# Electromagnetic radiation

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File:Light-wave.png
Electromagnetic radiation can be conceptualized as a self propagating transverse oscillating wave of electric and magnetic fields.

Electromagnetic radiation is a propagating wave in space with electric and magnetic components. These components oscillate at right angles to each other and to the direction of propagation.

The term electromagnetic radiation is also used as a synonym for electromagnetic waves in general, even if they are not radiating or travelling in free space. This sense includes, for example, light travelling through an optical fiber, or electrical energy travelling within a coaxial cable.

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

## Physics

### Theory

Electromagnetic waves of much lower frequency than light were predicted by Maxwell's equations and subsequently discovered by Heinrich Hertz. Maxwell derived a wave form of the electric and magnetic equations which made explicit the wave nature of the electric and magnetic fields. These equations displayed the symmetry of the fields.

According to the theory, a time-varying electric field generates a magnetic field and vice versa. Thus, an oscillating electric field creates an oscillating magnetic field, which in turn creates an oscillating electric field, and so on. By this means an EM wave is produced which propagates through space.

### Properties

Electric and magnetic fields exhibit the property of superposition. This means that the field due to a particular particle or time-varying electric or magnetic field adds to the fields due to other causes. (As magnetic and electric fields are vector fields, this is the vector addition of all the individual electric and magnetic field vectors.) As a result, EM radiation is influenced by various phenomena such as refraction and diffraction. For example, a travelling EM wave incident on a particular arrangement of atoms induces oscillation in the atoms and thus causes them to emit their own EM waves (called wavelets). These emissions interfere with the impinging wave and alter its form.

In refraction, a wave moving from one medium to another of a different density changes its speed and direction when it enters the new medium. The ratio of the refractive indices of the media determines the extent of refraction. Refraction is the mechanism by which light disperses into a spectrum when it is shone through a prism.

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). These characteristics are mutually exclusive and appear separately in different circumstances: the wave characteristics appear when EM radation is measured over relatively larger timescales and over larger distances, and the particle characteristics are evident when measuring smaller distances and timescales. EM radiation's behaviours as a wave and as a stream of particles have been confirmed by a large number of experiments.

### Wave model

An important aspect of the wave 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 comprises a spectrum of frequencies which sum to form the resultant wave. In addition, frequency affects properties like refraction, in which different frequencies undergo a different level of refraction.

### Particle model

In the particle model of EM radiation, EM radiation is quantized as particles called photons. Quantisation of light represents the discrete packets of energy which constitute the radiation. The frequency of the radiation determines the magnitude of the energy of the particles. Moreover, these particles are emitted and absorbed by charged particles, so photons act as transporters of energy.

A photon absorbed by an atom excites an electron and elevates it to a higher energy level. If the energy is great enough, the electron is liberated from the atom in a process called ionisation. Conversely, an electron which descends to a lower energy level in an atom emits a photon of light equal to the energy difference. The energy levels of electrons in atoms are discrete. Therefore, each element has 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 which absorb different frequencies of the light. The composition of the medium through which the light travels determines the nature of the absorption spectrum. For instance, in a distant star, dark bands in the light it emits are due to the atoms in the atmosphere of the star. 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 which represents the jumps between the energy levels of the electrons is exhibited. This is manifested in the emission spectrum of nebulae.

### 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.)

## Electromagnetic spectrum

File:SNS 033.jpg
Klystrons give off both ionizing radiation in the form of X-rays and non-ionizing radiation in the form of radio and microwave, all of which are forms of electromagnetic radiation.
Main article: electromagnetic spectrum

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 behavior depends on the amount of energy per quantum it carries.

Spectroscopy can detect a much wider region of the EM spectrum than the visible range of 400 nm to 700 nm. A common laboratory spectroscope can detect wavelengths from 2 nm to 2500 nm. More in-depth 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

Main article: light

EM radiation with a wavelength between 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 shines on an object, say a bowl of fruit, this results in our visual perception identifying information from the scene. Our brain's visual system processes the multitude of reflected frequencies into different shades and hues, and through this not-entirely-explained "psychophysical phenomenon," most humans perceive a bowl of fruit.

In the vast majority of cases, however, the information carried by light is not directly apprehensible by human senses. Natural sources produce EM radiations across the spectrum; so, too, can human technology manipulate a broad range of wavelengths. Optical fiber transmits light which, although not suitable for direct viewing, can carry data. Those data can be translated into sound or even into an image. The coded form of such data is similar to that used with radio waves.

### Radio waves

Main article: radio wave

Radio waves carry information by varying amplitude and by varying frequency 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, that is no charges or currents, then you will find that along with the possiblity of nothing happening, the theory will also admit nontrivial solutions of changing electric and magnetic fields.

$\displaystyle \nabla \cdot \mathbf{E} = 0$
$\displaystyle \nabla \times \mathbf{E} = -\frac{\partial}{\partial t} \mathbf{B}$
$\displaystyle \nabla \cdot \mathbf{B} = 0$
$\displaystyle \nabla \times \mathbf{B} = \mu_0 \epsilon_0 \frac{\partial}{\partial t} \mathbf{E}$

$\displaystyle \mathbf{E}=\mathbf{B}=\mathbf{0}$ is a solution, but there might be other solutions as well. Let us employ a useful identity from vector calculus.

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

Where $\displaystyle \mathbf{A}$ can be any vector function. Taking the curl of the curl equations and applying the identity, we get the following.

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

These types of equations are identified as linear wave equations with wave speed $\displaystyle \frac{1}{\sqrt{\mu_0 \epsilon_0}}$ . Amazingly, this speed happens to be exactly the speed of light! Maxwell's equations have unified the permittivity of free space $\displaystyle \epsilon_0$ , the permeability of free space $\displaystyle \mu_0$ , and the speed of light itself: $\displaystyle c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$ . 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.

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

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

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

for a generic wave traveling in the $\displaystyle \hat{\mathbf{k}}$ 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?

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

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

$\displaystyle \nabla \times \mathbf{E} = \hat{\mathbf{k}} \times \mathbf{E}_0 f'\left( \hat{\mathbf{k}} \cdot \mathbf{x} - c t \right) = -\frac{\partial}{\partial t} \mathbf{B}$
$\displaystyle \mathbf{B} = \frac{1}{c} \hat{\mathbf{k}} \times \mathbf{E}$

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

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, $\displaystyle \mathbf{E}_0 = c \mathbf{B}_0$ . The electric field, magnetic field, and direction of wave propagation are all orthogonal and the wave propagates in the same direction as $\displaystyle \mathbf{E} \times \mathbf{B}$ .

Visualizing yourself as an electromagnetic wave traveling forward, the electric field might be oscillating up and down, while the magnetic field oscillates right and left; but you can rotate this picture around 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.

## References

• Hecht, Eugene (2001). Optics (4th ed.), Pearson Education. ISBN 0805385665.
• Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.), Brooks/Cole. ISBN 0534408427.
• Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.), W. H. Freeman. ISBN 0716708108.