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## PowerPedia:Electromagnetic wave

Lasted edited by Andrew Munsey, updated on June 14, 2016 at 9:21 pm.

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Electromagnetic radiation is generally described as a self-propagating There was an error working with the wiki: Code[16] and Magnetic field components. These components There was an error working with the wiki: Code[17] with each other. Electromagnetic radiation is classified into types according to the Frequency of the wave: these types include, in order of increasing frequency, There was an error working with the wiki: Code[36], There was an error working with the wiki: Code[37], There was an error working with the wiki: Code[38], There was an error working with the wiki: Code[39], There was an error working with the wiki: Code[40], There was an error working with the wiki: Code[41]s and There was an error working with the wiki: Code[42]. In some technical contexts the entire range is referred to as just 'light'.

EM radiation carries Energy and There was an error working with the wiki: Code[43], which may be imparted when it interacts with There was an error working with the wiki: Code[44].

Electromagnetic waves of much lower frequency than visible light were first predicted by There was an error working with the wiki: Code[18], revealing the wavelike nature of electric and magnetic fields and their symmetry.

According to these 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.

##### Properties

Electric and magnetic fields obey the properties of There was an error working with the wiki: Code[19], 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 There was an error working with the wiki: Code[20] addition.) These properties cause various phenomena including There was an error working with the wiki: Code[21] structure induces oscillation in the atoms, thereby causing them to emit their own EM waves. These There was an error working with the wiki: Code[22] 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 crystals, however, interactions can occur between light and static electric and magnetic fields - these interactions include the There was an error working with the wiki: Code[45] and the There was an error working with the wiki: Code[46].

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, summarized by There was an error working with the wiki: Code[23] as light is shone through a prism because of refraction.

The Physics of electromagnetic radiation is There was an error working with the wiki: Code[47], a subfield of Electromagnetism.

EM radiation exhibits both wave properties and particle properties at the same time (see There was an error working with the wiki: Code[48]). However, these characteristics are mutually exclusive and appear separately in different circumstances: the wave characteristics appear when EM radiation is measured over relatively large timescales and over large distances, and the particle characteristics are evident when measuring small distances and timescales. Both characteristics have been confirmed in a large number of experiments.

##### 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 There was an error working with the wiki: Code[49], the SI unit of frequency, equal to one oscillation per There was an error working with the wiki: Code[50]. 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 is called the There was an error working with the wiki: Code[51]. 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 the inverse of wavelength, according to the equation:

:v=f\lambda

where v is the speed of the wave (There was an error working with the wiki: Code[24] in a vacuum, or less in other media), f is the frequency and ? is the wavelength. As waves cross boundaries between different media, their speed changes but their frequency remains constant.

There was an error working with the wiki: Code[52] 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

In the particle model of EM radiation, a wave consists of discrete packets of energy, or There was an error working with the wiki: Code[53], called There was an error working with the wiki: Code[54]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.

As a photon is absorbed by an Atom, it excites an Electron, elevating it to a higher There was an error working with the wiki: Code[55]. 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 There was an error working with the wiki: Code[56]. 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 There was an error working with the wiki: Code[57]. 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 There was an error working with the wiki: Code[58]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 There was an error working with the wiki: Code[59].

##### 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 There was an error working with the wiki: Code[25]) conducts There was an error working with the wiki: Code[26]s. As a wave, it is characterized by a velocity (the There was an error working with the wiki: Code[27] relation E = h?, where E is the energy of the photon, h = 6.626 &times 10-34 J·s is There was an error working with the wiki: Code[60], and ? is the frequency of the wave.

One rule is always obeyed regardless of the circumstances: EM radiation in a vacuum always travels at the There was an error working with the wiki: Code[61], relative to the observer, regardless of the observer's velocity. (This observation led to There was an error working with the wiki: Code[62]'s development of the theory of There was an error working with the wiki: Code[63].)

In a medium (other than vacuum), There was an error working with the wiki: Code[64] or There was an error working with the wiki: Code[65] 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

There was an error working with the wiki: Code[1]

? = There was an error working with the wiki: Code[66]s

HX = Hard There was an error working with the wiki: Code[67]s

SX = Soft X-Rays

EUV = Extreme There was an error working with the wiki: Code[68]

NUV = Near ultraviolet

There was an error working with the wiki: Code[69]

NIR = Near There was an error working with the wiki: Code[70]

MIR = Moderate infrared

FIR = Far infrared

There was an error working with the wiki: Code[71]:

EHF = There was an error working with the wiki: Code[72] (Microwaves)

SHF = There was an error working with the wiki: Code[73] (Microwaves)

UHF = There was an error working with the wiki: Code[74]

VHF = There was an error working with the wiki: Code[75]

HF = There was an error working with the wiki: Code[76]

MF = There was an error working with the wiki: Code[77]

LF = There was an error working with the wiki: Code[78]

VLF = There was an error working with the wiki: Code[79]

VF = There was an error working with the wiki: Code[80]

ELF = There was an error working with the wiki: Code[81]

Generally, EM radiation is classified by wavelength into Electrical energy, Radio, There was an error working with the wiki: Code[82], There was an error working with the wiki: Code[83], the There was an error working with the wiki: Code[84] we perceive as light, There was an error working with the wiki: Code[85], There was an error working with the wiki: Code[86]s and There was an error working with the wiki: Code[87].

