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ield 78 languages العربية asturianu azərbaycanca تۆرکجه беларуская тарашкевіца беларуская български বাংলা bosanski català کوردی čeština чӑвашла dansk deutsch zazaki ελληνικά esperanto español eesti euskara فارسی suomi français galego עברית हिन्दी hrvatski magyar հայերեն bahasa indonesia ido íslenska italiano 日本語 ქართული қазақша 한국어 кыргызча limburgs lietuvių latviešu मगही malagasy македонски മലയാളം монгол bahasa melayu napulitano nederlands norsk nynorsk norsk bokmål occitan ਪੰਜਾਬੀ polski پښتو português română русский srpskohrvatski српскохрватски slovenčina slovenščina shqip српски srpski svenska தமிழ் ไทย toki pona türkçe українська اردو oʻzbekcha ўзбекча tiếng việt wolof 吴语 閩南語 bân lâm gí 粵語 中文 edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikimedia commons wikibooks wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia electric and magnetic fields produced by moving charged objects this article is about a representation of electromagnetism not to be confused with electromotive force or electromagnetic field festival electromagnetism electricity magnetism optics history computational textbooks phenomena electrostatics electric charge charge density coulomb s law electric field electric flux gauss s law electric potential potential energy conductor electret electric dipole electrostatic discharge electrostatic induction insulator permittivity polarization static electricity triboelectricity magnetostatics magnetic field ampère s law ampère s force law biot savart law gauss s law for magnetism magnetic dipole magnetic flux magnetic scalar potential magnetic vector potential magnetization permeability right hand rule electrodynamics maxwell s equations displacement current electromagnetic field lorentz force helmholtz theorem retarded potentials liénard wiechert potential jefimenko s equations radiation cyclotron radiation faraday s law eddy current induction lenz s law electromagnetic mass abraham lorentz force larmor formula poynting s theorem maxwell tensor electrical network alternating current capacitance current density direct current electric current electric power electrolysis electromotive force impedance inductance joule heating kirchhoff s laws network analysis ohm s law parallel circuit resistance resonant cavities series circuit voltage watt waveguides london equations magnetic circuit ac motor dc motor electric machine electric motor gyrator capacitor induction motor linear motor magnetomotive force permeance reluctance complex reluctance real rotor stator transformer covariant formulation electromagnetic tensor electromagnetism and special relativity four current four potential mathematical descriptions maxwell equations in curved spacetime relativistic electromagnetism stress energy tensor synchrotron radiation bremsstrahlung scientists ampère arago biot coulomb davy einstein faraday fitzgerald fizeau franklin galvani gauss gibbs gilbert green heaviside helmholtz henry hertz hopkinson joule kelvin kirchhoff larmor lenz liénard lorentz maxwell neumann ohm ørsted poisson poynting ritchie savart singer steinmetz tesla thomson volta weber wiechert v t e an electromagnetic field also em field is a physical field varying in space and time that represents the electric and magnetic influences generated by and acting upon electric charges 1 the field at any point in space and time can be regarded as a combination of an electric field and a magnetic field because of the interrelationship between the fields a disturbance in the electric field can create a disturbance in the magnetic field which in turn affects the electric field leading to an oscillation that propagates through space known as an electromagnetic wave 2 3 mathematically the electromagnetic field is a pair of vector fields consisting of one vector for the electric field and one for the magnetic field at each point in space the vectors may change over time and space in accordance with maxwell s equations the vectors are subject to the rules of special relativity different observers may determine different vectors the way in which charges and currents i e streams of charges interact with the electromagnetic field is described by maxwell s equations 4 and the lorentz force law 5 maxwell s equations detail how the electric field converges towards or diverges away from electric charges how the magnetic field curls around electrical currents and how changes in the electric and magnetic fields influence each other the lorentz force law states that a charge subject to an electric field feels a force along the direction of the field and a charge moving through a magnetic field feels a force that is perpendicular both to the magnetic field and to its direction of motion the electromagnetic field is described by classical electrodynamics an example of a classical field theory this theory describes many macroscopic physical phenomena accurately 6 however it was unable to explain the photoelectric effect and atomic absorption spectroscopy experiments at the atomic scale that required the use of quantum mechanics specifically the quantization of the electromagnetic field and the development of quantum electrodynamics history edit main article history of electromagnetic theory results of michael faraday s iron filings experiment the empirical investigation of electromagnetism is at least as old as the ancient greek philosopher mathematician and scientist thales of miletus who around 600 bce described his experiments rubbing fur of animals on various materials such as amber creating static electricity 7 by the 18th century it was understood that objects can carry positive or negative electric charge that two objects carrying charge of the same sign repel each other that two objects carrying charges of opposite sign attract one another and that the strength of this force falls off as the square of the distance between them michael faraday visualized this in terms of the charges interacting via the electric field an electric field is produced when the charge is stationary with respect to an observer measuring the properties of the charge and a magnetic field as well as an electric field are produced when the charge moves creating an electric current with respect to this observer over time it was realized that the electric and magnetic fields are better thought of as two parts of a greater whole the electromagnetic field in 1820 hans christian ørsted showed that an electric current can deflect a nearby compass needle establishing that electricity and magnetism are closely related phenomena 8 faraday then made the seminal observation that time varying magnetic fields could induce electric currents in 1831 in 1861 james clerk maxwell synthesized all the work to date on electrical and magnetic phenomena into a single mathematical theory from which he then deduced that light is an electromagnetic wave maxwell s continuous field theory was very successful until evidence supporting the atomic model of matter emerged beginning in 1877 hendrik lorentz developed an atomic model of electromagnetism and in 1897 j j thomson completed experiments that defined the electron the lorentz theory works for free charges in electromagnetic fields but fails to predict the energy spectrum for bound charges in atoms and molecules for that problem