# Magnetic field

The shape of the magnetic field produced by a horseshoe magnet is revealed by the orientation of iron filings sprinkled on a piece of paper above the magnet.

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

The term 'magnetic field' is used for two distinct but closely related fields denoted by the symbols B and H. In the International System of Units, H is measured in units of amperes per meter and B is measured in teslas or newtons per meter per ampere. H and B differ in how they account for magnetization. In a vacuum, B and H are the same aside from units; but in a magnetized material, B/${\displaystyle \mu _{0}}$ and H differ by the magnetization M of the material at that point in the material.

Magnetic fields are produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin.[1][2] Magnetic fields and electric fields are interrelated, and are both components of the electromagnetic force, one of the four fundamental forces of nature.

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

## History

One of the first drawings of a magnetic field, by René Descartes, 1644, showing the Earth attracting lodestones. It illustrated his theory that magnetism was caused by the circulation of tiny helical particles, "threaded parts", through threaded pores in magnets.

Although magnets and magnetism were studied much earlier, the research of magnetic fields began in 1269 when French scholar Petrus Peregrinus de Maricourt mapped out the magnetic field on the surface of a spherical magnet using iron needles.[nb 1] Noting that the resulting field lines crossed at two points he named those points 'poles' in analogy to Earth's poles. He also clearly articulated the principle that magnets always have both a north and south pole, no matter how finely one slices them.

Almost three centuries later, William Gilbert of Colchester replicated Petrus Peregrinus' work and was the first to state explicitly that Earth is a magnet.[3] Published in 1600, Gilbert's work, De Magnete, helped to establish magnetism as a science.

In 1750, John Michell stated that magnetic poles attract and repel in accordance with an inverse square law.[4] Charles-Augustin de Coulomb experimentally verified this in 1785 and stated explicitly that the north and south poles cannot be separated.[5] Building on this force between poles, Siméon Denis Poisson (1781–1840) created the first successful model of the magnetic field, which he presented in 1824.[6] In this model, a magnetic H-field is produced by 'magnetic poles' and magnetism is due to small pairs of north/south magnetic poles.

Hans Christian Ørsted, Der Geist in der Natur, 1854

Three discoveries challenged this foundation of magnetism, though. First, in 1819, Hans Christian Ørsted discovered that an electric current generates a magnetic field encircling it. Then in 1820, André-Marie Ampère showed that parallel wires with currents attract one another if the currents are in the same direction and repel if they are in opposite directions.[7] Finally, Jean-Baptiste Biot and Félix Savart discovered the Biot–Savart law in 1820, which correctly predicts the magnetic field around any current-carrying wire.

Extending these experiments, Ampère published his own successful model of magnetism in 1825. In it, he showed the equivalence of electrical currents to magnets[8] and proposed that magnetism is due to perpetually flowing loops of current instead of the dipoles of magnetic charge in Poisson's model.[nb 2] This has the additional benefit of explaining why magnetic charge can not be isolated. Further, Ampère derived both Ampère's force law describing the force between two currents and Ampère's law, which, like the Biot–Savart law, correctly described the magnetic field generated by a steady current. Also in this work, Ampère introduced the term electrodynamics to describe the relationship between electricity and magnetism.

In 1831, Michael Faraday discovered electromagnetic induction when he found that a changing magnetic field generates an encircling electric field. He described this phenomenon in what is known as Faraday's law of induction. Later, Franz Ernst Neumann proved that, for a moving conductor in a magnetic field, induction is a consequence of Ampère's force law.[9] In the process, he introduced the magnetic vector potential, which was later shown to be equivalent to the underlying mechanism proposed by Faraday.

In 1850, Lord Kelvin, then known as William Thomson, distinguished between two magnetic fields now denoted H and B. The former applied to Poisson's model and the latter to Ampère's model and induction.[10] Further, he derived how H and B relate to each other.

The reason H and B are used for the two magnetic fields has been a source of some debate among science historians. Most agree that Kelvin avoided M to prevent confusion with the SI fundamental unit of length, the Metre, abbreviated "m". Others believe the choices were purely random.[11][12]

Between 1861 and 1865, James Clerk Maxwell developed and published Maxwell's equations, which explained and united all of classical electricity and magnetism. The first set of these equations was published in a paper entitled On Physical Lines of Force in 1861. These equations were valid although incomplete. Maxwell completed his set of equations in his later 1865 paper A Dynamical Theory of the Electromagnetic Field and demonstrated the fact that light is an electromagnetic wave. Heinrich Hertz experimentally confirmed this fact in 1887.

The twentieth century extended electrodynamics to include relativity and quantum mechanics. Albert Einstein, in his paper of 1905 that established relativity, showed that both the electric and magnetic fields are part of the same phenomena viewed from different reference frames. (See moving magnet and conductor problem for details about the thought experiment that eventually helped Albert Einstein to develop special relativity.) Finally, the emergent field of quantum mechanics was merged with electrodynamics to form quantum electrodynamics (QED).

Other Languages
Afrikaans: Magneetveld
Alemannisch: Magnetfeld
العربية: حقل مغناطيسي
aragonés: Campo magnetico
asturianu: Campu magnéticu
azərbaycanca: Maqnit sahəsi
башҡортса: Магнит ҡыры
беларуская: Магнітнае поле
беларуская (тарашкевіца)‎: Магнітнае поле
български: Магнитно поле
bosanski: Magnetno polje
čeština: Magnetické pole
Cymraeg: Maes magnetig
dansk: Magnetfelt
Deutsch: Magnetfeld
Esperanto: Magneta kampo
estremeñu: Campu manéticu
Fiji Hindi: Magnetic field
한국어: 자기장
hrvatski: Magnetsko polje
Bahasa Indonesia: Medan magnet
interlingua: Campo magnetic
íslenska: Segulsvið
italiano: Campo magnetico
עברית: שדה מגנטי
қазақша: Магнит өрісі
Kiswahili: Uga sumaku
Kreyòl ayisyen: Chan mayetik
македонски: Магнетно поле
Bahasa Melayu: Medan magnet
မြန်မာဘာသာ: သံလိုက်စက်ကွင်း
Nederlands: Magnetisch veld

Nordfriisk: Magneetisk fial
norsk: Magnetfelt
norsk nynorsk: Magnetfelt
occitan: Camp magnetic
oʻzbekcha/ўзбекча: Magnit maydon
português: Campo magnético
română: Câmp magnetic
русиньскый: Маґнетічне поле
Simple English: Magnetic field
slovenčina: Magnetické pole
slovenščina: Magnetno polje
српски / srpski: Магнетно поље
srpskohrvatski / српскохрватски: Magnetno polje
Basa Sunda: Médan magnétik
svenska: Magnetfält
татарча/tatarça: Магнит кыры
Türkçe: Manyetik alan
українська: Магнітне поле
Tiếng Việt: Từ trường