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## Qualitative considerations on the propagation of electromagnetic waves

So far we have dealt almost exclusively with the generation of electromagnetic waves in the form of the Hertz dipole, now our further focus is in particular on the propagation or the electromagnetic waves emitted by the dipole propagate at the speed of light. At a sufficiently distant point, one then speaks of the far field, the waves pass this point as a plane wave with negligible curvature. As we have already mentioned above, the electromagnetic wave consists of two constantly changing fields, the electric and the magnetic field (electric field, magnetic field). These two components of the electromagnetic wave cannot exist independently of one another, but each of them can nevertheless form a separate wave in the sense of an electrical or a magnetic component. In the far field, these two waves are in the same phase and oscillate at the same frequency. The electric and the magnetic wave, i.e. the electric field $\overrightarrow{\mathrm{E.}}$ and the magnetic field $\overrightarrow{\mathrm{B.}}$, are perpendicular to each other and at the same time always perpendicular to the direction of propagation $\overrightarrow{c}$. The electromagnetic wave is therefore necessarily a transverse wave. Electric field $\overrightarrow{\mathrm{E.}}$, magnetic field $\overrightarrow{\mathrm{B.}}$ and the speed of propagation $\overrightarrow{c}$ form a three-dimensional right-angled coordinate system, where $\overrightarrow{c}$ in $x$-Direction, $\overrightarrow{\mathrm{E.}}$ in $y$-Direction, and $\overrightarrow{\mathrm{B.}}$ in $z$-Direction shows (right-handed 3-finger rule: $\overrightarrow{\mathrm{B.}}$ = outstretched thumb upwards, $\overrightarrow{c}$ = Index finger to the left, $\overrightarrow{\mathrm{E.}}$ = extended remaining fingers forward, coordinate systems).

Since both fields of the electromagnetic wave are sinusoidal, we can now use the following sinus functions of the location $x$ and time $t$ formulate:

- $$\text{Electric field strength:}\phantom{\rule{3px}{0ex}}\mathrm{E.}={\mathrm{E.}}_{0}\xb7sin\left(kx-\omega t\right)$$

- $$\text{Magnetic flux density:}\phantom{\rule{3px}{0ex}}\mathrm{B.}={\mathrm{B.}}_{0}\xb7sin\left(kx-\omega t\right)$$

with the amplitudes ${\mathrm{E.}}_{0}$ and ${\mathrm{B.}}_{0}$, the angular frequency $\omega $ and the circular wavenumber $k$. The following applies to the propagation speed of the wave $c=\nu \lambda =\frac{\omega}{k}$.

In the following we want to try to find a clear representation for the complicated facts of electromagnetic waves. As such, an electromagnetic wave can be represented by a beam in the direction of the speed of propagation. The wavelength $\lambda =\frac{2\pi}{k}$ marks the distance between two wave fronts with the same deflection.

Another meaningful representation of an electromagnetic wave is the vector representation with arrowheads. In a snapshot, any point on the $x$-Axis each in the direction of the $y$- An arrow for the strength of the electric field and in the direction of the axis $z$- Axis an arrow drawn for the strength of the magnetic field. The two envelopes of the arrowheads represent the sine functions of the electrical and magnetic components of the electromagnetic wave at a specific point in time.

One point $\mathrm{P.}$ on the $x$-Axis in the direction of the velocity of propagation $\overrightarrow{c}$ results in a flat surface in the $\mathrm{Y\; Z}$-Plane with the vectors of the electric and magnetic field. The cross product$\overrightarrow{\mathrm{E.}}\times \overrightarrow{\mathrm{B.}}$ is perpendicular to this plane in the direction of the propagation speed of the wave. If the electromagnetic wave is now at such a point $\mathrm{P.}$ Passing by, one can infinitesimally see a small slice of thickness $dx$ with the vectors $\overrightarrow{\mathrm{E.}}$ and $\overrightarrow{\mathrm{B.}}$ in the $\mathrm{Y\; Z}$- Mark the level that is constantly changing in phase.

Without a simplified illustration above, we would not be able to understand the following relationships. The complicated interaction of an electromagnetic wave is shown by the fact that a changing magnetic field induces an electric field and that this then also changes and thereby generates a magnetic field again.

