.

Gigerenzer has been critical of this view, arguing that it builds from a flawed assumption that a unified "normative theory" of statistical prediction and probability exists. His contention is that cognitive psychologists neglect the diversity of ideas and assumptions in probability theory, and in some cases, their mutual incompatibility. Consequently, Gigerenzer argues that many cognitive illusions are not violations of probability theory per se, but involve some kind of experimenter confusion between subjective probabilities with degrees of confidence and long-run outcome frequencies. Cosmides and Tooby similarly claim that different probabilistic assumptions can be more or less normative and rational in different types of situations, and that there is not general-purpose statistical toolkit for making inferences across all informational domains. In a review of several experiments they conclude, in support of Gigerenzer, that previous heuristics and biases experiments did not represent problems in an ecologically valid way, and that re-representing problems in terms of frequencies rather than single-event probabilities can make cognitive illusions largely vanish.

Tversky and Kahneman refuted this claim, arguing that making illusions disappear by manipulating them, whether they are cognitive or visual, does not undermine the initially discovered illusion. They also note that Gigerenzer ignores cognitive illusions resulting from frequency data, e.g., illusory correlations such as the hot hand in basketball. This, they note, is an example of an illusory positive autocorrelation that cannot be corrected by converted data to natural frequencies.

For adaptationists, EMT can be applied to inference under any informational domain, where risk or uncertainty are present, such as predator avoidance, agency detection, or foraging. Researchers advocating this adaptive rationality view argue that evolutionary theory casts heuristics and biases in a new light, namely, as computationally efficient and ecologically rational shortcuts, or instances of adaptive error management.

Base rate neglect

People often neglect base rates, or true actuarial facts about the probability or rate of a phenomenon, and instead give inappropriate amounts of weight to specific observations. In a Bayesian model of inference, this would amount to an underweighting of the prior probability, which has been cited as evidence against the appropriateness of a normative Bayesian framework for modeling cognition. Frequency representations can resolve base rate neglect, and some consider the phenomenon to be an experimental artifact, i.e., a result of probabilities or rates being represented as mathematical abstractions, which are difficult to intuitively think about. Gigerenzer speculates an ecological reason for this, noting that individuals learn frequencies through successive trials in nature. Tversky and Kahneman refute Gigerenzer's claim, pointing to experiments where subjects predicted a disease based on the presence vs. absence of pre-specified symptoms across 250 trials, with feedback after each trial. They note that base rate neglect was still found, despite the frequency formulation of subject trials in the experiment.

Conjunction fallacy

Another popular example of a supposed cognitive illusion is the conjunction fallacy, described in an experiment by Tversky and Kahneman known as the "Linda problem." In this experiment, participants are presented with a short description of a person called Linda, who is 31 years old, single, intelligent, outspoken, and went to a university where she majored in philosophy, was concerned about discrimination and social justice, and participated in anti-nuclear protests. When participants were asked if it were more probable that Linda is (1) a bank teller, or (2) a bank teller and a feminist, 85% responded with option 2, even though it option 1 cannot be less probable than option 2. They concluded that this was a product of a representativeness heuristic, or a tendency to draw probabilistic inferences based on property similarities between instances of a concept, rather than a statistically structured inference.

Gigerenzer argued that the conjunction fallacy is based on a single-event probability, and would dissolve under a frequentist approach. He and other researchers demonstrate that conclusions from the conjunction fallacy result from ambiguous language, rather than robust statistical errors or cognitive illusions. In an alternative version of the Linda problem, participants are told that 100 people fit Linda's description and are asked how many are (1) bank tellers and (2) bank tellers and feminists. Experimentally, this version of the task appears to eliminate or mitigate the conjunction fallacy.

Computational models

There has been some question about how concept structuring and generalization can be understood in terms of brain architecture and processes. This question is impacted by a neighboring debate among theorists about the nature of thought, specifically between connectionist and language of thought models. Concept generalization and classification have been modeled in a variety of connectionist models, or neural networks, specifically in domains like language learning and categorization. Some emphasize the limitations of pure connectionist models when they are expected to generalize future instances after training on previous instances. Gary Marcus, for example, asserts that training data would have to be completely exhaustive for generalizations to occur in existing connectionist models, and that as a result, they do not handle novel observations well. He further advocates an integrationist perspective between a language of thought, consisting of symbol representations and operations, and connectionist models than retain the distributed processing that is likely used by neural networks in the brain.

