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Encyclopedia > Electromagnetic field
Electrostatics Electromagnetism Electricity · Magnetism Electric charge Coulomb's law Electric field Gauss's law Electric potential Electric dipole moment Ampère's law Magnetic field Magnetic dipole moment Electric current Lorentz force law Electromotive force (EM) Electromagnetic induction Faraday-Lenz law Displacement current Maxwell's equations (EMF) Electromagnetic field (EM) Electromagnetic radiation Electrical conduction Electrical resistance Capacitance Inductance Impedance Resonant cavities Waveguides This box: view • talk • edit

From a classical point of view, the electromagnetic field can be regarded as a smooth, continuous field, propagated in a wavelike manner, whereas from a quantum mechanical point of view, the field can be viewed as being composed of photons. Classical physics is physics based on principles developed before the rise of quantum theory, usually including the special theory of relativity and general theory of relativity. ... Fig. ... In physics, the photon (from Greek Ï†Ï‰Ï‚, phÅs, meaning light) is the quantum of the electromagnetic field; for instance, light. ...

## Structure of the electromagnetic field GA_googleFillSlot("encyclopedia_square");

The electromagnetic field may be viewed in two distinct ways.

### Continuous structure

Classically, electric and magnetic fields are thought of as being produced by smooth motions of charged objects. For example, oscillating charges produce electric and magnetic fields that may be viewed in a 'smooth', continuous, wavelike manner. In this case, energy is viewed as being transferred continuously through the electromagnetic field between any two locations. For instance, the metal atoms in a radio transmitter appear to transfer energy continuously. This view is useful to a certain extent (radiation of low frequency), but problems are found at high frequencies (see ultraviolet catastrophe). This problem leads to another view. Antenna tower of Crystal Palace transmitter, London A transmitter (sometimes abbreviated XMTR) is an electronic device which with the aid of an antenna propagates an electromagnetic signal such as radio, television, or other telecommunications. ... The ultraviolet catastrophe, also called the Rayleigh-Jeans catastrophe, was a prediction of early 20th century classical physics that an ideal black body at thermal equilibrium will emit radiation with infinite power. ...

### Discrete structure

The electromagnetic field may be thought of in a more 'coarse' way. Experiments reveal that electromagnetic energy transfer is better described as being carried away in 'packets' or 'chunks' called photons with a fixed frequency. Planck's relation links the energy E of a photon to its frequency ν through the equation: The word light is defined here as electromagnetic radiation of any wavelength; thus, X-rays, gamma rays, ultraviolet light, infrared radiation, microwaves, radio waves, and visible light are all forms of light. ...

$E= , h , nu$

where h is Planck's constant, named in honour of Max Planck, and ν is the frequency of the photon . For example, in the photoelectric effect —the emission of electrons from metallic surfaces by electromagnetic radiation— it is found that increasing the intensity of the incident radiation has no effect, and that only the frequency of the radiation is relevant in ejecting electrons. A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ... Max Karl Ernst Ludwig Planck (April 23, 1858 â€“ October 4, 1947 in GÃ¶ttingen, Germany) was a German physicist. ... A diagram illustrating the emission of photoelectrons from a metal plate, requiring energy gained from an incoming photon to be more than the work function of the material. ...

This quantum picture of the electromagnetic field has proved very successful, giving rise to quantum electrodynamics, a quantum field theory describing the interaction of electromagnetic radiation with charged matter. In physics, a quantum (plural: quanta) is an indivisible entity of energy. ... Quantum electrodynamics (QED) is a relativistic quantum field theory of electromagnetism. ... Quantum field theory (QFT) is the quantum theory of fields. ...

## Dynamics of the electromagnetic field

In the past, electrically charged objects were thought to produce two types of field associated with their charge property. 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) is 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.

Once this electromagnetic field has been produced from a given charge distribution, other charged objects in this field will experience a force (in a similar way that planets experience a force in the gravitational field of the Sun). If these other charges and currents are comparable in size to the sources producing the above electromagnetic field, then a new net electromagnetic field will be produced. Thus, the electromagnetic field may be viewed as a dynamic entity that causes other charges and currents to move, and which is also affected by them. These interactions are described by Maxwell's equations and the Lorentz force law. In electromagnetism, Maxwells equations are a set of equations developed in the latter half of the nineteenth century by James Clerk Maxwell. ... In physics, the Lorentz force is the force exerted on a charged particle in an electromagnetic field. ...

