Electromagnetic radiation
9426
225986905
2008-07-16T09:50:36Z
Martin Hogbin
1435029
/* Electromagnetic spectrum */ Deleted '81 octaves' pending clarification.
{{Electromagnetism|cTopic=[[Classical electromagnetism|Electrodynamics]]}}
'''Electromagnetic (EM) radiation''' is a [[wave propagation|self-propagating]] [[wave]] in space or through matter. EM radiation has an [[electric field|electric]] and [[magnetic field]] component which [[oscillate]] in phase perpendicular to each other and to the direction of energy [[Wave propagation|propagation]]. Electromagnetic radiation is classified into types according to the [[frequency]] of the wave, these types include (in order of increasing frequency): [[radio waves]], [[microwaves]], [[terahertz radiation]], [[infrared radiation]], [[visible light]], [[ultraviolet radiation]], [[X-ray]]s and [[gamma rays]]. Of these, radio waves have the longest wavelengths and Gamma rays have the shortest. A small window of frequencies, called [[visible spectrum]] or [[light]], is [[sense]]d by the eye of various [[organism]]s, with variations of the limits of this narrow spectrum. The word 'light' is sometimes used in a broader sense, referring to EM radiation.
EM radiation carries [[energy]] and [[momentum]], which may be imparted when it interacts with [[matter]].
== Physics ==
=== Theory ===
[[Image:Visible EM modes.png|thumb|Shows three electromagnetic modes (blue, green and red) with a distance scale in microns along the x-axis.]]
'''Electromagnetic waves''' were first postulated by [[James Clerk Maxwell]] and subsequently confirmed by [[Heinrich Hertz]]. Maxwell derived a [[Electromagnetic wave equation|wave form of the electric and magnetic equations]], revealing the wave-like nature of electric and magnetic fields, and their symmetry. Because the speed of EM waves predicted by the wave equation coincided with the measured [[speed of light]], Maxwell concluded that [[light]] itself is an EM wave.
According to [[Maxwell's equations]], a time-varying [[electric field]] generates a [[magnetic field]] and ''vice versa''. Therefore, as an oscillating electric field generates an oscillating magnetic field, the magnetic field in turn generates an oscillating electric field, and so on. These oscillating fields together form an electromagnetic wave.
A [[quantum theory]] of the interaction between electromagnetic radiation and matter such as electrons is described by the theory of [[quantum electrodynamics]].
=== Properties ===
[[Image:Light-wave.svg|thumb|left|350px|Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This diagram shows a plane linearly polarized wave propagating from right to left. The electric field is in a vertical plane, the magnetic field in a horizontal plane.]]
[[Image:Onde electromagnetique.svg|thumb|left|350px]]
Electric and magnetic fields obey the properties of [[superposition principle|superposition]], so fields due to particular particles or time-varying electric or magnetic fields contribute to the fields due to other causes. (As these fields are vector fields, all magnetic and electric field vectors add together according to [[vector (spatial)|vector]] addition.) These properties cause various phenomena including [[refraction]] and [[diffraction]]. For instance, a travelling EM wave incident on an atomic structure induces oscillation in the [[atom]]s, thereby causing them to emit their own EM waves. These [[Emission (electromagnetic radiation)|emissions]] then alter the impinging wave through interference.
Since light is an oscillation, it is not affected by travelling through static electric or magnetic fields in a linear medium such as a vacuum. In nonlinear media such as some [[crystal]]s, however, interactions can occur between light and static electric and magnetic fields - these interactions include the [[Faraday effect]] and the [[Kerr effect]].
In refraction, a wave crossing from one medium to another of different [[density]] alters its speed and direction upon entering the new medium. The ratio of the refractive indices of the media determines the degree of refraction, and is summarized by [[Snell's law]]. Light disperses into a visible [[electromagnetic spectrum|spectrum]] as light is shone through a prism because of refraction.
The [[physics]] of electromagnetic radiation is [[electrodynamics]], a subfield of [[electromagnetism]].