Evidence in humans

In practice, humans routinely make conceptual, linguistic, and probabilistic generalizations from small amounts of data. There is some debate about the utility of various tools of statistical inference in understanding the mind, but it is commonly accepted that the human mind is somehow an exceptionally apt prediction machine, and that action-oriented processes underlying this phenomenon, whatever they might entail, are at the core of cognition. Probabilistic inferences and generalization play central roles in concepts and categories and language learning, and infant studies are commonly used to understand the developmental trajectory of humans' intuitive statistical toolkit(s).

Infant studies

Developmental psychologists such as Jean Piaget have traditionally argued that children do not develop the general cognitive capacities for probabilistic inference and hypothesis testing until concrete operational (age 7–11 years) and formal operational (age 12 years-adulthood) stages of development, respectively.

This is sometimes contrasted to a growing preponderance of empirical evidence suggesting that humans are capable generalizers in infancy. For example, looking-time experiments using expected outcomes of red and white ping pong ball proportions found that 8-month-old infants appear to make inferences about population characteristics from which the sample came, and vice versa when given population-level data. Other experiments have similarly supported a capacity for probabilistic inference with 6- and 11-month-old infants, but not in 4.5-month-olds.

The colored ball paradigm in these experiments did not distinguish the possibilities of infants' inferences based on quantity vs. proportion, which was addressed in follow-up research where 12-month-old infants seemed to understand proportions, basing probabilistic judgments - motivated by preferences for the more probable outcomes - on initial evidence of the proportions in their available options. Critics of the effectiveness of looking-time tasks allowed infants to search for preferred objects in single-sample probability tasks, supporting the notion that infants can infer probabilities of single events when given a small or large initial sample size. The researchers involved in these findings have argued that humans possess some statistically structured, inferential system during preverbal stages of development and prior to formal education.

It is less clear, however, how and why generalization is observed in infants: It might extend directly from detection and storage of similarities and differences in incoming data, or frequency representations. Conversely, it might be produced by something like general-purpose Bayesian inference, starting with a knowledge base that is iteratively conditioned on data to update subjective probabilities, or beliefs. This ties together questions about the statistical toolkit(s) that might be involved in learning, and how they apply to infant and childhood learning specifically.

Gopnik advocates the hypothesis that infant and childhood learning are examples of inductive inference, a general-purpose mechanism for generalization, acting upon specialized information structures ("theories") in the brain. On this view, infants and children are essentially proto-scientists because they regularly use a kind of scientific method, developing hypotheses, performing experiments via play, and updating models about the world based on their results. For Gopnik, this use of scientific thinking and categorization in development and everyday life can be formalized as models of Bayesian inference. An application of this view is the "sampling hypothesis," or the view that individual variation in children's causal and probabilistic inferences is an artifact of random sampling from a diverse set of hypotheses, and flexible generalizations based on sampling behavior and context. These views, particularly those advocating general Bayesian updating from specialized theories, are considered successors to Piaget’s theory rather than wholesale refutations because they maintain its domain-generality, viewing children as randomly and unsystematically considering a range of models before selecting a probable conclusion.

In contrast to the general-purpose mechanistic view, some researchers advocate both domain-specific information structures and similarly specialized inferential mechanisms. For example, while humans do not usually excel at conditional probability calculations, the use of conditional probability calculations are central to parsing speech sounds into comprehensible syllables, a relatively straightforward and intuitive skill emerging as early as 8 months. Infants also appear to be good at tracking not only spatiotemporal states of objects, but at tracking properties of objects, and these cognitive systems appear to be developmentally distinct. This has been interpreted as domain specific toolkits of inference, each of which corresponds to separate types of information and has applications to concept learning.