- $$\frac{\partial \overrightarrow{\mathrm{B.}}}{\partial t}\sim \overrightarrow{\mathrm{E.}}\phantom{\rule{3em}{0ex}}\frac{\partial \overrightarrow{\mathrm{E.}}}{\partial t}\sim \overrightarrow{\mathrm{B.}}\phantom{\rule{3em}{0ex}}t=\text{Time}$$

This process takes place continuously, one also speaks of Faraday's and Maxwell's law of induction in this regard. Quantitative considerations are dealt with in the next section.

But first we have to emphasize again that electromagnetic waves and thus also visible light, in contrast to all waves treated so far, propagate without any medium in vacuum, air or substances. The speed of spread depends on the substance, but is always lower than the speed of spread $\overrightarrow{c}$ in a vacuum and approximately in air. The so-called speed of light $c=\mathrm{299.792.458}\text{}\phantom{\rule{0.3em}{0ex}}\text{m}\phantom{\rule{0.2em}{0ex}}{\text{s}}^{-1}$ is independent of the reference system, as Einstein's special theory of relativity has shown.

## Mechanical waves

Waves occur in many different areas in our environment. The pictures show some examples of waves.

Kuebi = Armin Kübelbeck, CC BY-SA 3.0, via Wikimedia Commons Jon Sullivan, Public domain, via Wikimedia Commons Dr G. Schmitz, CC BY-SA 3.0, via Wikimedia Commons PS-2507 (Peter Stehlik), CC BY-SA 3.0, via Wikimedia Commons

##### Definition of a wave

One - admittedly somewhat abstract - definition of the wave is:

A wave is a spatial and temporal change in the state of physical quantities, which usually takes place according to certain periodic laws.

#### Mechanical waves

The spread **mechanical waves** requires a carrier in which there are vibrating particles. Carriers can be solid, liquid or gaseous bodies.

Furthermore, these vibrating particles must be coupled to one another so that the external disturbance can propagate through the system.

For illustration, one often works with the so-called ball-spring model (cf. **Fig. 5**). The spheres symbolize the vibrating particles, the springs indicate the coupling between the particles. For the sake of simplicity, one often only draws lines between the particles instead of the feathers.

#### Propagation of a wave

A pathogen forces a particle of the body out of its rest position. Due to its inertia, the next particle takes over this disturbance somewhat delayed in time, a phase shift ( Delta varphi ) occurs between the movements of neighboring particles. This is how the disorder propagates through the body.

The speed with which the disturbance moves through the body is called **Speed of propagation** (c ).

Very often the externally excited particle is excited to a sinusoidal oscillation. The resulting wave is called **harmonic wave**.

With the propagation of the wave is a **Energy transport**, but **no matter transport** tied together. This propagation of energy into space with a wave is an essential one **Difference to vibration**where the energy only shuttles back and forth between two locations.

Expes, Public domain, via Wikimedia Commons

Expes, Public domain, via Wikimedia Commons

#### Wave fronts and wave rays

There is a phase difference between the forced oscillation at a certain point in the wave field and the oscillation of the exciter. All points that are equidistant from the excitation center vibrate in phase.

Neighboring points in the same phase form the so-called **Wavefront**.

They run perpendicular to the wave fronts **Wave normals** (they are also called **Wave rays**), which indicate the direction of propagation of the wave.

the **Fig. 4** and **5** show the wave fronts and the wave rays in two different types of waves, the circular and the plane waves.

## Hans Lassen (physicist)

After graduating from high school in Sonderburg, he was employed as a soldier in the First World War 1914–1918. 1919–1924 Hans Lassen studied physics, mathematics and chemistry in Kiel and Jena, with Winfried Otto Schumann, with whom he worked *Experimental investigation in circuits with mercury vapor rectifiers* PhD. [2] For a short time he worked at Siemens & amp; Halske in Berlin and in 1925 became Karl Försterling's assistant at the Institute for Theoretical Physics at the University of Cologne, where he dealt specifically with the propagation of electromagnetic waves and their overreaches. Two years later he switched to Hans Rukop and in 1933 became a private lecturer.

In 1928 he married Annemarie Hollaender (* 1901), the daughter of the Cologne regional court director. Her son Lars Lassen (* 1929) became a professor of physics in Heidelberg.

After Lassen was dismissed in 1935 because of his Jewish wife [3], he worked again at Siemens in Berlin until 1946. With the resumption of studies at the Humboldt University in Berlin, he received an extraordinary professorship for physics and in 1948 became head of the 1st Physics Institute. In April 1949 he was appointed full professor and director of the new Physics Institute by the newly founded Free University of Berlin. In 1965 he was retired.

