Electromagnetic radiation

Electromagnetism

Electricity · Magnetism

Electrodynamics
· Free space · Lorentz force law · EMF · Electromagnetic induction · Faraday’s law · Displacement current · Maxwell’s equations · EM field · Electromagnetic radiation · Liénard-Wiechert Potentials · Maxwell tensor · Eddy current ·

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Electromagnetic (EM) radiation is a self-propagating wave in space or through transparent matter. Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of In Physics, magnetism is one of the Phenomena by which Materials exert attractive or repulsive Forces on other Materials. Classical electromagnetism (or classical electrodynamics) is a theory of Electromagnetism that was developed over the course of the 19th century most prominently In Classical physics, free space is a concept of Electromagnetic theory, corresponding to a theoretically "perfect" Vacuum, and sometimes In Physics, the Lorentz force is the Force on a Point charge due to Electromagnetic fields It is given by the following equation Electromotive force ( emf, \mathcal{E} is a term used to characterize electrical devices such as Voltaic cells thermoelectric devices electrical Faraday's law of induction describes an important basic law of electromagnetism which is involved in the working of Transformers Inductors and many forms of Faraday's law of induction describes an important basic law of electromagnetism which is involved in the working of Transformers Inductors and many forms of Displacement current is a quantity that arises in a changing electric field In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric The electromagnetic field is a physical field produced by electrically charged objects. The Liénard-Wiechert potential describes the electromagnetic effect of a moving Electric charge. The Maxwell Stress Tensor (also known as Maxwell's Stress Tensor is used to calculate the stresses on objects in magnetic or electrical fields An eddy current (also known as Foucault current) is an electrical phenomenon discovered by French physicist Léon Foucault in Wave propagation is any of the ways in which waves travel through a Waveguide. A wave is a disturbance that propagates through Space and Time, usually with transference of Energy. EM radiation has an electric and magnetic field component which oscillate in phase perpendicular to each other and to the direction of energy propagation. In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges Oscillation is the repetitive variation typically in Time, of some measure about a central value (often a point of Equilibrium) or between two or more different states Wave propagation is any of the ways in which waves travel through a Waveguide. 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-rays and gamma rays. Frequency is a measure of the number of occurrences of a repeating event per unit Time. Radio waves are electromagnetic waves occurring on the Radio frequency portion of the Electromagnetic spectrum. Microwaves are electromagnetic waves with Wavelengths ranging from 1 mm to 1 m or frequencies between 0 Electromagnetic waves sent at terahertz frequencies, known as terahertz radiation, submillimeter radiation, terahertz waves, terahertz Infrared ( IR) radiation is Electromagnetic radiation whose Wavelength is longer than that of Visible light, but shorter than that of Ultraviolet ( UV) light is Electromagnetic radiation with a Wavelength shorter than that of Visible light, but longer than X-rays X-radiation (composed of X-rays) is a form of Electromagnetic radiation. Gamma rays (denoted as &gamma) are a form of Electromagnetic radiation or light emission of frequencies produced by sub-atomic particle interactions 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 sensed by the eye of various organisms, with variations of the limits of this narrow spectrum. Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700 Senses are the physiological methods of Perception. The senses and their operation classification and theory are overlapping topics studied by a variety of fields 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. In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product Matter is commonly defined as being anything that has mass and that takes up space.

1 Physics
2 Electromagnetic spectrum
- 2.1 Light
- 2.2 Radio waves
3 Derivation
4 See also
5 References
6 External links

Physics

Theory

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. James Clerk Maxwell (13 June 1831 &ndash 5 November 1879 was a Scottish mathematician and theoretical physicist. Heinrich Rudolf Hertz ( February 22, 1857 – January 1, 1894) was a German physicist who clarified and expanded the electromagnetic theory Maxwell derived a wave form of the electric and magnetic equations, revealing the wave-like nature of electric and magnetic fields, and their symmetry. The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of Electromagnetic waves through a medium 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. Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700

According to Maxwell's equations, a time-varying electric field generates a magnetic field and vice versa. In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges 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. Quantum electrodynamics ( QED) is a relativistic Quantum field theory of Electrodynamics.

