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Electromagnetic field

For the British hacker convention, see Electromagnetic Field (festival).

An electromagnetic field (also EMF or EM field) is a physical field produced byelectrically charged objects.^[1] It affects the behavior of charged objects in the vicinity of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction. It is one of the four fundamental forces of nature (the others are gravitation, weak interaction andstrong interaction).

The field can be viewed as the combination of an electric field and a magnetic field. The electric field is produced by stationary charges, and the magnetic field by moving charges (currents); these two are often described as the sources of the field. The way in which charges and currents interact with the electromagnetic field is described byMaxwell's equations and the Lorentz force law.^[2] The force created by the electric field is much stronger than the force created by the magnetic field.^[3]

From a classical perspective in the history of electromagnetism, the electromagnetic field can be regarded as a smooth, continuous field, propagated in a wavelike manner; whereas from the perspective of quantum field theory, the field is seen as quantized, being composed of individual particles.

StructureEdit

The electromagnetic field may be viewed in two distinct ways: a continuous structure or a discrete structure.

Continuous structureEdit

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 fashion. 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).^{[citation needed]}

Discrete structureEdit

The electromagnetic field may be thought of in a more 'coarse' way. Experiments reveal that in some circumstances electromagnetic energy transfer is better described as being carried in the form of packets called quanta(in this case, photons) with a fixed frequency. Planck's relation links the photon energy E of a photon to its frequency ν through the equation:^[4]

${\displaystyle E=\,h\,\nu }$

where h is Planck's constant, and ν is the frequency of the photon . Although modern quantum optics tells us that there also is a semi-classical explanation of thephotoelectric effect—the emission of electrons from metallic surfaces subjected toelectromagnetic radiation—the photon was historically (although not strictly necessarily) used to explain certain observations. It is found that increasing the intensity of the incident radiation (so long as one remains in the linear regime) increases only the number of electrons ejected, and has almost no effect on the energy distribution of their ejection. Only the frequency of the radiation is relevant to the energy of the ejected electrons.

This quantum picture of the electromagnetic field (which treats it as analogous toharmonic oscillators) has proved very successful, giving rise to quantum electrodynamics, a quantum field theorydescribing the interaction of electromagnetic radiation with charged matter. It also gives rise to quantum optics, which is different from quantum electrodynamics in that the matter itself is modelled using quantum mechanicsrather than quantum field theory.

DynamicsEdit

In the past, electrically charged objects were thought to produce two different, unrelated 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. Until 1820, when the Danish physicist H. C. Ørsteddiscovered the effect of electricity through a wire on a compass needle, electricity and magnetism had been viewed as unrelated phenomena^{[citation needed]}. In 1831, Michael Faraday, one of the great thinkers of his time, made the seminal observation that time-varying magnetic fields could induce electric currents and then, in 1864, James Clerk Maxwell published his famous paper A Dynamical Theory of the Electromagnetic Field.^[5]

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. This discussion ignores the radiation reaction force.

Feedback loopEdit

The behavior of the electromagnetic field can be divided into four different parts of a loop:^{[citation needed]}

• the electric and magnetic fields are generated by electric charges,
• the electric and magnetic fields interact with each other,
• the electric and magnetic fields produce forces on electric charges,
• the electric charges move in space.

A common misunderstanding is that (a) the quanta of the fields act in the same manner as (b) the charged particles that generate the fields. In our everyday world, chargedparticles, such as electrons, move slowly through matter with a drift velocity of a fraction of a centimeter (or inch) per second, but fields propagate at the speed of light - approximately 300 thousand kilometers (or 186 thousand miles) a second. The mundane speed difference between charged particles and field quanta is on the order of one to a million, more or less. Maxwell's equationsrelate (a) the presence and movement of charged particles with (b) the generation of fields. Those fields can then affect the force on, and can then move other slowly moving charged particles. Charged particles can move at relativistic speeds nearing field propagation speeds, but, as Einsteinshowed^{[citation needed]}, this requires enormous field energies, which are not present in our everyday experiences with electricity, magnetism, matter, and time and space.

The feedback loop can be summarized in a list, including phenomena belonging to each part of the loop:^{[citation needed]}

• charged particles generate electric and magnetic fields
• the fields interact with each other
  • changing electric field acts like a current, generating 'vortex' of magnetic field
  • Faraday induction: changing magnetic field induces (negative) vortex of electric field
  • Lenz's law: negative feedback loop between electric and magnetic fields
• fields act upon particles
  • 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
• particles move
  • current is movement of particles
• particles generate more electric and magnetic fields; cycle repeats

Mathematical descriptionEdit

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 anelectrostatic 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.^[6]

With the advent of special relativity, physical laws became susceptible to the formalism oftensors. Maxwell's equations can be written in tensor form, generally viewed by physicists as a more elegant means of expressing physical laws.

The behaviour 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:

${\displaystyle \nabla \cdot \mathbf {E} ={\frac {\rho }{\varepsilon _{0}}}}$ (Gauss's law)

${\displaystyle \nabla \cdot \mathbf {B} =0}$ (Gauss's law for magnetism)

${\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}}$ (Faraday's law)

${\displaystyle \nabla \times \mathbf {B} =\mu _{0}\mathbf {J} +\mu _{0}\varepsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}}$ (Maxwell–Ampère law)

where ${\displaystyle \rho }$  is the charge density, which can (and often does) depend on time and position, ${\displaystyle \epsilon _{0}}$  is the permittivity of free space, ${\displaystyle \mu _{0}}$  is thepermeability of free space, and 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 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 properties of the field change according to the various boundary conditions. These equations are derived from Maxwell's equations. The tangential components of the electric and magnetic fields as they relate on the boundary of two media are as follows:^[7]

${\displaystyle \mathbf {E} _{1}=\mathbf {E} _{2}}$ 

${\displaystyle \mathbf {H} _{1}=\mathbf {H} _{2}}$  (current-free)

${\displaystyle \mathbf {D} _{1}=\mathbf {D} _{2}}$  (charge-free)

${\displaystyle \mathbf {B} _{1}=\mathbf {B} _{2}}$ 

The angle of refraction of an electric field between media is related to the permittivity ${\displaystyle (\varepsilon )}$  of each medium:

${\displaystyle {\frac {\tan \theta _{1}}{\tan \theta _{2}}}={\frac {\varepsilon _{r2}}{\varepsilon _{r1}}}}$ 

The angle of refraction of a magnetic field between media is related to the permeability ${\displaystyle (\mu )}$ of each medium:

${\displaystyle {\frac {\tan \theta _{1}}{\tan \theta _{2}}}={\frac {\mu _{r2}}{\mu _{r1}}}}$

Properties of the fieldEdit

Reciprocal behavior of electric and magnetic fieldsEdit

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.

Ampere's 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.

Behavior of the fields in the absence of charges or currentsEdit

Maxwell's equations take the form of anelectromagnetic wave in a volume of space not containing charges or currents (free space) – that is, where ${\displaystyle \rho }$ and J are zero. Under these conditions, the electric and magnetic fields satisfy the electromagnetic wave equation:^[8]

${\displaystyle \left(\nabla ^{2}-{1 \over {c}^{2}}{\partial ^{2} \over \partial t^{2}}\right)\mathbf {E} \ \ =\ \ 0}$

${\displaystyle \left(\nabla ^{2}-{1 \over {c}^{2}}{\partial ^{2} \over \partial t^{2}}\right)\mathbf {B} \ \ =\ \ 0}$

James Clerk Maxwell was the first to obtain this relationship by his completion ofMaxwell's equations with the addition of adisplacement current term to Ampere's Circuital law.