Concept formation

Infants use form similarities and differences to develop concepts relating to objects, and this relies on multiple trials with multiple patterns, exhibiting some kind of common property between trials. Infants appear to become proficient at this ability in particular by 12 months, but different concepts and properties employ different relevant principles of Gestalt psychology, many of which might emerge at different stages of development. Specifically, infant categorization at as early as 4.5 months involves iterative and interdependent processes by which exemplars (data) and their similarities and differences are crucial for drawing boundaries around categories. These abstract rules are statistical by nature, because they can entail common co-occurrences of certain perceived properties in past instances and facilitate inferences about their structure in future instances. This idea has been extrapolated by Douglas Hofstadter and Emmanuel Sander, who argue that because analogy is a process of inference relying on similarities and differences between concept properties, analogy and categorization are fundamentally the same process used for organizing concepts from incoming data.

Language learning

Infants and small children are not only capable generalizers of trait quantity and proportion, but of abstract rule-based systems such as language and music. These rules can be referred to as “algebraic rules” of abstract informational structure, and are representations of rule systems, or grammars. For language, creating generalizations with Bayesian inference and similarity detection has been advocated by researchers as a special case of concept formation. Infants appear to be proficient in inferring abstract and structural rules from streams of linguistic sounds produced in their developmental environments, and to generate wider predictions based on those rules.

For example, 9-month-old infants are capable of more quickly and dramatically updating their expectations when repeated syllable strings contain surprising features, such as rare phonemes. In general, preverbal infants appear to be capable of discriminating between grammars with which they have been trained with experience, and novel grammars. In 7-month-old infant looking-time tasks, infants seemed to pay more attention to unfamiliar grammatical structures than to familiar ones, and in a separate study using 3-syllable strings, infants appeared to similarly have generalized expectations based on abstract syllabic structure previously presented, suggesting that they used surface occurrences, or data, in order to infer deeper abstract structure. This was taken to support the “multiple hypotheses [or models]” view by the researchers involved.

Evidence in non-human animals

Grey parrots

Multiple studies by Irene Pepperberg and her colleagues suggested that Grey parrots (Psittacus erithacus) have some capacity for recognizing numbers or number-like concepts, appearing to understand ordinality and cardinality of numerals. Recent experiments also indicated that, given some language training and capacity for referencing recognized objects, they also have some ability to make inferences about probabilities and hidden object type ratios.

Non-human primates

Experiments found that when reasoning about preferred vs. non-preferred food proportions, capuchin monkeys were able to make inferences about proportions inferred by sequentially sampled data. Rhesus monkeys were similarly capable of using probabilistic and sequentially sampled data to make inferences about rewarding outcomes, and neural activity in the parietal cortex appeared to be involved in the decision-making process when they made inferences. In a series of 7 experiments using a variety of relative frequency differences between banana pellets and carrots, orangutans, bonobos, chimpanzees and gorillas also appeared to guide their decisions based on the ratios favoring the banana pellets after this was established as their preferred food item.

Applications

Reasoning in medicine

Research on reasoning in medicine, or clinical reasoning, usually focuses on cognitive processes and/or decision-making outcomes among physicians and patients. Considerations include assessments of risk, patient preferences, and evidence-based medical knowledge. On a cognitive level, clinical inference relies heavily on interplay between abstraction, abduction, deduction, and induction. Intuitive "theories," or knowledge in medicine, can be understood as prototypes in concept spaces, or alternatively, as semantic networks. Such models serve as a starting point for intuitive generalizations to be made from a small number of cues, resulting in the physician's tradeoff between the "art and science" of medical judgement. This tradeoff was captured in an artificially intelligent (AI) program called MYCIN, which outperformed medical students, but not experienced physicians with extensive practice in symptom recognition. Some researchers argue that despite this, physicians are prone to systematic biases, or cognitive illusions, in their judgment (e.g., satisficing to make premature diagnoses, confirmation bias when diagnoses are suspected a priori).

Communication of patient risk

Statistical literacy and risk judgments have been described as problematic for physician-patient communication. For example, physicians frequently inflate the perceived risk of non-treatment, alter patients' risk perceptions by positively or negatively framing single statistics (e.g., 97% survival rate vs. 3% death rate), and/or fail to sufficiently communicate "reference classes" of probability statements to patients. The reference class is the object of a probability statement: If a psychiatrist says, for example, “this medication can lead to a 30-50% chance of a sexual problem,” it is ambiguous whether this means that 30-50% of patients will develop a sexual problem at some point, or if all patients will have problems in 30-50% of their sexual encounters.