Properties

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.

Electric and magnetic fields obey the properties of superposition, so fields due to particular particles or time-varying electric or magnetic fields contribute to the fields due to other causes. In Physics and Systems theory, the superposition principle, also known as superposition property, states that for all Linear systems (As these fields are vector fields, all magnetic and electric field vectors add together according to vector addition. ) These properties cause various phenomena including refraction and diffraction. Refraction is the change in direction of a Wave due to a change in its Speed. Diffraction is normally taken to refer to various phenomena which occur when a wave encounters an obstacle For instance, a travelling EM wave incident on an atomic structure induces oscillation in the atoms, thereby causing them to emit their own EM waves. History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny These emissions then alter the impinging wave through interference. In Physics, emission is the process by which the Energy of a Photon is released by another entity for example by an Atom whose Electrons

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 crystals, however, interactions can occur between light and static electric and magnetic fields - these interactions include the Faraday effect and the Kerr effect. In Materials science, a crystal is a Solid in which the constituent Atoms Molecules or Ions are packed in a regularly ordered repeating In Physics, the Faraday effect or Faraday rotation is a Magneto-optical phenomenon or an interaction between Light and a Magnetic The Kerr effect or the quadratic electro-optic effect ( QEO effect) is a change in the Refractive index of a material in response to an Electric field

In refraction, a wave crossing from one medium to another of different density alters its speed and direction upon entering the new medium. The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different The ratio of the refractive indices of the media determines the degree of refraction, and is summarized by Snell's law. In Optics and Physics, Snell's law (also known as Descartes' law or the law of refraction) is a formula used to describe the relationship Light disperses into a visible spectrum as light is shone through a prism because of refraction. The electromagnetic (EM spectrum is the range of all possible Electromagnetic radiation frequencies

The physics of electromagnetic radiation is electrodynamics, a subfield of electromagnetism. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. Classical electromagnetism (or classical electrodynamics) is a theory of Electromagnetism that was developed over the course of the 19th century most prominently Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of

EM radiation exhibits both wave properties and particle properties at the same time (see wave-particle duality). A subatomic particle is an elementary or composite Particle smaller than an Atom. In Physics and Chemistry, wave–particle duality is the concept that all Matter and Energy exhibits both Wave -like and 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. In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena 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. Photomultiplier tubes ( photomultipliers or PMT s for short members of the class of Vacuum tubes and more specifically Phototubes are extremely Similar self-interference is observed when a single photon is sent into a Michelson interferometer or other interferometers. Michelson interferometer is the most common configuration for optical Interferometry and was invented by Albert Abraham Michelson. Interferometry is the technique of using the pattern of Interference created by the superposition of two or more Waves to diagnose the properties of

Wave model

Depicts white light being separated into different frequency waves.

An important aspect of the nature of light is frequency. Frequency is a measure of the number of occurrences of a repeating event per unit Time. 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. The hertz (symbol Hz) is a measure of Frequency, informally defined as the number of events occurring per Second. The second ( SI symbol s) sometimes abbreviated sec, is the name of a unit of Time, and is the International System of Units 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. In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency. 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:

$\displaystyle v=f\lambda$

where v is the speed of the wave (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. In physics interference is the addition ( superposition) of two or more Waves that result 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. Radiant energy is the Energy of Electromagnetic waves The quantity of radiant energy may be calculated by integrating Radiant flux (or power

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 photons. In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena 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. In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός The energy per photon can be calculated by Planck's equation:

$\displaystyle E=hf$

where E is the energy, h is Planck's constant, and f is frequency. In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena The Planck constant (denoted h\ is a Physical constant used to describe the sizes of quanta. 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 principle at low temperature, thereby establishes a failure of equipartition due to quantum effects at low temperature^[1]. In classical Statistical mechanics, the equipartition theorem is a general formula that relates the Temperature of a system with its average energies

