Electromagnetic field
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For the British hacker convention, see Electromagnetic Field (festival).
An electromagnetic field (also EM field or EMF) is a classical (i.e. non-
quantum) field produced by accelerating electric charges. It is the field [1]
described by classical electrodynamics and is the classical counterpart to
the quantized electromagnetic field tensor in quantum electrodynamics. The
electromagnetic field propagates at the speed of light (in fact, this field can be
identified as light) and interacts with charges and currents. Its quantum
counterpart is one of the four fundamental forces of nature (the others
are gravitation, weak interaction and strong 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 by Maxwell's equations and the Lorentz
force law. [2]
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. By contrast, from the perspective
of quantum field theory, this field is seen as quantized; meaning that the free
quantum field (i.e. non-interacting field) can be expressed as the Fourier sum
of creation and annihilation operators in energy-momentum space while the
effects of the interacting quantum field may be analyzed in perturbation
theory via the S-matrix with the aid of a whole host of mathematical techniques
such as the Dyson series, Wick's theorem, correlation functions, time-
evolution operators, Feynman diagrams etc. Note that the quantized field is
still spatially continuous; its energy states however are discrete (the field's
energy states must not be confused with its energy values, which are
continuous; the quantum field's creation operators create
multiple discrete states of energy called photons.)
A sinusoidal electromagnetic wave propagating along the positive z-axis, showing the electric field (blue) and magnetic field (red)
vectors.
Structure[edit]
The electromagnetic field may be viewed in two distinct ways: a continuous
structure or a discrete structure.
, Continuous structure[edit]
Classically, electric and magnetic fields are thought of as being produced by
smooth motions of charged objects. For example, oscillating charges produce
variations in 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), however, problems are found at high frequencies
(see ultraviolet catastrophe).
[3]
Discrete structure[edit]
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 with a fixed frequency. Planck's relation links the photon
energy E of a photon to its frequency f through the equation: [4]
where h is Planck's constant, and f is the frequency of the photon. Although
modern quantum optics tells us that there also is a semi-classical explanation
of the photoelectric effect—the emission of electrons from metallic surfaces
subjected to electromagnetic 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
to harmonic oscillators) has proven very successful, giving rise to quantum
electrodynamics, a quantum field theory describing 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 mechanics rather than quantum field theory.
Dynamics[edit]
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
Jump to navigationJump to search
For the British hacker convention, see Electromagnetic Field (festival).
An electromagnetic field (also EM field or EMF) is a classical (i.e. non-
quantum) field produced by accelerating electric charges. It is the field [1]
described by classical electrodynamics and is the classical counterpart to
the quantized electromagnetic field tensor in quantum electrodynamics. The
electromagnetic field propagates at the speed of light (in fact, this field can be
identified as light) and interacts with charges and currents. Its quantum
counterpart is one of the four fundamental forces of nature (the others
are gravitation, weak interaction and strong 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 by Maxwell's equations and the Lorentz
force law. [2]
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. By contrast, from the perspective
of quantum field theory, this field is seen as quantized; meaning that the free
quantum field (i.e. non-interacting field) can be expressed as the Fourier sum
of creation and annihilation operators in energy-momentum space while the
effects of the interacting quantum field may be analyzed in perturbation
theory via the S-matrix with the aid of a whole host of mathematical techniques
such as the Dyson series, Wick's theorem, correlation functions, time-
evolution operators, Feynman diagrams etc. Note that the quantized field is
still spatially continuous; its energy states however are discrete (the field's
energy states must not be confused with its energy values, which are
continuous; the quantum field's creation operators create
multiple discrete states of energy called photons.)
A sinusoidal electromagnetic wave propagating along the positive z-axis, showing the electric field (blue) and magnetic field (red)
vectors.
Structure[edit]
The electromagnetic field may be viewed in two distinct ways: a continuous
structure or a discrete structure.
, Continuous structure[edit]
Classically, electric and magnetic fields are thought of as being produced by
smooth motions of charged objects. For example, oscillating charges produce
variations in 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), however, problems are found at high frequencies
(see ultraviolet catastrophe).
[3]
Discrete structure[edit]
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 with a fixed frequency. Planck's relation links the photon
energy E of a photon to its frequency f through the equation: [4]
where h is Planck's constant, and f is the frequency of the photon. Although
modern quantum optics tells us that there also is a semi-classical explanation
of the photoelectric effect—the emission of electrons from metallic surfaces
subjected to electromagnetic 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
to harmonic oscillators) has proven very successful, giving rise to quantum
electrodynamics, a quantum field theory describing 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 mechanics rather than quantum field theory.
Dynamics[edit]
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