EM radiation exhibits both wave properties and [[Subatomic particle|particle]] properties at the same time (see [[wave-particle duality]]). The wave characteristics are more apparent when EM radiation is measured over relatively large timescales and over large distances, and the particle characteristics are more evident when measuring small distances and timescales. Both characteristics have been confirmed in a large number of experiments.
There are experiments in which the wave and particle natures of electromagnetic waves appear in the same experiment, such as the diffraction of a single [[photon]]. When a single photon is sent through two slits, it passes through both of them interfering with itself, as waves do, yet is detected by a [[photomultiplier]] or other sensitive detector only once. Similar self-interference is observed when a single photon is sent into a [[Michelson interferometer]] or other [[interferometer]]s.
===Wave model===
[[Image:Light dispersion conceptual waves.gif|thumb|right|Depicts white light being separated into different frequency waves.]]
An important aspect of the nature of light is [[frequency]]. The frequency of a wave is its rate of oscillation and is measured in [[hertz]], the [[SI]] unit of frequency, where one hertz is equal to one oscillation per [[second]]. Light usually has a spectrum of frequencies which sum together to form the resultant wave. Different frequencies undergo different angles of refraction.
A wave consists of successive troughs and crests, and the distance between two adjacent crests or troughs is called the [[wavelength]]. Waves of the electromagnetic spectrum vary in size, from very long radio waves the size of buildings to very short gamma rays smaller than atom nuclei. Frequency is inversely proportional to wavelength, according to the equation:
:<math>\displaystyle v=f\lambda</math>
where ''v'' is the speed of the wave (''[[speed of light|c]]'' in a vacuum, or less in other media), ''f'' is the frequency and λ is the wavelength. As waves cross boundaries between different media, their speeds change but their frequencies remain constant.
[[Interference]] is the superposition of two or more waves resulting in a new wave pattern. If the fields have components in the same direction, they constructively interfere, while opposite directions cause destructive interference.
The energy in electromagnetic waves is sometimes called [[radiant energy]].
=== Particle model===
Because energy of an EM wave is quantized, in the particle model of EM radiation, a wave consists of discrete packets of energy, or [[quanta]], called [[photon]]s. The frequency of the wave is proportional to the magnitude of the particle's energy. Moreover, because photons are emitted and absorbed by charged particles, they act as transporters of [[energy]]. The energy per [[photon]] can be calculated by [[Max Planck|Planck's]] equation:
:<math>\displaystyle E=hf</math>
where ''E'' is the energy, ''h'' is [[Planck's constant]], and ''f'' is frequency.
This photon-energy expression
is a particular case of the energy levels of the more general
''electromagnetic oscillator''
whose average energy, which is used to obtain Planck's radiation law,
can be shown to differ sharply from that predicted by the
[[equipartition theorem|equipartition principle]]
at low temperature, thereby establishes a failure
of equipartition due to quantum effects at low temperature<ref>
Vu-Quoc, L.,
[http://clesm.mae.ufl.edu/wiki.pub/index.php/Configuration_integral_%28statistical_mechanics%29 Configuration integral (statistical mechanics)], 2008.
</ref>.
As a photon is absorbed by an [[atom]], it excites an [[electron]], elevating it to a higher [[energy level]]. If the energy is great enough, so that the electron jumps to a high enough energy level, it may escape the positive pull of the nucleus and be liberated from the atom in a process called [[photoionisation]]. Conversely, an electron that descends to a lower energy level in an atom emits a photon of light equal to the energy difference. Since the energy levels of electrons in atoms are discrete, each element emits and absorbs its own characteristic frequencies.