Hans Lassen died in Berlin in 1974 at the age of 77. His grave is in the Dahlem forest cemetery. [5]

## Creation of electromagnetic waves

A dipole (e.g. long straight wire), in which the direction of the current flow is periodically changed, can be the starting point for electromagnetic waves. When the direction of the current is changed, the charge carriers in the line wire are accelerated. As a model, the origin of the electromagnetic wave can be understood in the following way:

A periodically changing current flows in the dipole. When the current is at its greatest, a circular magnetic field builds up around the dipole, the orientation of which is determined by the direction of the current. During a complete oscillation, the current flow comes to a complete standstill twice. Then the charge carriers are concentrated at the ends of the dipole. Electric field lines emanate from the positive dipole end and run to the negatively charged dipole end.

After polarity reversal, the dipole ends discharge and the electric field becomes weaker, while at the same time a magnetic field builds up again around the wire. In this process, the build-up and breakdown of electrical and magnetic fields alternate with one another. A periodic alternating electromagnetic field is created. This field is able to detach itself from the surface of the dipole. Once released, it spreads through space at the speed of light. An electromagnetic wave was created (pictures 1 and 2).

Generation of electromagnetic waves in a dipole

In addition to the processes at the dipole, there are many processes in nature and technology in which charge carriers are accelerated or decelerated. This happens, for example, when very fast electrons in a vacuum electron tube collide with the anode and are suddenly stopped. This creates very short-wave electromagnetic radiation, the X-rays.

Many molecules have an uneven internal charge distribution of the electrons in the shell of the molecular assembly. If these molecules rotate or oscillate, the charge carriers execute an accelerated movement (e.g. radial acceleration of the circular movement) and consequently emit electromagnetic radiation. This radiation has a longer wavelength than X-ray radiation and can e.g. **visible area** of the electromagnetic spectrum or in the infrared range.

Large-scale flows of charged particles on the surface of the sun are the starting point for radio waves.

If the human senses were to be equally sensitive to all wavelengths of electromagnetic radiation, then we would have to perceive a veritable thunderstorm of signals and noise from the most varied of electromagnetic waves. With the help of our eyes, however, we can only register the visible part of the electromagnetic radiation and are thus spared the confusing multitude of all incoming waves.

Propagation of electromagnetic waves in the immediate vicinity of a dipole

## Wave

**wave**, a spatially spreading excitation that transports energy. This means that waves can be used as the propagation of the *Faults* physical quantities, such as the deflection of particles in a medium or the field quantities of a physical field. The disturbance can be a one-time excitation or a periodic process. The speed of propagation of waves is always finite.

The wave propagation within a medium occurs through the excitation of particles to vibrate due to particles that are already vibrating. One speaks of *Longitudinal waves* or *Longitudinal waves*when these vibrations occur in the direction of propagation of the wave. In the case of vibrations perpendicular to the direction of propagation, one speaks of *Transverse waves* or *Longitudinal waves*. Water waves are an example of transverse waves, sound waves are longitudinal waves.

Excitations of physical fields, on the other hand, do not require a medium of propagation, so such waves can also propagate in a vacuum. The most important example are the electromagnetic waves, in which both the electrical and the magnetic field strength vibrate. Due to the form of Maxwell's equations, they can only appear as transverse waves. Light is also an electromagnetic wave, so its propagation including diffraction, refraction and interference can be treated within the framework of wave theory (Huygens principle). The propagation of electromagnetic waves in matter can lead to very complicated conditions, in particular the investigation of electrical and magnetic waves in plasmas (plasma waves, extraordinary waves) is often only possible with a great deal of effort. In this case, the electromagnetic waves can be coupled with oscillations of the plasma particles, i.e. sound waves. The same applies to solids, in which phonons can be generated and destroyed by processes in which electromagnetic waves are involved. Electromagnetic waves always travel at the speed of light. Since the speed of propagation in solids does not match the speed of light, this is an effect that can be explained by the constant absorption and delayed re-emission of the electromagnetic waves by the atoms of the medium.

As part of the *Quantum theory* photons are assigned to the electromagnetic waves (quantum electrodynamics), which due to their propagation at the speed of light must have a rest mass of zero. Conversely, particles with rest masses other than zero can also be assigned to matter fields and thus to matter waves (De Broglie wave).

With transverse waves it can happen that the oscillations of the underlying physical quantity only occur in one spatial direction. In this case the wave is called linear *polarized*. In the case of matter waves, the polarization is given by the direction of the spin of the associated particle streams.

