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Electromagnetic (EM) radiation is a , Microwaves , Terahertz Radiation , Infrared Radiation , Visible Light , Ultraviolet Radiation , X-ray s and Gamma Rays . EM radiation carries Energy and Momentum , which may be imparted when it interacts with Matter . PHYSICS Theory Electromagnetic waves were first predicted by James Clerk Maxwell and subsequently confirmed by Heinrich Hertz . Maxwell derived a 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 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. (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 . 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 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 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 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 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, 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: :$v=f\backslash lambda$ 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. 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 Planck's equation: :$E=hf$ where ''E'' is the energy, ''h'' is Planck's Constant , and ''f'' is frequency. 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 . 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 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 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 ) 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 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 Planck's relation ''E = hν'', where ''E'' is the energy of the photon, ''h'' = 6.626 × 10-34 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 See Also: electromagnetic spectrum

Evaluating the left hand side:

::$$
abla imes \left(
abla imes \mathbf{E} ight) =
abla\left(
abla \cdot \mathbf{E} ight) -
abla^2 \mathbf{E} = -
abla^2 \mathbf{E} \qquad \quad \ (6) \,
:where we simplified the above by using equation (1).

Evaluate the right hand side:

::$$
abla imes \left(-rac{\partial \mathbf{B}}{\partial t} ight) = -rac{\partial}{\partial t} \left(
abla imes \mathbf{B} ight) = -\mu_0 \epsilon_0 rac{\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

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

These differential equations are equivalent to the Wave Equation :

::$$
abla^2 f = rac{1}{c^2} rac{\partial^2 f}{\partial t^2} \,
:where
::''c'' is the speed of the wave and
::''f'' describes a displacement

Or more simply:
::$\backslash Box^2\; f\; =\; 0$
:where $\backslash Box^2$ is D'Alembertian :
::$\backslash Box^2\; =$
abla^2 - rac{1}{c^2} rac{\partial^2}{\partial t^2} = rac{\partial^2}{\partial x^2} + rac{\partial^2}{\partial y^2} + rac{\partial^2}{\partial z^2} - rac{1}{c^2} rac{\partial^2}{\partial t^2} \

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

::

Which, as it turns out, is the Speed Of Light . Maxwell's equations have unified the permittivity of free space $\backslash epsilon\_0$, the permeability of free space $\backslash mu\_0$, and the speed of light itself, c. Before this derivation it was not known that there was such a strong 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.

:$\backslash mathbf\{E\}\; =\; \backslash mathbf\{E\}\_0\; f\backslash left(\; \backslash hat\{\backslash mathbf\{k\}\}\; \backslash cdot\; \backslash mathbf\{x\}\; -\; c\; t\; ight)$

Here $\backslash mathbf\{E\}\_0$ is the constant amplitude, $f$ is any second differentiable function, $\backslash hat\{\backslash mathbf\{k\}\}$ is a unit vector in the direction of propagation, and $\{\backslash mathbf\{x\}\}$is a position vector. We observe that $f\backslash left(\; \backslash hat\{\backslash mathbf\{k\}\}\; \backslash cdot\; \backslash mathbf\{x\}\; -\; c\; t\; ight)$ is a generic solution to the wave equation. In other words
:$$
abla^2 f\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c t ight) = rac{1}{c^2} rac{\partial^2}{\partial^2 t} f\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c t ight),
for a generic wave traveling in the $\backslash hat\{\backslash mathbf\{k\}\}$ direction. The proof of this is trivial.

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

:$$
abla \cdot \mathbf{E} = \hat{\mathbf{k}} \cdot \mathbf{E}_0 f'\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c t ight) = 0
:$\backslash mathbf\{E\}\; \backslash cdot\; \backslash hat\{\backslash mathbf\{k\}\}\; =\; 0$

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

:$$
abla imes \mathbf{E} = \hat{\mathbf{k}} imes \mathbf{E}_0 f'\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c t ight) = -rac{\partial}{\partial t} \mathbf{B}
:

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

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, $E\_0\; =\; c\; B\_0$, 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 $\backslash mathbf\{E\}\; imes\; \backslash mathbf\{B\}$.

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 .


ELECTROMAGNETIC POLLUTION


The term ''electrosmog'', from '' Electromagnetic Smog '', is used to describe Electromagnetic Fields and radiation, at both power and radio frequencies. The term is usually used in a pejorative sense, and is also used to negatively describe the pervasiveness of wireless and microwave-emitting devices throughout the modern world.¹


SEE ALSO

• Control Of Electromagnetic Radiation


• Electromagnetic Pulse


• Electromagnetic Spectrum


• Electromagnetic Radiation And Health


• Electromagnetic Wave Equation


• Finite-difference Time-domain Method


• Helicon


• Klystron


• Light


• Maxwell's Equations


• Photon Polarization


• Radiant Energy


• Sinusoidal Plane-wave Solutions Of The Electromagnetic Wave Equation


• Radiation Reaction

REFERENCES

• ⁷

EXTERNAL LINKS

• Electromagnetism - a chapter from an online textbook


• '' Electromagnetic Waves from Maxwell's Equations '' on Project PHYSNET .


• Ecolibria:More information and testing for EMR in Australia


• 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.