Together, these effects explain the absorption spectra of [[light]]. The dark bands in the spectrum are due to the atoms in the intervening medium absorbing different frequencies of the light. The composition of the medium through which the light travels determines the nature of the absorption spectrum. For instance, dark bands in the light emitted by a distant [[star]] are due to the atoms in the star's atmosphere. These bands correspond to the allowed energy levels in the atoms. A similar phenomenon occurs for [[Emission (electromagnetic radiation)|emission]]. As the electrons descend to lower energy levels, a spectrum is emitted that represents the jumps between the energy levels of the electrons. This is manifested in the [[Emission (electromagnetic radiation)|emission]] spectrum of [[nebula]]e. Today, scientists use this phenomenon to observe what elements a certain star is composed of. It is also used in the determination of the distance of a star, using the so-called [[red shift]].
===Speed of propagation===
{{main|Speed of light}}
Any electric charge which accelerates, or any changing magnetic field, produces electromagnetic radiation. Electromagnetic information about the charge travels at the speed of light. Accurate treatment thus incorporates a concept known as [[retarded time]] (as opposed to advanced time, which is unphysical in light of [[causality]]), which adds to the expressions for the electrodynamic [[electric field]] and [[magnetic field]]. These extra terms are responsible for electromagnetic radiation. When any wire (or other conducting object such as an [[antenna (electronics)|antenna]]) conducts [[alternating current]], electromagnetic radiation is propagated at the same frequency as the electric current. Depending on the circumstances, it may behave as a [[wave]] or as [[photon|particle]]s. As a wave, it is characterized by a velocity (the [[speed of light]]), [[wavelength]], and [[frequency]]. When considered as particles, they are known as [[photon]]s, and each has an energy related to the frequency of the wave given by [[Max Planck|Planck's]] relation ''E = hν'', where ''E'' is the energy of the photon, ''h'' = 6.626 × 10<sup>-34</sup> J·s is [[Planck's constant]], and ''ν'' is the frequency of the wave.
One rule is always obeyed regardless of the circumstances: EM radiation in a vacuum always travels at the [[speed of light]], ''relative to the observer'', regardless of the observer's velocity. (This observation led to [[Albert Einstein]]'s development of the theory of [[special relativity]].)
In a medium (other than vacuum), [[velocity of propagation]] or [[refractive index]] are considered, depending on frequency and application. Both of these are ratios of the speed in a medium to speed in a vacuum.
== Electromagnetic spectrum ==
{{main|electromagnetic spectrum}}
[[Image:EM spectrum.svg|thumb|490px|right|Electromagnetic spectrum with light highlighted]]
[[Image:spectrum.png|right|frame|'''Legend:'''<br />
γ = [[Gamma ray]]s<br />
HX = Hard [[X-ray]]s<br />
SX = Soft X-Rays<br />
EUV = Extreme [[ultraviolet]]<br />
NUV = Near ultraviolet<br />
[[Visible light]]<br />
NIR = Near [[infrared]]<br />
MIR = Moderate infrared<br />
FIR = Far infrared<br />
<br />
'''[[Radio waves]]:'''<br />
EHF = [[Extremely high frequency]] (Microwaves)<br />
SHF = [[Super high frequency]] (Microwaves)<br />
UHF = [[Ultrahigh frequency]]<br />
VHF = [[Very high frequency]]<br />
HF = [[High frequency]]<br />
MF = [[Medium frequency]]<br />
LF = [[Low frequency]]<br />
VLF = [[Very low frequency]]<br />
VF = [[Voice frequency]]<br />
ELF = [[Extremely low frequency]]]]
Generally, EM radiation is classified by wavelength into [[electrical energy]], [[radio]], [[microwave]], [[infrared]], the [[visible region]] we perceive as light, [[ultraviolet]], [[X-ray]]s and [[gamma rays]].
The behavior of EM radiation depends on its wavelength. Higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths. When EM radiation interacts with single atoms and molecules, its behavior depends on the amount of energy per quantum it carries.
[[Spectroscopy]] can detect a much wider region of the EM spectrum than the visible range of 400 nm to 700 nm. A common laboratory spectroscope can detect wavelengths from 2 nm to 2500 nm. Detailed information about the physical properties of objects, gases, or even stars can be obtained from this type of device. It is widely used in [[astrophysics]]. For example, [[hydrogen]] [[atom]]s [[Emission (electromagnetic radiation)|emit]] [[radio wave]]s of [[wavelength]] 21.12 [[centimetre|cm]].