Base rates in clinical judgment

In studies of base rate neglect, the problems given to participants often use base rates of disease prevalence. In these experiments, physicians and non-physicians are similarly susceptible to base rate neglect, or errors in calculating conditional probability. Here is an example from an empirical survey problem given to experienced physicians: Suppose that a hypothetical cancer had a prevalence of 0.3% in the population, and the true positive rate of a screening test was 50% with a false positive rate of 3%. Given a patient with a positive test result, what is the probability that the patient has cancer? When asked this question, physicians with an average of 14 years experience in medical practice ranged in their answers from 1-99%, with most answers being 47% or 50%. (The correct answer is 5%.) This observation of clinical base rate neglect and conditional probability error has been replicated in multiple empirical studies. Physicians' judgments in similar problems, however, improved substantially when the rates were re-formulated as natural frequencies.

Electromagnetism

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Electromagnetism 

Aurora at Alaska showing light created by charged particles and magnetism, fundamental concepts to electromagnetism study

 

Articles about
Electromagnetism
Electricity Magnetism History Textbooks

Electrostatics

Magnetostatics

Electrodynamics

Electrical network

Covariant formulation

Scientists

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 is carried by electromagnetic fields composed of electric fields and magnetic fields, and it is responsible for electromagnetic radiation such as light. It is one of the four fundamental interactions (commonly called forces) in nature, together with 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. The electromagnetic attraction between atomic nuclei and their orbital electrons holds atoms together. Electromagnetic forces are responsible for the chemical bonds between atoms which create molecules, and intermolecular forces. The electromagnetic force governs all chemical processes, which arise from interactions between the electrons of neighboring atoms. Electromagnetism is very widely used in modern technology, and electromagnetic theory is the basis of electric power engineering and electronics including digital technology.

There are numerous mathematical descriptions of the electromagnetic field. Most prominently, 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.

History of the theory

Hans Christian Ørsted

 

See also: History of electromagnetic theory

Originally, electricity and magnetism were considered to be two separate forces. This view changed with the publication of James Clerk Maxwell's 1873 A Treatise on Electricity and Magnetism in which the interactions of positive and negative charges were shown to be mediated by one force. There are four main effects resulting from these interactions, all of which have been clearly demonstrated by experiments:

1. Electric charges attract or repel one another with a force inversely proportional to the square of the distance between them: unlike charges attract, like ones repel.
2. Magnetic poles (or states of polarization at individual points) attract or repel one another in a manner similar to positive and negative charges and always exist as pairs: every north pole is yoked to a south pole.
3. An electric current inside a wire creates a corresponding circumferential magnetic field outside the wire. Its direction (clockwise or counter-clockwise) depends on the direction of the current in the wire.
4. A current is induced in a loop of wire when it is moved toward or away from a magnetic field, or a magnet is moved towards or away from it; the direction of current depends on that of the movement.

André-Marie Ampère

In April 1820, Hans Christian Ørsted observed that an electrical current in a wire caused a nearby compass needle to move. At the time of discovery, Ørsted did not suggest any satisfactory explanation of the phenomenon, nor did he try to represent the phenomenon in a mathematical framework. However, three months later he began more intensive investigations. Soon thereafter he published his findings, proving that an electric current produces a magnetic field as it flows through a wire. The CGS unit of magnetic induction (oersted) is named in honor of his contributions to the field of electromagnetism.

James Clerk Maxwell

His findings resulted in intensive research throughout the scientific community in electrodynamics. They influenced French physicist André-Marie Ampère's developments of a single mathematical form to represent the magnetic forces between current-carrying conductors. Ørsted's discovery also represented a major step toward a unified concept of energy.