As a photon is absorbed by an atom, it excites an electron, elevating it to a higher energy level. History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J A quantum mechanical system or particle that is bound, confined spacially can only take on certain discrete values of energy as opposed to classical particles which 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. Photoionisation is the physical process in which an incident Photon ejects one or more Electrons from an Atom, Ion or Molecule 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. Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700 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. A star is a massive luminous ball of plasma. The nearest star to Earth is the Sun, which is the source of most of the Energy on Earth These bands correspond to the allowed energy levels in the atoms. A similar phenomenon occurs for emission. In Physics, emission is the process by which the Energy of a Photon is released by another entity for example by an Atom whose Electrons 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 spectrum of nebulae. In Physics, emission is the process by which the Energy of a Photon is released by another entity for example by an Atom whose Electrons A nebula (from Latin: "mist" pl nebulae or nebulæ, with ligature or nebulas) is an Interstellar cloud of 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. In Physics and Astronomy, redshift occurs when Electromagnetic radiation – usually Visible light – emitted or reflected by

Speed of propagation

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. According to Maxwell's Equations, Electromagnetic waves in a Vacuum travel at the Speed of light, c. Causality (but not causation) denotes a necessary relationship between one event (called cause and another event (called effect) which is the direct consequence In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges These extra terms are responsible for electromagnetic radiation. When any wire (or other conducting object such as an antenna) conducts alternating current, electromagnetic radiation is propagated at the same frequency as the electric current. An antenna is a Transducer designed to transmit or Receive electromagnetic waves In other words antennas convert electromagnetic waves into An alternating current ( AC) is an Electric current whose direction reverses cyclically as opposed to Direct current, whose direction remains constant Depending on the circumstances, it may behave as a wave or as particles. A wave is a disturbance that propagates through Space and Time, usually with transference of Energy. In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena As a wave, it is characterized by a velocity (the speed of light), wavelength, and frequency. In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency. Frequency is a measure of the number of occurrences of a repeating event per unit Time. When considered as particles, they are known as photons, and each has an energy related to the frequency of the wave given by Planck's relation E = hν, where E is the energy of the photon, h = 6. In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena 626 × 10^-34 J·s is Planck's constant, and ν is the frequency of the wave. The Planck constant (denoted h\ is a Physical constant used to describe the sizes of quanta.

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. Albert Einstein ( German: ˈalbɐt ˈaɪ̯nʃtaɪ̯n; English: ˈælbɝt ˈaɪnstaɪn (14 March 1879 – 18 April 1955 was a German -born theoretical Special relativity (SR (also known as the special theory of relativity or STR) is the Physical theory of Measurement in Inertial )

In a medium (other than vacuum), velocity of propagation or refractive index are considered, depending on frequency and application. The refractive index (or index of Refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves is reduced inside the medium Both of these are ratios of the speed in a medium to speed in a vacuum.

Electromagnetic spectrum

Main article: electromagnetic spectrum

Electromagnetic spectrum with light highlighted

Legend:
γ = Gamma rays
HX = Hard X-rays
SX = Soft X-Rays
EUV = Extreme ultraviolet
NUV = Near ultraviolet
Visible light
NIR = Near infrared
MIR = Moderate infrared
FIR = Far infrared