=== Light ===
{{main|light}}
EM radiation with a [[wavelength]] between approximately 400 [[nanometre|nm]] and 700 nm is detected by the [[human]] [[eye]] and perceived as visible [[light]]. Other wavelengths, especially nearby infrared (longer than 700 nm) and ultraviolet (shorter than 400 nm) are also sometimes referred to as light, especially when the visibility to humans is not relevant.
If radiation having a frequency in the visible region of the EM spectrum reflects off of an object, say, a bowl of fruit, and then strikes our eyes, this results in our [[visual perception]] of the scene. Our brain's visual system processes the multitude of reflected frequencies into different shades and hues, and through this not-entirely-understood psychophysical phenomenon, most people perceive a bowl of fruit.
At most wavelengths, however, the information carried by electromagnetic radiation is not directly detected by human senses. Natural sources produce EM radiation across the spectrum, and our technology can also manipulate a broad range of wavelengths. [[Optical fiber]] transmits light which, although not suitable for direct viewing, can carry data that can be translated into sound or an image. The coding used in such data is similar to that used with radio waves.
=== Radio waves ===
{{main|radio waves}}
Radio waves can be made to carry information by varying a combination of the amplitude, frequency and phase of the wave within a frequency band.
When EM radiation impinges upon a [[Electrical conductor|conductor]], it couples to the conductor, travels along it, and [[radio frequency induction|induces]] an electric current on the surface of that conductor by exciting the electrons of the conducting material. This effect (the [[skin effect]]) is used in antennas. EM radiation may also cause certain molecules to absorb energy and thus to heat up; this is exploited in [[microwave oven]]s.
==Derivation==
Electromagnetic waves as a general phenomenon were predicted by the classical laws of [[electricity]] and magnetism, known as [[Maxwell's equations]]. If you inspect Maxwell's equations without sources (charges or currents) then you will find that, along with the possibility of nothing happening, the theory will also admit nontrivial solutions of changing electric and magnetic fields. Beginning with Maxwell's equations for [[free space]]:
::<math>\nabla \cdot \mathbf{E} = 0 \qquad \qquad \qquad \ \ (1)</math>
::<math>\nabla \times \mathbf{E} = -\frac{\partial}{\partial t} \mathbf{B} \qquad \qquad (2)</math>
::<math>\nabla \cdot \mathbf{B} = 0 \qquad \qquad \qquad \ \ (3)</math>
::<math>\nabla \times \mathbf{B} = \mu_0 \epsilon_0 \frac{\partial}{\partial t} \mathbf{E} \qquad \ \ \ (4)</math>
:where
::<math>\nabla</math> is a vector differential operator (see [[Del]]).
One solution,
::<math>\mathbf{E}=\mathbf{B}=\mathbf{0}</math>,
is trivial.
To see the more interesting one, we utilize [[List of vector identities|vector identities]], which work for any vector, as follows:
::<math>\nabla \times \left( \nabla \times \mathbf{A} \right) = \nabla \left( \nabla \cdot \mathbf{A} \right) - \nabla^2 \mathbf{A}</math>
To see how we can use this take the curl of equation (2):
::<math>\nabla \times \left(\nabla \times \mathbf{E} \right) = \nabla \times \left(-\frac{\partial \mathbf{B}}{\partial t} \right) \qquad \qquad \qquad \quad \ \ \ (5) \,</math>
Evaluating the left hand side:
::<math> \nabla \times \left(\nabla \times \mathbf{E} \right) = \nabla\left(\nabla \cdot \mathbf{E} \right) - \nabla^2 \mathbf{E} = - \nabla^2 \mathbf{E} \qquad \quad \ (6) \,</math>
:where we simplified the above by using equation (1).
