Electrostatics Electromagnetism Magnetism Electric charge Coulomb's law Electric field Gauss's law Electric potential Ampere's law Magnetic field Magnetic moment Electric current Lorentz force law Electromotive force Electromagnetic induction Faraday-Lenz law Displacement current Maxwell's equations Electromagnetic field Electromagnetic radiation 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.

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.

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 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

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 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 ε0, the permeability of free space μ0, 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, E0 = cB0. 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.