Radio waves:
EHF = Extremely high frequency (Microwaves)
SHF = Super high frequency (Microwaves)
UHF = Ultrahigh frequency
VHF = Very high frequency
HF = High frequency
MF = Medium frequency
LF = Low frequency
VLF = Very low frequency
VF = Voice frequency
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-rays and gamma rays. The electromagnetic (EM spectrum is the range of all possible Electromagnetic radiation frequencies Gamma rays (denoted as &gamma) are a form of Electromagnetic radiation or light emission of frequencies produced by sub-atomic particle interactions X-radiation (composed of X-rays) is a form of Electromagnetic radiation. Ultraviolet ( UV) light is Electromagnetic radiation with a Wavelength shorter than that of Visible light, but longer than X-rays Infrared ( IR) radiation is Electromagnetic radiation whose Wavelength is longer than that of Visible light, but shorter than that of Radio waves are electromagnetic waves occurring on the Radio frequency portion of the Electromagnetic spectrum. Extremely high frequency is the highest Radio frequency band. Super high frequency (or SHF) refers to radio frequencies (RF in the range of 3 GHz and 30 GHz Very high frequency (VHF is the Radio frequency range from 30 MHz to 300 MHz. High frequency (HF radio frequencies are between 3 and 30 MHz. Medium frequency ( MF) refers to radio frequencies (RF in the range of 300 kHz to 3000 kHz Low Frequency or LF refers to Radio Frequencies (RF in the range of 30 kHz&ndash300 kHz Very low frequency or VLF refers to radio frequencies (RF in the range of 3 KHz to 30 KHz. A voice frequency (VF or voice band is one of the frequencies within part of the audio range that is used for the transmission of speech. Extremely low frequency (ELF is the band of Radio frequencies from 3 to 30 Hz. Electric energy is the potential energy associated with the conservative Coulomb forces between Charged particles contained within a system, where Radio is the transmission of signals by Modulation of electromagnetic waves with frequencies below those of visible Light. Microwaves are electromagnetic waves with Wavelengths ranging from 1 mm to 1 m or frequencies between 0 Infrared ( IR) radiation is Electromagnetic radiation whose Wavelength is longer than that of Visible light, but shorter than that of Ultraviolet ( UV) light is Electromagnetic radiation with a Wavelength shorter than that of Visible light, but longer than X-rays X-radiation (composed of X-rays) is a form of Electromagnetic radiation. Gamma rays (denoted as &gamma) are a form of Electromagnetic radiation or light emission of frequencies produced by sub-atomic particle interactions

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. Electromagnetic radiation can be divided into octaves — as sound waves are — winding up with eighty-one octaves. In Music, an octave ( is the the use of which is "common in most musical systems ^[2]

Spectroscopy can detect a much wider region of the EM spectrum than the visible range of 400 nm to 700 nm. Spectroscopy was originally the study of the interaction between Radiation and Matter as a function of Wavelength (λ 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. Astrophysics is the branch of Astronomy that deals with the Physics of the Universe, including the physical properties ( Luminosity, For example, hydrogen atoms emit radio waves of wavelength 21. Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1 History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny In Physics, emission is the process by which the Energy of a Photon is released by another entity for example by an Atom whose Electrons Radio waves are electromagnetic waves occurring on the Radio frequency portion of the Electromagnetic spectrum. In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency. 12 cm. A centimetre ( American spelling: centimeter, symbol cm) is a unit of Length in the Metric system, equal to one hundredth

Light

Main article: light

EM radiation with a wavelength between approximately 400 nm and 700 nm is detected by the human eye and perceived as visible light. Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700 In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency. A nanometre ( American spelling: nanometer, symbol nm) ( Greek: νάνος nanos dwarf; μετρώ metrό count) is a Human beings, humans or man (Origin 1590–1600 L homō man OL hemō the earthly one (see Humus Eyes are organs that detect Light, and send signals along the Optic nerve to the visual areas of the brain Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700 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. In Psychology, visual perception is the ability to interpret information from Visible light reaching the Eyes The resulting Perception is also 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. An optical fiber (or fibre) is a Glass or Plastic fiber that carries Light along its length The coding used in such data is similar to that used with radio waves.

Radio waves

Main article: radio frequency

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. Radio frequency ( RF) is a Frequency or rate of Oscillation within the range of about 3 Hz to 300 GHz

When EM radiation impinges upon a conductor, it couples to the conductor, travels along it, and induces an electric current on the surface of that conductor by exciting the electrons of the conducting material. In Science and engineering, a conductor is a material which contains movable Electric charges. For the common use of RF induction process of heating a metal object by electromagnetic induction see Induction heating Radio-frequency induction This effect (the skin effect) is used in antennas. The skin effect is the tendency of an alternating electric current (AC to distribute itself within a conductor so that the current density near the surface of the EM radiation may also cause certain molecules to absorb energy and thus to heat up; this is exploited in microwave ovens. A microwave oven, or a microwave, is a Kitchen appliance that cooks or heats Food by Dielectric heating.