quantum mechanics is needed ultimately leading to the theory of quantum electrodynamics practical applications of the new understanding of electromagnetic fields emerged in the late 1800s the electrical generator and motor were invented using only the empirical findings like faraday s and ampere s laws combined with practical experience mathematical description edit main article mathematical descriptions of the electromagnetic field there are different mathematical ways of representing the electromagnetic field the first one views the electric and magnetic fields as three dimensional vector fields these vector fields each have a value defined at every point of space and time and are thus often regarded as functions of the space and time coordinates as such they are often written as e x y z t electric field and b x y z t magnetic field if only the electric field e is non zero and is constant in time the field is said to be an electrostatic field similarly if only the magnetic field b is non zero and is constant in time the field is said to be a magnetostatic field however if either the electric or magnetic field has a time dependence then both fields must be considered together as a coupled electromagnetic field using maxwell s equations 9 with the advent of special relativity physical laws became amenable to the formalism of tensors maxwell s equations can be written in tensor form generally viewed by physicists as a more elegant means of expressing physical laws the behavior of electric and magnetic fields whether in cases of electrostatics magnetostatics or electrodynamics electromagnetic fields is governed by maxwell s equations in the vector field formalism these are gauss s law e ρ ε 0 displaystyle nabla cdot mathbf e frac rho varepsilon _ 0 gauss s law for magnetism b 0 displaystyle nabla cdot mathbf b 0 faraday s law e b t displaystyle nabla times mathbf e frac partial mathbf b partial t ampère maxwell law b μ 0 j μ 0 ε 0 e t displaystyle nabla times mathbf b mu _ 0 mathbf j mu _ 0 varepsilon _ 0 frac partial mathbf e partial t where ρ displaystyle rho is the charge density which is a function of time and position ε 0 displaystyle varepsilon _ 0 is the vacuum permittivity μ 0 displaystyle mu _ 0 is the vacuum permeability and j is the current density vector also a function of time and position inside a linear material maxwell s equations change by switching the permeability and permittivity of free space with the permeability and permittivity of the linear material in question inside other materials which possess more complex responses to electromagnetic fields these terms are often represented by complex numbers or tensors the lorentz force law governs the interaction of the electromagnetic field with charged matter when a field travels across to different media the behavior of the field changes according to the properties of the media 10 properties of the field edit electrostatics and magnetostatics edit main articles electrostatics and magnetostatics electric field of a positive point electric charge suspended over an infinite sheet of conducting material the field is depicted by electric field lines lines which follow the direction of the electric field in space the maxwell equations simplify when the charge density at each point in space does not change over time and all electric currents likewise remain constant all of the time derivatives vanish from the equations leaving two expressions that involve the electric field e ρ ϵ 0 displaystyle nabla cdot mathbf e frac rho epsilon _ 0 and e 0 displaystyle nabla times mathbf e 0 along with two formulae that involve the magnetic field b 0 displaystyle nabla cdot mathbf b 0 and b μ 0 j displaystyle nabla times mathbf b mu _ 0 mathbf j these expressions are the basic equations of electrostatics which focuses on situations where electrical charges do not move and magnetostatics the corresponding area of magnetic phenomena 11 transformations of electromagnetic fields edit further information classical electromagnetism and special relativity electromagnetic four potential and electromagnetic tensor whether a physical effect is attributable to an electric field or to a magnetic field is dependent upon the observer in a way that special relativity makes mathematically precise for example suppose that a laboratory contains a long straight wire that carries an electrical current in the frame of reference where the laboratory is at rest the wire is motionless and electrically neutral the current composed of negatively charged electrons moves against a background of positively charged ions and the densities of positive and negative charges cancel each other out a test charge near the wire would feel no electrical force from the wire however if the test charge is in motion parallel to the current the situation changes in the rest frame of the test charge the positive and negative charges in the wire are moving at different speeds and so the positive and negative charge distributions are lorentz contracted by different amounts consequently the wire has a nonzero net charge density and the test charge must experience a nonzero electric field and thus a nonzero force in the rest frame of the laboratory there is no electric field to explain the test charge being pulled towards or pushed away from the wire so an observer in the laboratory rest frame concludes that a magnetic field must be present 12 13 in general a situation that one observer describes using only an electric field will be described by an observer in a different inertial frame using a combination of electric and magnetic fields analogously a phenomenon that one observer describes using only a magnetic field will be in a relatively moving reference frame described by a combination of fields the rules for relating the fields required in different reference frames are the lorentz transformations of the fields 14 thus electrostatics and magnetostatics are now seen as studies of the static em field when a particular frame has been selected to suppress the other type of field and since an em field with both electric and magnetic will appear in any other frame these simpler effects are merely a consequence of different frames of measurement the fact that the two field variations can be reproduced just by changing the motion of the observer is further evidence that there is only a single actual field involved which is simply being observed differently reciprocal behavior of electric and magnetic fields edit main articles faraday s law of induction and ampère s circuital law the two maxwell equations faraday s law and the ampère maxwell law illustrate a very practical feature of the electromagnetic field faraday s law may be stated roughly as a changing magnetic field inside a loop creates an electric voltage around the loop this is the principle behind the electric generator ampere s law roughly states that an electrical current around a loop creates a magnetic field through the loop thus this law can be applied to generate a magnetic field and run an electric motor behavior of the fields in the absence of charges or currents edit a linearly polarized electromagnetic plane wave propagating parallel to the z axis is a possible solution for the electromagnetic wave equations in free space the electric field e and the magnetic field b are perpen...