This unification, which was observed by Michael Faraday, extended by James Clerk Maxwell, and partially reformulated by Oliver Heaviside and Heinrich Hertz, is one of the key accomplishments of 19th-century mathematical physics. It has had far-reaching consequences, one of which was the understanding of the nature of light. Unlike what was proposed by the electromagnetic theory of that time, light and other electromagnetic waves are at present seen as taking the form of quantized, self-propagating oscillatory electromagnetic field disturbances called photons. Different frequencies of oscillation give rise to the different forms of electromagnetic radiation, from radio waves at the lowest frequencies, to visible light at intermediate frequencies, to gamma rays at the highest frequencies.

Ørsted was not the only person to examine the relationship between electricity and magnetism. In 1802, Gian Domenico Romagnosi, an Italian legal scholar, deflected a magnetic needle using a Voltaic pile. The factual setup of the experiment is not completely clear, so if current flowed across the needle or not. An account of the discovery was published in 1802 in an Italian newspaper, but it was largely overlooked by the contemporary scientific community, because Romagnosi seemingly did not belong to this community.

An earlier (1735), and often neglected, connection between electricity and magnetism was reported by a Dr. Cookson. The account stated:

A tradesman at Wakefield in Yorkshire, having put up a great number of knives and forks in a large box ... and having placed the box in the corner of a large room, there happened a sudden storm of thunder, lightning, &c. ... The owner emptying the box on a counter where some nails lay, the persons who took up the knives, that lay on the nails, observed that the knives took up the nails. On this the whole number was tried, and found to do the same, and that, to such a degree as to take up large nails, packing needles, and other iron things of considerable weight ...

E. T. Whittaker suggested in 1910 that this particular event was responsible for lightning to be "credited with the power of magnetizing steel; and it was doubtless this which led Franklin in 1751 to attempt to magnetize a sewing-needle by means of the discharge of Leyden jars."

Fundamental forces

Representation of the electric field vector of a wave of circularly polarized electromagnetic radiation.

The electromagnetic force is one of the four known fundamental forces. The other fundamental forces are:

• the strong nuclear force, which binds quarks to form nucleons, and binds nucleons to form nuclei.
• the weak nuclear force, which binds to all known particles in the Standard Model, and causes certain forms of radioactive decay. (In particle physics though, the electroweak interaction is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction);
• the gravitational force.

All other forces (e.g., friction, contact forces) are derived from these four fundamental forces and they are known as non-fundamental forces.

The electromagnetic force is responsible for practically all phenomena one encounters in daily life above the nuclear scale, with the exception of gravity. Roughly speaking, all the forces involved in interactions between atoms can be explained by the electromagnetic force acting between the electrically charged atomic nuclei and electrons of the atoms. Electromagnetic forces also explain how these particles carry momentum by their movement. This includes the forces we experience in "pushing" or "pulling" ordinary material objects, which result from the intermolecular forces that act between the individual molecules in our bodies and those in the objects. The electromagnetic force is also involved in all forms of chemical phenomena.

A necessary part of understanding the intra-atomic and intermolecular forces is the effective force generated by the momentum of the electrons' movement, such that as electrons move between interacting atoms they carry momentum with them. As a collection of electrons becomes more confined, their minimum momentum necessarily increases due to the Pauli exclusion principle. The behaviour of matter at the molecular scale including its density is determined by the balance between the electromagnetic force and the force generated by the exchange of momentum carried by the electrons themselves.

Classical electrodynamics

Main article: Classical electrodynamics

In 1600, William Gilbert proposed, in his De Magnete, that electricity and magnetism, while both capable of causing attraction and repulsion of objects, were distinct effects. Mariners had noticed that lightning strikes had the ability to disturb a compass needle. The link between lightning and electricity was not confirmed until Benjamin Franklin's proposed experiments in 1752. One of the first to discover and publish a link between man-made electric current and magnetism was Gian Romagnosi, who in 1802 noticed that connecting a wire across a voltaic pile deflected a nearby compass needle. However, the effect did not become widely known until 1820, when Ørsted performed a similar experiment. Ørsted's work influenced Ampère to produce a theory of electromagnetism that set the subject on a mathematical foundation.