Derivation

Electromagnetic waves as a general phenomenon were predicted by the classical laws of electricity and magnetism, known as Maxwell's equations. In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric 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:

$\nabla \cdot \mathbf{E} = 0 \qquad \qquad \qquad \ \ (1)$

$\nabla \times \mathbf{E} = -\frac{\partial}{\partial t} \mathbf{B} \qquad \qquad (2)$

$\nabla \cdot \mathbf{B} = 0 \qquad \qquad \qquad \ \ (3)$

$\nabla \times \mathbf{B} = \mu_0 \epsilon_0 \frac{\partial}{\partial t} \mathbf{E} \qquad \ \ \ (4)$

where

$\nabla$ is a vector differential operator (see Del). In Classical physics, free space is a concept of Electromagnetic theory, corresponding to a theoretically "perfect" Vacuum, and sometimes &nablaDel

One solution,

$\mathbf{E}=\mathbf{B}=\mathbf{0}$ ,

is trivial.

To see the more interesting one, we utilize vector identities, which work for any vector, as follows:

$\nabla \times \left( \nabla \times \mathbf{A} \right) = \nabla \left( \nabla \cdot \mathbf{A} \right) - \nabla^2 \mathbf{A}$

To see how we can use this take the curl of equation (2):

$\nabla \times \left(\nabla \times \mathbf{E} \right) = \nabla \times \left(-\frac{\partial \mathbf{B}}{\partial t} \right) \qquad \qquad \qquad \quad \ \ \ (5) \,$

Evaluating the left hand side:

$\nabla \times \left(\nabla \times \mathbf{E} \right) = \nabla\left(\nabla \cdot \mathbf{E} \right) - \nabla^2 \mathbf{E} = - \nabla^2 \mathbf{E} \qquad \quad \ (6) \,$

where we simplified the above by using equation (1). This article lists a few helpful mathematical identities which are useful in Vector algebra.

Evaluate the right hand side:

$\nabla \times \left(-\frac{\partial \mathbf{B}}{\partial t} \right) = -\frac{\partial}{\partial t} \left( \nabla \times \mathbf{B} \right) = -\mu_0 \epsilon_0 \frac{\partial^2}{\partial^2 t} \mathbf{E} \qquad (7)$

Equations (6) and (7) are equal, so this results in a vector-valued differential equation for the electric field, namely

$\nabla^2 \mathbf{E} = \mu_0 \epsilon_0 \frac{\partial^2}{\partial t^2} \mathbf{E}$

Applying a similar pattern results in similar differential equation for the magnetic field:

$\nabla^2 \mathbf{B} = \mu_0 \epsilon_0 \frac{\partial^2}{\partial t^2} \mathbf{B}$ . A differential equation is a mathematical Equation for an unknown function of one or several variables that relates the values of the

These differential equations are equivalent to the wave equation:

$\nabla^2 f = \frac{1}{{c_0}^2} \frac{\partial^2 f}{\partial t^2} \,$

where

c₀ is the speed of the wave in free space and

f describes a displacement

Or more simply:

$\Box^2 f = 0$

where $\Box^2$ is d'Alembertian:

$\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} \$

Notice that in the case of the electric and magnetic fields, the speed is:

$c_0 = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$

Which, as it turns out, is the speed of light in free space. The wave equation is an important second-order linear Partial differential equation that describes the propagation of a variety of Waves such as Sound waves In Special relativity, Electromagnetism and wave theory, the d'Alembert operator \Box also called the d'Alembertian or the Maxwell's equations have unified the permittivity of free space $ε 0$ , the permeability of free space $μ 0$ , and the speed of light itself, c₀. Before this derivation it was not known that there was such a strong relationship between light and electricity and magnetism. The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of Electromagnetic waves through a medium

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.

$\mathbf{E} = \mathbf{E}_0 f\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right)$

Here $\mathbf{E}_0$ is the constant amplitude, $f$ is any second differentiable function, $\hat{\mathbf{k}}$ is a unit vector in the direction of propagation, and ${\mathbf{x}}$ is a position vector. We observe that $f\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right)$ is a generic solution to the wave equation. In other words

$\nabla^2 f\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right) = \frac{1}{{c_0}^2} \frac{\partial^2}{\partial^2 t} f\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right)$ ,

for a generic wave traveling in the $\hat{\mathbf{k}}$ direction.