Evaluate the right hand side:
::<math>\nabla \times \left(-\frac{\partial \mathbf{B}}{\partial t} \right) = -\frac{\partial}{\partial t} \left( \nabla \times \mathbf{B} \right) = -\mu_0 \epsilon_0 \frac{\partial^2}{\partial^2 t} \mathbf{E} \qquad (7)</math>
Equations (6) and (7) are equal, so this results in a vector-valued [[differential equation]] for the electric field, namely
::{|cellpadding="2" style="border:2px solid #ccccff"
|<math>\nabla^2 \mathbf{E} = \mu_0 \epsilon_0 \frac{\partial^2}{\partial t^2} \mathbf{E}</math>
|}
Applying a similar pattern results in similar differential equation for the magnetic field:
::{|cellpadding="2" style="border:2px solid #ccccff"
|<math>\nabla^2 \mathbf{B} = \mu_0 \epsilon_0 \frac{\partial^2}{\partial t^2} \mathbf{B}</math>.
|}
These differential equations are equivalent to the [[wave equation]]:
::<math>\nabla^2 f = \frac{1}{{c_0}^2} \frac{\partial^2 f}{\partial t^2} \,</math>
:where
::''c''<sub>0</sub> is the speed of the wave in free space and
::''f'' describes a displacement
Or more simply:
::<math>\Box^2 f = 0</math>
:where <math>\Box^2</math> is [[d'Alembert operator|d'Alembertian]]:
::<math>\Box^2 = \nabla^2 - \frac{1}{{c_0}^2} \frac{\partial^2}{\partial t^2} = \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + \frac{\partial^2}{\partial z^2} - \frac{1}{{c_0}^2} \frac{\partial^2}{\partial t^2} \ </math>
Notice that in the case of the electric and magnetic fields, the speed is:
::<math>c_0 = \frac{1}{\sqrt{\mu_0 \epsilon_0}}</math>
Which, as it turns out, is the [[speed of light]] in free space. Maxwell's equations have unified the permittivity of free space <math>\epsilon_0</math>, the permeability of free space <math>\mu_0</math>, and the speed of light itself, ''c''<sub>0</sub>. Before this derivation it was not known that there was such a strong [[Electromagnetic wave equation|relationship]] between light and electricity and magnetism.
But these are only two equations and we started with four, so there is still more information pertaining to these waves hidden within Maxwell's equations. Let's consider a generic vector wave for the electric field.
:<math>\mathbf{E} = \mathbf{E}_0 f\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right)</math>
Here <math>\mathbf{E}_0</math> is the constant amplitude, <math>f</math> is any second differentiable function, <math> \hat{\mathbf{k}}</math> is a unit vector in the direction of propagation, and <math> {\mathbf{x}} </math>is a position vector. We observe that <math>f\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right)</math> is a generic solution to the wave equation. In other words
:<math>\nabla^2 f\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right) = \frac{1}{{c_0}^2} \frac{\partial^2}{\partial^2 t} f\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right)</math>,
for a generic wave traveling in the <math>\hat{\mathbf{k}}</math> direction.
This form will satisfy the wave equation, but will it satisfy all of Maxwell's equations, and with what corresponding magnetic field?
:<math>\nabla \cdot \mathbf{E} = \hat{\mathbf{k}} \cdot \mathbf{E}_0 f'\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right) = 0</math>
:<math>\mathbf{E} \cdot \hat{\mathbf{k}} = 0</math>
The first of Maxwell's equations implies that electric field is orthogonal to the direction the wave propagates.
:<math>\nabla \times \mathbf{E} = \hat{\mathbf{k}} \times \mathbf{E}_0 f'\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right) = -\frac{\partial}{\partial t} \mathbf{B}</math>
:<math>\mathbf{B} = \frac{1}{c_0} \hat{\mathbf{k}} \times \mathbf{E}</math>
The second of Maxwell's equations yields the magnetic field. The remaining equations will be satisfied by this choice of <math>\mathbf{E},\mathbf{B}</math>.