A theory of electromagnetism, known as classical electromagnetism, was developed by various physicists during the period between 1820 and 1873 when it culminated in the publication of a treatise by James Clerk Maxwell, which unified the preceding developments into a single theory and discovered the electromagnetic nature of light. In classical electromagnetism, the behavior of the electromagnetic field is described by a set of equations known as Maxwell's equations, and the electromagnetic force is given by the Lorentz force law.

One of the peculiarities of classical electromagnetism is that it is difficult to reconcile with classical mechanics, but it is compatible with special relativity. According to Maxwell's equations, the speed of light in a vacuum is a universal constant that is dependent only on the electrical permittivity and magnetic permeability of free space. This violates Galilean invariance, a long-standing cornerstone of classical mechanics. One way to reconcile the two theories (electromagnetism and classical mechanics) is to assume the existence of a luminiferous aether through which the light propagates. However, subsequent experimental efforts failed to detect the presence of the aether. After important contributions of Hendrik Lorentz and Henri Poincaré, in 1905, Albert Einstein solved the problem with the introduction of special relativity, which replaced classical kinematics with a new theory of kinematics compatible with classical electromagnetism. (For more information, see History of special relativity.)

In addition, relativity theory implies that in moving frames of reference, a magnetic field transforms to a field with a nonzero electric component and conversely, a moving electric field transforms to a nonzero magnetic component, thus firmly showing that the phenomena are two sides of the same coin. Hence the term "electromagnetism". (For more information, see Classical electromagnetism and special relativity and Covariant formulation of classical electromagnetism.)

Extension to nonlinear phenomena

Magnetic reconnection in the solar plasma gives rise to solar flares, a complex magnetohydrodynamical phenomenon.

The Maxwell equations are linear, in that a change in the sources (the charges and currents) results in a proportional change of the fields. Nonlinear dynamics can occur when electromagnetic fields couple to matter that follows nonlinear dynamical laws. This is studied, for example, in the subject of magnetohydrodynamics, which combines Maxwell theory with the Navier–Stokes equations.

Quantities and units

See also: List of physical quantities and List of electromagnetism equations

Electromagnetic units are part of a system of electrical units based primarily upon the magnetic properties of electric currents, the fundamental SI unit being the ampere. The units are:

• ampere (electric current)
• coulomb (electric charge)
• farad (capacitance)
• henry (inductance)
• ohm (resistance)
• siemens (conductance)
• tesla (magnetic flux density)
• volt (electric potential)
• watt (power)
• weber (magnetic flux)

In the electromagnetic CGS system, electric current is a fundamental quantity defined via Ampère's law and takes the permeability as a dimensionless quantity (relative permeability) whose value in a vacuum is unity. As a consequence, the square of the speed of light appears explicitly in some of the equations interrelating quantities in this system.

SI electromagnetism units
Symbol	Name of quantity	Unit name	Symbol	Base units
E	energy	joule	J	kg⋅m2⋅s−2 = C⋅V
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
ΔV; Δφ; ε	potential difference; voltage; 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
µ	magnetic dipole moment	ampere square meter	A⋅m2	A⋅m2 = J⋅T−1 = 103 emu
σ	mass magnetization	ampere square meter per kilogram	A⋅m2/kg	A⋅m2⋅kg−1 = emu⋅g−1 = erg⋅G−1⋅g−1

Formulas for physical laws of electromagnetism (such as Maxwell's equations) need to be adjusted depending on what system of units one uses. This is because there is no one-to-one correspondence between electromagnetic units in SI and those in CGS, as is the case for mechanical units. Furthermore, within CGS, there are several plausible choices of electromagnetic units, leading to different unit "sub-systems", including Gaussian, "ESU", "EMU", and Heaviside–Lorentz. Among these choices, Gaussian units are the most common today, and in fact the phrase "CGS units" is often used to refer specifically to CGS-Gaussian units.

