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Electromagnetic radiation

2007 Schools Wikipedia Selection. Related subjects: Electricity and
Electronics

   Electromagnetism
   Magnetism
        Electrostatics
   Electric charge
   Coulomb's law
   Electric field
   Gauss's law
   Electric potential
        Magnetostatics
   Ampere's law
   Magnetic field
   Magnetic moment
        Electrodynamics
   Electric current
   Lorentz force law
   Electromotive force
   Electromagnetic induction
   Faraday-Lenz law
   Displacement current
   Maxwell's equations
   Electromagnetic field
   Electromagnetic radiation
      Electrical circuits
   Electrical conduction
   Electrical resistance
   Capacitance
   Inductance
   Impedance
   Resonant cavities
   Waveguides
   Electromagnetic radiation can be imagined as a self-propagating
   transverse oscillating wave of electric and magnetic fields. This
   diagram shows a plane linearly polarised wave propagating from left to
   right.
   Enlarge
   Electromagnetic radiation can be imagined as a self-propagating
   transverse oscillating wave of electric and magnetic fields. This
   diagram shows a plane linearly polarised wave propagating from left to
   right.

   Electromagnetic radiation is generally described as a self-propagating
   wave in space with electric and magnetic components. These components
   oscillate at right angles to each other and to the direction of
   propagation, and are in phase with each other. Electromagnetic
   radiation is classified into types according to the frequency of the
   wave: these types include, in order of increasing frequency, radio
   waves, microwaves, infrared radiation, visible light, ultraviolet
   radiation, X-rays and gamma rays. In some technical contexts the entire
   range is referred to as just 'light'.

   EM radiation carries energy and momentum, which may be imparted when it
   interacts with matter.

   Electromagnetic waves of much lower frequency than visible light were
   first predicted by Maxwell's equations and subsequently discovered by
   Heinrich Hertz. Maxwell derived a wave form of the electric and
   magnetic equations, 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

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 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 = fλ

   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 speed changes but their
   frequency remains 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

   In the particle model of EM radiation, a wave consists of discrete
   packets of energy, or quanta, called photons. 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 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 ionization. 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 nebulae. 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 particles. As a wave, it is characterized
   by a velocity (the speed of light), wavelength, and frequency. 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 = 6.626 × 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

   Electromagnetic spectrum with light highlighted
   Enlarge
   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
   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 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 behaviour 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, many hydrogen atoms emit radio waves which have a wavelength
   of 21.12 cm.

Light

   EM radiation with a wavelength between approximately 400 nm and 700 nm
   is detected by the human eye and perceived as visible light.

   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.

   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. Optical fibre 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

   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 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. 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 ovens.

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 a vacuum:

                \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)

   One solution is trivial,

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

   But there is a more interesting one. To see it one can use a useful
   vector identity which works for any vector:

                \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).

   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 differential
   equation for the electric field:

          \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}

   These differential equations are equivalent to the wave equation:

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

          where

                v is the velocity of the wave and
                f describes a displacement

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

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

   Which, as it turns out, is the speed of light. 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, 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.

          \mathbf{E} = \mathbf{E}_0 f\left( \hat{\mathbf{k}} \cdot
          \mathbf{x} - c 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 t \right) is
   a generic solution to the wave equation. In other words

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

   for a generic wave traveling in the \hat{\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?

          \nabla \cdot \mathbf{E} = \hat{\mathbf{k}} \cdot \mathbf{E}_0
          f'\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c 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 t \right) =
          -\frac{\partial}{\partial t} \mathbf{B}
          \mathbf{B} = \frac{1}{c} \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] = cB[0]. 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.

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