# Electric current is a wave

As **electromagnetic wave** is a wave of coupled electric and magnetic fields. These include radio waves, microwaves, infrared radiation, visible light, UV radiation as well as X-ray and gamma radiation - in short, the entire electromagnetic wave spectrum. The only difference between these types of waves is their frequency and thus their energy. However, there is a continuous spectrum (see graph below); The classification into the above-mentioned types is based on the properties of the radiation, which change continuously with frequency, or its origin, as well as the different uses or manufacturing processes or the various measurement methods used for this.

Electromagnetic waves do not need a medium to propagate. They propagate in a vacuum at the speed of light regardless of their frequency. They are transverse waves, i. H. their direction of propagation is perpendicular to the direction of oscillation of the electromagnetic fields.

Under certain circumstances electromagnetic waves behave like particles (see wave-particle dualism). These are called photons.

### properties

### Wave character

From a physical point of view, electromagnetic waves are propagating oscillations of the electromagnetic field. Here, the electric and magnetic fields are perpendicular to each other in linearly polarized waves and have a fixed size ratio. This is given by the wave impedance. In particular, the electric and magnetic fields disappear in the same places at the same time, so that the frequently read representation that electric and magnetic energy are cyclically converted into one another is not correct. However, she agrees z. B. for the near field of an electromagnetic wave generating electrical dipole or resonant circuit.

The creation of electromagnetic waves is explained by Maxwell's equations: The change in the electrical field over time is always linked to a spatial change in the magnetic field. Likewise, the change in the magnetic field over time is again linked to a spatial change in the electric field. For fields that change periodically (especially sinusoidally), these effects together result in a progressive wave.

### Particle character

For certain properties of electromagnetic waves (e.g. photoelectric effect), the wave model described above is no longer sufficient to describe all observable phenomena, rather the particle properties of individual photons, the quanta of the electromagnetic field, come to the fore. The wave character (e.g. interference) remains fully intact. One therefore speaks of the dualism of particle and wave.

Within the framework of this particle conception of light, every frequency becomes *f* the energy of a single photon assigned, where *H* is Planck's quantum of action. On the other hand, particles such as B. electrons moving over several atoms, wave properties (see also electrical current). Both aspects of electromagnetic waves are theoretically discussed in the context of quantum electrodynamics.

### Waves in the medium

In a medium (i.e. in matter) the speed decreases depending on the permittivity (dielectric conductivity) and the permeability (magnetic conductivity) of the substance. The following then applies: . In addition, it is refracted depending on the frequency ω of the wave (dispersion) and (depending on the medium) depending on its polarization and its direction of propagation. A direct force (e.g. change of direction) on a propagating electromagnetic wave can only occur through the medium of propagation (including limitations such as mirrors) or the force of gravity.

Some newer theories, for example loop quantum gravity, say that the speed of light has a low frequency dependence *c* in a vacuum ahead.

### spectrum

Electromagnetic waves are sorted according to wavelength in the electromagnetic spectrum *(A list of frequencies and examples of electromagnetic waves can be found in the article there)*.

The best known and most studied example of an electromagnetic wave is visible light. It represents only a tiny part of the entire spectrum and is the only area that can be perceived by people without technical aids. To the right of this, the energy of the photons is too low to trigger chemical processes. To the left of this begins the area of ionizing radiation (radioactivity), in which a single photon can destroy molecules.

With light, the frequency determines the color of the light and not, as is often wrongly assumed, the wavelength. This becomes clear when one observes light in optically denser media, where it propagates at a slower speed than c. The frequency is not influenced during the transition into optically denser media and consequently it has to be loud have a shorter wavelength. Since the color does not change in the medium, only the frequency is characteristic of the color of the light. For historical reasons, however, the wavelength is still given in spectra as a characteristic property of light. This relationship between color and wavelength then only applies in a vacuum (and to a good approximation in air). Monochromatic light, i.e. light only of a single wavelength, always has a spectral color.

### Mathematical description

The formal description of electromagnetic waves can be traced back to Maxwell's equations. In fact, electromagnetic waves were theoretically postulated by James Clerk Maxwell as early as 1865 before Heinrich Rudolf Hertz was able to prove them experimentally in 1888.

At this point, we will first consider electromagnetic waves in a vacuum, i.e. waves in a charge-free space with the exclusion of dielectric, dia- and paramagnetic effects ( and , see material equations of electrodynamics). Current density and charge density are zero.

One starts with the third Maxwell equation (with ):

and applies the rotation operator to both sides. For one thing, it gives you

and inserts Maxwell's fourth equation,

On the other hand, the vector analytical relationship applies in general

with the Laplace operator Δ

- .

Applying this relation to (1) and considering that the charge-free space is being considered, in which the divergence of D is zero according to Maxwell's first equation, then we get:

- .

If you now put (2) and (3) together, the following wave equation results

- .

Almost all waves can be expressed by equations of form

describe, where v is the speed of propagation of the wave. The speed of propagation of electromagnetic waves is the speed of light *c*. Therefore applies to them

- .

This gives the equation from (4)

which represents a wave equation of the form (5) for each component. Your solutions are waves that travel at the speed of light *c* spread.

If the wave propagates in isotropic materials with the dielectric constant ε and the permeability μ, then the propagation speed is *c* slightly lower, namely

but in general the material constants are not linear, but rather themselves e.g. B. depend on the field strength or the frequency.

While light is still in the air at almost the speed of light in a vacuum *c* spreads (the material constants are in a good approximation 1), this no longer applies to water, which among other things. enables the Cherenkov effect.

### Electrostatic potentials

Furthermore, a mathematical description with the help of the electrostatic potentials is also possible, because because of

and

the field vector of the magnetic flux density can also be understood as the rotation of a vector field A. A is therefore called the vector potential of B and the following applies:

This relationship can now be used further. The rotation of the electric field is determined by

If one now substitutes the relation just obtained from (3) in (4), one obtains

and it follows

But now the rotation of every gradient disappears, so that the inner expression of (6) can be understood as the gradient of a scalar function:

This can now be used again in the original Maxwell equations in a source-free vacuum. With

and (8) and the relationship (Graßmann expansion theorem)

you get

In order to decouple these equations (11) and (12) from one another, it is required that the term under the gradient in (12) vanishes (see calibration transformation), i.e.

If the condition from (13) is fulfilled, the wave equation for the vector potential A with is automatically derived from (12)

and from (11) and (13) the wave equation of the scalar potential function with

follows

This description of electromagnetic phenomena can be adapted to various problems by means of calibration transformation in order to simplify them. The Aharonov-Bohm effect caused a controversy about the role of the potentials, especially the vector potential. In this case, electrons fly through a space free of magnetic fields, but are still influenced. It was thought that this is how the vector potential, which was also present in field-free space, appears directly. In reality, however, only the rotation of the vector potential is decisive, and thus, according to Stokes' theorem, the magnetic field at the edge of the field-free space. All other interpretations and claims have been proven wrong.

### literature

Claus Müller: Basic problems of the mathematical theory of electromagnetic oscillations, Springer Verlag, Heidelberg, 1957.

### See also

Categories: Electrodynamics | Spectroscopy

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