Magnetism

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Magnetism 

Ferrofluid "spiked" up by a cube neodymium magnet, following its magnetic field

 

Articles about
Electromagnetism
Electricity Magnetism History Textbooks

Electrostatics

Magnetostatics

Electrodynamics

Electrical network

Covariant formulation

Scientists

Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomenon in other entities. Electric currents and the magnetic moments of elementary particles give rise to a magnetic field, which acts on other currents and magnetic moments. Magnetism is one aspect of the combined phenomenon of electromagnetism. 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. Demagnetizing a magnet is also possible. Only a few substances are ferromagnetic; the most common ones are iron, cobalt and nickel and their alloys. The rare-earth metals neodymium and samarium are less common examples. The prefix ferro- refers to iron, because permanent magnetism was first observed in lodestone, a form of natural iron ore called magnetite, Fe₃O₄.

All substances exhibit some type of magnetism. Magnetic materials are classified according to their bulk susceptibility. Ferromagnetism is responsible for most of the effects of magnetism encountered in everyday life, but there are actually several 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, pressure, and the applied magnetic field. A material may exhibit more than one form of magnetism as these variables change.

The strength of a magnetic field almost always decreases with distance, though the exact mathematical relationship between strength and distance varies. Different configurations of magnetic moments and electric currents can result in complicated magnetic fields.

Only magnetic dipoles have been observed, although some theories predict the existence of magnetic monopoles.

History

Main article: History of electromagnetism

 

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

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

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 (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 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, 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

See also: Magnetic moment

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 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. Due to high longitude of the alpha system the hirearchy doesnt work as well.

Types of magnetism

Hierarchy of types of magnetism.

Diamagnetism

Main article: 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. 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.

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.

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

Main article: 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

Main article: 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

Main article: Magnetic domains

 

Magnetic domains boundaries (white lines) in ferromagnetic material (black rectangle)

 

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

Antiferromagnetic ordering

 

Main article: 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

 

Main article: Ferrimagnetism

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

Main article: 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

• Metamagnetism
• Molecule-based magnets
• Single-molecule magnet
• Spin glass

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. 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. Electromagnetism was discovered in 1820.

Magnetism, electricity, and special relativity

Main article: Classical electromagnetism and special relativity

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. 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.

Magnetic fields in a material

See also: Magnetic field § H and B inside and outside of magnetic materials

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 force

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

 

Main article: Magnetic field

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:

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

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.

Magnetic dipoles

Main article: Magnetic dipole

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

Main article: Magnetic monopole

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.

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.

Units

SI

SI electromagnetism units
Symbol	Name of quantity	Unit name	Symbol	Base units
E	energy	joule	J	kg⋅m2⋅s−2 = C⋅V
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
ΔV; Δφ; ε	potential difference; voltage; 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
µ	magnetic dipole moment	ampere square meter	A⋅m2	A⋅m2 = J⋅T−1 = 103 emu
σ	mass magnetization	ampere square meter per kilogram	A⋅m2/kg	A⋅m2⋅kg−1 = emu⋅g−1 = erg⋅G−1⋅g−1

Other

• 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 (4π × 10⁻⁷ newton/(ampere-turn)²)

Living things

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. 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.

Quantum-mechanical origin of magnetism

While heuristic explanations based on classical physics can be formulated, diamagnetism, paramagnetism and ferromagnetism can be fully explained only using quantum theory. 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 (= ±½); 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

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) Spin-transfer torque on the magnetization. This phenomena 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).

Method

Optically induced magnetism occurs when an initial photon establishes an electrical polarization within a material and that causes an orbital angular momentum. This occurs on all electric dipoles within the material that transition between L = 0 and L = 1. A second photon can exert a magnetic torque on the orbital angular momentum, and that causes an exchange of orbital angular momentum to rotational angular momentum. The change from orbital angular momentum to rotational angular momentum de-excites the molecule and increases the radius of charge motion. When the radius of charge motion increases, the magnetic dipole Electron magnetic moment increases. This is because the magnetic dipole depends on the area enclosed by the current within the molecule (m = ids). This type of magnetism can occur in materials that are thought to be "non magnetic," such as diamagnets. Diamagnetism, as long as the material is dielectric.

The more you optically excite the dielectric material, the more magnetic dipoles are formed, and therefore the more magnetic the material becomes. However, the electric dipole Electric dipole moment magnitude will always be larger than the magnetic dipole magnitude, and the magnetic dipole moment will always be relative to the electric dipole moment.