Not only are the electric and magnetic field waves traveling at the speed of light, but they have a special restricted orientation and proportional magnitudes, <math>E_0 = c_0 B_0</math>, which can be seen immediately from the [[Poynting vector]]. The electric field, magnetic field, and direction of wave propagation are all orthogonal, and the wave propagates in the same direction as <math>\mathbf{E} \times \mathbf{B}</math>.
From the viewpoint of an electromagnetic wave traveling forward, the electric field might be oscillating up and down, while the magnetic field oscillates right and left; but this picture can be rotated with the electric field oscillating right and left and the magnetic field oscillating down and up. This is a different solution that is traveling in the same direction. This arbitrariness in the orientation with respect to propagation direction is known as [[polarization]].
==See also==
<div style="-moz-column-count:3; -webkit-column-count:3; column-count:3;">
*[[Control of electromagnetic radiation]]
*[[Electromagnetic pulse]]
*[[Electromagnetic spectrum]]
*[[Bioelectromagnetism]]
*[[Electromagnetic radiation and health]]
*[[Electromagnetic wave equation]]
*[[Finite-difference time-domain method]]
*[[Helicon (physics)|Helicon]]
*[[Klystron]]
*[[Light]]
*[[Maxwell's equations]]
*[[Photon polarization]]
*[[Radiant energy]]
*[[Sinusoidal plane-wave solutions of the electromagnetic wave equation]]
*[[Radiation reaction]]
</div>
==References==
<div class="references-small">
<!--See http://en.wikipedia.org/wiki/Wikipedia:Footnotes for an explanation of how to generate footnotes using the <ref(erences/)> tags-->
<references/>
</div>
* {{cite book
| last = Hecht | first = Eugene
| title = Optics
| edition = 4th ed.
| publisher = Pearson Education
| year = 2001
| id = ISBN 0-8053-8566-5
}}
* {{cite book
| last = Serway | first = Raymond A.
| coauthors = Jewett, John W.
| title = Physics for Scientists and Engineers
| edition = 6th ed.
| publisher = Brooks/Cole
| year = 2004
| id = ISBN 0-534-40842-7
}}
* {{cite book
| last = Tipler | first = Paul
| title = Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics
| edition = 5th ed.
| publisher = W. H. Freeman
| year = 2004
| id = ISBN 0-7167-0810-8
}}
* {{cite book
| last = Reitz | first = John
| coauthors = Milford, Frederick; Christy, Robert
| title = Foundations of Electromagnetic Theory
| edition = 4th ed.
| publisher = Addison Wesley
| year = 1992
| id = ISBN 0-201-52624-7
}}
* {{cite book
| last = Jackson | first = John David
| title = Classical Electrodynamics
| edition = 2nd ed
| publisher = John Wiley & Sons
| year = 1975
| id = ISBN 0-471-43132-X
}}
*{{cite book | author=Allen Taflove and Susan C. Hagness | title=Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. | publisher=Artech House Publishers | year=2005 | id=ISBN 1-58053-832-0 | url=http://www.artechhouse.com/default.asp?Frame=Book.asp&Book=1-58053-832-0&Country=US&Continent=NO&State=}}
==External links==
* [http://www.lightandmatter.com/html_books/0sn/ch11/ch11.html Electromagnetism] - a chapter from an online textbook
*[http://www.physnet.org/modules/pdfmodules/m210.pdf '' Electromagnetic Waves from Maxwell's Equations ''] on [http://www.physnet.org Project PHYSNET].
*[http://www.sengpielaudio.com/calculator-wavelength.htm Conversion of frequency to wavelength and back - electromagnetic, radio and sound waves]
*[http://www.rfzone.org/free-rf-ebooks/ eBooks on Electromagnetic radiation and RF]
*[http://www.scienceofspectroscopy.info The Science of Spectroscopy] - supported by NASA. Spectroscopy education wiki and films - introduction to light, its uses in NASA, space science, astronomy, medicine & health, environmental research, and consumer products.
[[Category:Electromagnetic radiation| ]]
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