## The electromagnetic field as a feedback loop

The behavior of the electromagnetic field can be resolved into four different parts of a loop: (1) the electric and magnetic fields are generated by electric charges, (2) the electric and magnetic fields interact only with each other, (3) the electric and magnetic fields produce forces on electric charges, (4) the electric charges move in space.

The feedback loop can be summarized in a list, including phenomena belonging to each part of the loop:

• charges generate fields
• the fields interact with each other
• fields act upon charges
• Lorentz force: force due to electromagnetic field
• electric force: same direction as electric field
• magnetic force: perpendicular both to magnetic field and to velocity of charge ($star$)
• charges move

Phenomena in the list are marked with a star ($star$) if they consist of magnetic fields and moving charges which can be reduced by suitable Lorentz transformations to electric fields and static charges. This means that the magnetic field ends up being (conceptually) reduced to an appendage of the electric field, i.e. something which interacts with reality only indirectly through the electric field. In physics and mathematical analysis, Gausss law, closely related to Gausss theorem, gives the relation between the electric or gravitational flux flowing out of a closed surface and, respectively, the electric charge or mass enclosed in the surface. ... Coulombs torsion balance In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrostatic force that one stationary, electrically charged object of small dimensions (ideally, a point source) exerts on another. ... An electric current produces a magnetic field. ... Displacement current is a quantity related to a changing electric field. ... In vector calculus, curl is a vector operator that shows a vector fields rate of rotation: the direction of the axis of rotation and the magnitude of the rotation. ... Faradays law of induction (more generally, the law of electromagnetic induction) states that the induced emf (electromotive force) in a closed loop equals the negative of the time rate of change of magnetic flux through the loop. ... Lenzs law (pronounced (IPA) ) was formulated by German physicist Heinrich Lenz in 1833 and gives the direction of the induced electromotive force (emf) resulting from electromagnetic induction. ... In electromagnetism, Maxwells equations are a set of equations developed in the latter half of the nineteenth century by James Clerk Maxwell. ... The wave equation is an important partial differential equation that describes the propagation of a variety of waves, such as sound waves, light waves and water waves. ... In physics, the Lorentz force is the force exerted on a charged particle in an electromagnetic field. ... All the examples of continuity equations below express the same idea; they are all really examples of the same concept. ... A Lorentz transformation (LT) is a linear transformation that preserves the spacetime interval between any two events in Minkowski space, while leaving the origin fixed (=rotation of Minkowski space). ...

## Mathematical description

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 $mathbf{E}(x, y, z, t)$ (electric field) and $mathbf{B}(x, y, z, t)$ (magnetic field). There are various mathematical descriptions of the electromagnetic field that are used in the study of electromagnetism, one of the four fundamental forces of nature. ... Vector field given by vectors of the form (-y, x) In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a Euclidean space. ... It has been suggested that optical field be merged into this article or section. ... In physics, a magnetic field is a force field that surrounds electric current circuits. ...

If only the electric field ($mathbf{E}$) is non-zero, and is constant in time, the field is said to be an electrostatic field. Similarly, if only the magnetic field ($mathbf B$) 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. It has been suggested that optical field be merged into this article or section. ... In physics, an electric field or E-field is an effect produced by an electric charge that exerts a force on charged objects in its vicinity. ... In physics, a magnetic field is a force field that surrounds electric current circuits. ... Brief explanation of magnetostatics Magnetostatics is the study of static magnetic fields. ... In electromagnetism, Maxwells equations are a set of equations developed in the latter half of the nineteenth century by James Clerk Maxwell. ...

With the advent of special relativity, physical laws became susceptible 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 special theory of relativity was proposed in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. Some three centuries earlier, Galileos principle of relativity had stated that all uniform motion was relative, and that there was no absolute and well-defined state of rest... In mathematics, a tensor is (in an informal sense) a generalized linear quantity or geometrical entity that can be expressed as a multi-dimensional array relative to a choice of basis; however, as an object in and of itself, a tensor is independent of any chosen frame of reference. ...

The behaviour of electric and magnetic fields, whether in cases of electrostatics, magnetostatics, or electrodynamics (electromagnetic fields), is governed in a vacuum by Maxwell's equations. In the vector field formalism, these are: Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ...