This form will satisfy the wave equation, but will it satisfy all of Maxwell's equations, and with what corresponding magnetic field?

$\nabla \cdot \mathbf{E} = \hat{\mathbf{k}} \cdot \mathbf{E}_0 f'\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right) = 0$

$\mathbf{E} \cdot \hat{\mathbf{k}} = 0$

The first of Maxwell's equations implies that electric field is orthogonal to the direction the wave propagates.

$\nabla \times \mathbf{E} = \hat{\mathbf{k}} \times \mathbf{E}_0 f'\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c_0 t \right) = -\frac{\partial}{\partial t} \mathbf{B}$

$\mathbf{B} = \frac{1}{c_0} \hat{\mathbf{k}} \times \mathbf{E}$

The second of Maxwell's equations yields the magnetic field. The remaining equations will be satisfied by this choice of $\mathbf{E},\mathbf{B}$ .

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, $E 0 = c 0 B 0$ , which can be seen immediately from the Poynting vector. In Physics, the Poynting vector can be thought of as representing the Energy Flux (in W/m2 of an Electromagnetic field. The electric field, magnetic field, and direction of wave propagation are all orthogonal, and the wave propagates in the same direction as $\mathbf{E} \times \mathbf{B}$ .

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. Polarization ( ''Brit'' polarisation) is a property of Waves that describes the orientation of their oscillations

References

^ Vu-Quoc, L. CONELRAD ( Con trol of El ectromagnetic '''El'''ectronic Rad iation was a method of emergency Broadcasting to the public of the The term electromagnetic pulse ( EMP) has the following meanings Electromagnetic radiation from an Explosion (especially a Nuclear The electromagnetic (EM spectrum is the range of all possible Electromagnetic radiation frequencies Bioelectromagnetism (sometimes equated with bioelectricity) refers to the electrical magnetic or Electromagnetic fields produced by living cells tissues Electromagnetic radiation can be classified into ionizing radiation and Non-ionizing radiation, based on whether it is capable of ionizing atoms and breaking The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of Electromagnetic waves through a medium Finite-difference time-domain (FDTD is a popular computational electrodynamics modeling technique A helicon is a low frequency Electromagnetic wave. Helicons have the special ability to propagate through pure metals given conditions of low temperature and high magnetic A klystron is a specialized linear-beam Vacuum tube (evacuated electron tube Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700 In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric Photon polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave Radiant energy is the Energy of Electromagnetic waves The quantity of radiant energy may be calculated by integrating Radiant flux (or power Sinusoidal plane-wave solutions are particular solutions to the Electromagnetic wave equation. In the Physics of Electromagnetism, the Abraham-Lorentz force is the Recoil Force on an accelerating Charged particle caused , Configuration integral (statistical mechanics), 2008.
^ Isaac Asimov, Isaac Asimov's Book of Facts. Hastingshouse/Daytrips Publ. , 1992. Page 389.

Hecht, Eugene (2001). Optics, 4th ed. , Pearson Education. ISBN 0-8053-8566-5.
Serway, Raymond A. ; Jewett, John W. (2004). Physics for Scientists and Engineers, 6th ed. , Brooks/Cole. ISBN 0-534-40842-7.
Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics, 5th ed. , W. H. Freeman. ISBN 0-7167-0810-8.
Reitz, John; Milford, Frederick; Christy, Robert (1992). Foundations of Electromagnetic Theory, 4th ed. , Addison Wesley. ISBN 0-201-52624-7.
Jackson, John David (1975). Classical Electrodynamics, 2nd ed, John Wiley & Sons. ISBN 0-471-43132-X.
Allen Taflove and Susan C. Hagness (2005). Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed.. Artech House Publishers. ISBN 1-58053-832-0.

External links

Electromagnetism - a chapter from an online textbook
Electromagnetic Waves from Maxwell's Equations on Project PHYSNET.
Conversion of frequency to wavelength and back - electromagnetic, radio and sound waves
eBooks on Electromagnetic radiation and RF
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.

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