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.

There was an error working with the wiki: Code[28] There was an error working with the wiki: Code[29].

##### Light

EM radiation with a There was an error working with the wiki: Code[30] and 700 nm is detected by the There was an error working with the wiki: Code[88] There was an error working with the wiki: Code[89] and perceived as visible There was an error working with the wiki: Code[90]. 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 There was an error working with the wiki: Code[91] 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.

In the vast majority of cases, however, the information carried by light 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. There was an error working with the wiki: Code[92] 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 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 There was an error working with the wiki: Code[31], it couples to the conductor, travels along it, and There was an error working with the wiki: Code[32] an electric current on the surface of that conductor by exciting the electrons of the conducting material. This effect (the There was an error working with the wiki: Code[93]) is used in antennas. EM radiation may also cause certain molecules to absorb energy and thus to heat up this is exploited in There was an error working with the wiki: Code[94]s.

#### Derivation

Electromagnetic waves as a general phenomenon were predicted by the classical laws of Electricity and magnetism, known as There was an error working with the wiki: Code[95]. 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. So, beginning with Maxwell's equations for a vacuum:

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

:where

::\nabla is a vector differential operator (see There was an error working with the wiki: Code[96])

One solution is trivial,

::{E}={B}={0}

But there is a more interesting one. To see it one can use a useful There was an error working with the wiki: Code[33] which works for any vector:

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

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

Evaluating the left hand side:

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

:where we simplified the above by using equation (1).

Evaluate the right hand side:

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

Equations (6) and (7) are equal, so this results in a There was an error working with the wiki: Code[97] for the electric field:

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

|}

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

|\nabla^2 {B} = \mu_0 \epsilon_0 \frac{\partial^2}{\partial t^2} {B}

|}

These differential equations are equivalent to the There was an error working with the wiki: Code[98]:

::\nabla^2 f = \frac{1}{v^2} \frac{\partial^2 f}{\partial t} \,

:where

::v is the velocity of the wave and

::f describes a displacement

So notice that in the case of the electric and magenetic fields, the velocity is:

::v = \frac{1}{\sqrt{\mu_0 \epsilon_0}}

Which, as it turns out, is the There was an error working with the wiki: Code[34] 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.

:{E} = {E}_0 f\left( \hatThere was an error working with the wiki: Code[2] \cdot {x} - c t \right)

Here {E}_0 is the constant amplitude, f is any second differentiable function, \hatThere was an error working with the wiki: Code[3] is a unit vector in the direction of propagation, and There was an error working with the wiki: Code[4] is a position vector. We observe that f\left( \hatThere was an error working with the wiki: Code[3] \cdot {x} - c t \right) is a generic solution to the wave equation. In other words

:\nabla^2 f\left( \hatThere was an error working with the wiki: Code[6] \cdot {x} - c t \right) = \frac{1}{c^2} \frac{\partial^2}{\partial^2 t} f\left( \hatThere was an error working with the wiki: Code[6] \cdot {x} - c t \right),

for a generic wave traveling in the \hatThere was an error working with the wiki: Code[8] 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?

:\nabla \cdot {E} = \hatThere was an error working with the wiki: Code[9] \cdot {E}_0 f'\left( \hatThere was an error working with the wiki: Code[9] \cdot {x} - c t \right) = 0

:{E} \cdot \hatThere was an error working with the wiki: Code[11] = 0

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

:\nabla \times {E} = \hatThere was an error working with the wiki: Code[12] \times {E}_0 f'\left( \hatThere was an error working with the wiki: Code[12] \cdot {x} - c t \right) = -\frac{\partial}{\partial t} {B}

:{B} = \frac{1}{c} \hatThere was an error working with the wiki: Code[14] \times {E}

The second of Maxwell's equations yields the magnetic field. The remaining equations will be satisfied by this choice of {E},{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. The electric field, magnetic field, and direction of wave propagation are all orthogonal and the wave propagates in the same direction as {E} \times {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 There was an error working with the wiki: Code[99].

#### Related pages

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Energy-dependent Electromagnetic Wave

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#### External articles and references

Books

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). Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed.. Artech House Publishers. ISBN 1-58053-832-0.

National Synchrotron Light Source, U.S.A.

General

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.

Patents

Greenleaf Whittier Pickard - There was an error working with the wiki: Code[15] - Intelligence intercommunication by There was an error working with the wiki: Code[110] component