$nabla cdot mathbf{E} = frac{rho}{varepsilon_0}$ (Gauss' law - electrostatics)
$nabla cdot mathbf{B} = 0$ (Gauss' law - magnetostatics)
$nabla times mathbf{E} = -frac {partial mathbf{B}}{partial t}$ (Faraday's law)
$nabla times mathbf{B} = mu_0 mathbf{J} + mu_0varepsilon_0 frac{partial mathbf{E}}{partial t}$ (Ampère-Maxwell law)

where ρ is the charge density, which can (and often does) depend on time and position, ε0 is the permittivity of free space, μ0 is the permeability of free space, and $mathbf J$ is the current density vector, also a function of time and position. The units used above are the standard SI units. Inside a linear material, Maxwell's equations change by switching the permeability and permitivity of free space with the permeability and permitivity 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. In physics, Gausss law gives the relation between the electric flux flowing out a closed surface and the charge enclosed in the surface. ... Faradays law can mean: Faradays law of induction (electromagnetic fields) Faradays law of electrolysis Category: ... Permittivity is a physical quantity that describes how an electric field affects and is affected by a dielectric medium and is determined by the ability of a material to polarize in response to an applied electric field, and thereby to cancel, partially, the field inside the material. ... In electromagnetism, permeability is the degree of magnetization of a material that responds linearly to an applied magnetic field. ...

The Lorentz force law governs the interaction of the electromagnetic field with charged matter. In physics, the Lorentz force is the force exerted on a charged particle in an electromagnetic field. ...

## Properties of the field

### Reciprocal behaviour of electric and magnetic fields

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 creates an electric field'. This is the principle behind the electric generator. Generator redirects here. ...

The Ampère-Maxwell Law roughly states that 'a changing electric field creates a magnetic field'. Thus, this law can be applied to generate a magnetic field and run an electric motor. Rotating magnetic field as a sum of magnetic vectors from 3 phase coils An electric motor converts electrical energy into mechanical energy. ...

### Light as an electromagnetic disturbance

Maxwell's equations take the following, free space, form in an area that is very far away from any charges or currents - that is where ρ and $mathbf J$ are zero. In electromagnetism, Maxwells equations are a set of equations developed in the latter half of the nineteenth century by James Clerk Maxwell. ...

$nabla cdot mathbf{E} = 0$
$nabla cdot mathbf{B} = 0$
$nabla times mathbf{E} = -frac {partial mathbf{B}}{partial t}$
$nabla times mathbf{B} = frac{1}{c^2} frac{partial mathbf{E}}{partial t}$

In the above, the substitution $mu_0 epsilon_0 = frac{1}{c^2}$ has been made, where c is the speed of light. Taking the curl of the last two equations, the result is as follows.

$nabla times nabla times mathbf{E} = nabla left ( nabla cdot mathbf E right ) - nabla^2 mathbf E = nabla times left ( -frac {partial mathbf{B}}{partial t} right )$
$nabla times nabla times mathbf{B} = nabla left ( nabla cdot mathbf B right ) - nabla^2 mathbf B = nabla times left ( frac{1}{c^2} frac{partial mathbf{E}}{partial t} right )$

However, the first two equations mean $nabla left ( nabla cdot mathbf E right ) = nabla left ( nabla cdot mathbf B right ) = 0$. So plugging this in, and moving the curls within the time derivates and then plugging in for the resultant curls, the result is as follows.

$- nabla^2 mathbf E = -frac{partial}{partial t} left (nabla times mathbf{B} right ) = -frac{partial}{partial t} left ( frac{1}{c^2} frac{partial mathbf{E}}{partial t} right ) = - frac{1}{c^2} frac{partial^2 mathbf E}{partial t^2}$
$- nabla^2 mathbf B = frac{1}{c^2} frac{partial}{partial t} left ( nabla times mathbf{E} right ) = frac{1}{c^2} frac{partial}{partial t} left ( -frac {partial mathbf{B}}{partial t} right ) = - frac{1}{c^2} frac{partial^2 mathbf B}{partial t^2}$

Or:

$nabla^2 mathbf E = frac{1}{c^2} frac{partial^2 mathbf E}{partial t^2}$
$nabla^2 mathbf B = frac{1}{c^2} frac{partial^2 mathbf B}{partial t^2}$

Or even:

$Box^2 mathbf E = 0$
$Box^2 mathbf B = 0$

In this last form, the $Box^2$ is the d'Alembertian, which is $nabla^2 - frac{1}{c^2} frac{partial^2}{partial t^2}$, so the last two forms are the same thing written in two different ways. These can be identified as wave equations, that is, valid electric fields and magnetic fields have an oscillatory form, such as a sinusoid, which result in wave behaviors. Moreover, the first two of the free space Maxwell's equations imply that the waves are transverse waves. The last two of the free space Maxwell's equations imply that the wave of the electric field is in phase with and perpendicular to the magnetic field wave. Moreover, the c2 term represents the speed of the wave. So these electromagnetic waves travel at the speed of light. James Clerk Maxwell, after whom Maxwell's equations are named, suggested when he made these calculations that as these waves travel at the same speed as light, that light would actually be such a wave. His suggestion proved correct, and light is indeed an electromagnetic wave. In special relativity, electromagnetism and wave theory, the dAlembert operator, also called dAlembertian, is the Laplace operator of Minkowski space. ... The wave equation is an important partial differential equation that describes the propagation of a variety of waves, such as sound waves, light waves and water waves. ... A light wave is an example of a transverse wave. ... Electromagnetic radiation is a propagating wave in space with electric and magnetic components. ... James Clerk Maxwell (13 June 1831 â€“ 5 November 1879) was a Scottish mathematician and theoretical physicist. ...

## Relation to and comparison with other physical fields

Main article: Fundamental forces

Being one of the four fundamental forces of nature, it is useful to compare the electromagnetic field with the gravitational, strong and weak fields. The word 'force' is sometimes replaced by 'interaction'. A fundamental interaction is a mechanism by which particles interact with each other, and which cannot be explained by another more fundamental interaction. ... This article covers the physics of gravitation. ... The strong interaction or strong force is today understood to represent the interactions between quarks and gluons as detailed by the theory of quantum chromodynamics (QCD). ... The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four fundamental interactions of nature. ...

### Electromagnetic and gravitational fields

Sources of electromagnetic fields consist of two types of charge - positive and negative. This contrasts with the sources of the gravitational field, which are masses. Masses are sometimes described as gravitational charges, the important feature of them being that there is only one type (no negative masses), or, in more colloquial terms, 'gravity is always attractive'. In physics, a charge may refer to one of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. ... Exotic matter is a hypothetical concept of particle physics. ...

The relative strengths and ranges of the four interactions and other information are tabulated below:

Theory Interaction mediator Relative Magnitude Behavior Range
Chromodynamics Strong interaction gluon 1038 1 10-15 m
Electrodynamics Electromagnetic interaction photon 1036 1/r2 infinite
Flavordynamics Weak interaction W and Z bosons 1025 1/r5 to 1/r7 10-16 m
Geometrodynamics Gravitation graviton 100 1/r2 infinite

Quantum chromodynamics (QCD) is the theory describing one of the fundamental forces, the strong interaction. ... The strong interaction or strong force is today understood to represent the interactions between quarks and gluons as detailed by the theory of quantum chromodynamics (QCD). ... In particle physics, gluons are subatomic particles that cause quarks to interact, and are indirectly responsible for the binding of protons and neutrons together in atomic nuclei. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ... Electromagnetic interaction is a fundamental force of nature and is felt by charged leptons and quarks. ... The word light is defined here as electromagnetic radiation of any wavelength; thus, X-rays, gamma rays, ultraviolet light, infrared radiation, microwaves, radio waves, and visible light are all forms of light. ... In quantum mechanics, quantum flavordynamics (or flavourdynamics) is a mathematical model used to describe the interaction of flavored particles through the exchange of intermediate vector bosons, but the term is rarely used by practicing particle physicists. ... The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four fundamental interactions of nature. ... In physics, the W and Z bosons are the elementary particles that mediate the weak nuclear force. ... In theoretical physics, geometrodynamics generally denotes a program of reformulation and unification which was enthusiastically promoted by John Archibald Wheeler in the 1960s. ... â€œGravityâ€ redirects here. ... In physics, the graviton is a hypothetical elementary particle that mediates the force of gravity in the framework of quantum field theory. ...

Results from FactBites:

 Electromagnetism - Wikipedia, the free encyclopedia (1172 words) Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, which exerts a force on those particles that possess the property of electric charge, and is in turn affected by the presence and motion of such particles. A non-zero electric field is produced by the presence of electrically charged particles, and gives rise to the electric force; this is the force that causes static electricity and drives the flow of electric charge (electric current) in electrical conductors. In classical electromagnetism, the electromagnetic field obeys a set of equations known as Maxwell's equations, and the electromagnetic force is given by the Lorentz force law.
 Electromagnetic field - Wikipedia, the free encyclopedia (1755 words) 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) is produced when the charge moves (creating an electric current) with respect to this observer. An alternative interpretation would be that the field is not actually a velocity field, but a flux density field of photonic fluid, which is constantly moving at the same speed: the speed of light, independent of the speed of the observer (the charged object). The tensor character of this combined electromagnetic field implies that the field is anisotropic with respect to the velocity of the charged particle on which it produces a force: the Lorentz force varies with the velocity of the charged particle.
More results at FactBites »

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