A surface within a wave, the points of which are in the same state of oscillation at the observed point in time (*phase*) are called *Wave surface* or *Wavefront*, the curves perpendicular to the wave fronts *Wave normals*. Depending on the shape of the wave fronts, one speaks of *cylinder*-, *Bullet*- or *levels* Waves. Plane waves result from the excitation of all points of a plane with the same phase, cylindrical waves from excitation in phase along a straight line and spherical waves from excitation in one point in space.

The one at a fixed point in time

The distance between two wave surfaces of the same phase measured in the direction of propagation is referred to as *Wavelength*

. Theirs serve as further characteristic variables for describing a wave *frequency*

as well as the *Oscillation period*

. The frequency is defined as the number of wave surfaces that wander past a fixed point in space per unit of time. The phase velocity (which corresponds to the propagation velocity & # 252 and must be strictly distinguished from the group velocity) is given by

. A quantity that is often used, especially in spectroscopy, is the *Wavenumber*

. Unfortunately, the definition of the wave number is not uniform, especially in the theoretical investigation of wave processes one often finds

. The wave number l & # 228 & # 223t together with the direction of propagation to the *Wave vector* (even *Wavenumber vector*)

summarize, where

is the unit vector in the direction of the wave normal. Strictly speaking it is

only defined for plane waves. The propagation of waves is described mathematically by a wave equation.

By superimposing two plane waves of the same amplitude and frequency, but in opposite directions of propagation, this results *standing waves*. In contrast to the advancing waves, their vibration bands and nodes maintain their position in space. This means that the nodes of vibration are at rest while the vibrations are through

can be described and thus experience maximum change. Standing waves can be created very easily by the undamped reflection of a wave on a denser medium. In this case there is a phase difference of

, i.e. there is a knot at the point of reflection. A standing wave is also obtained when reflecting on a thinner medium, only because in this case there is an antinode at the point of reflection. An example of standing waves are rope waves. They arise on a rope that is excited at one end. The other end is either fixed (in this case a vibration node is formed) or loose (you get a vibration antinode).

**Wave 1:** a) transverse wave and b) longitudinal wave during the propagation of vibrations on a pendulum chain (snapshots).

**Wave 2:** Wavelength *λ* and period of oscillation *T* with a harmonic wave. The speed of propagation is

.

**Wave 3:** Standing wave with vibrations (B) and nodes (K).

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### Articles on the topic

Load.## Experimental investigation of electromagnetic oscillations using the example of a detector radio

The thesis examines electromagnetic vibrations using the example of a detector radio by explaining the theory and trying to receive medium-wave radio with the help of a self-made detector radio.

The work is for a physics LK and was rated "very good".

1 Introduction

2. Electromagnetic oscillating circuit

2.1 General structure and function of an electromagnetic resonant circuit

2.2 Response

2.3 From the resonant circuit to the dipole

3. Electromagnetic wave

3.1 Radiation of electromagnetic waves

3.2 Chronological sequence of the formation of electromagnetic waves at the Hertzian dipole

3.3 Propagation of electromagnetic waves

4. Transfer of information

5. Detector radio

5.1 General structure and function

5.2 Components used

5.3 Carrying out the experiment

5.4 Consideration of errors

6. Reflection

7. Bibliography

7.1 Sources of literature

7.2 Internet sources

8. Declaration

9. Appendix

## On the theory of the birefringence of electromagnetic waves in an ionized gas under the influence of a constant magnetic field (ionosphere)

1. The complex refractive index and the waveform of electromagnetic waves in a homogeneous ionized gas in a constant magnetic field are easily calculated. A relationship is established between the earlier calculations by K. Försterling and the author and the formulas by Appleton, Goldstein and Hartree. 2. Within the ionized gas, the electric field strength and the electrons oscillate with an elliptical waveform in planes that are rotated out of the wave planes perpendicular to the direction of propagation (longitudinal component). The rotation takes place around an axis which is perpendicular to the plane determined by the direction of propagation and the constant magnetic field, and is greater for the electron path than for the electric field strength. The longitudinal component of the electric field strength is proportional to the longitudinal displacement of the electrons. It disappears when it propagates in the direction of the constant magnetic field and when the wave emerges from the ionized gas.

## Investigations into the propagation of electromagnetic waves in the THz frequency range

The increasing demand for free and unregulated bandwidth means that future communication systems will also be operated at very high frequencies of 300 GHz and above. Within the framework of the Terahertz Communication Lab, a cooperation with the TU Braunschweig, the working group 2.21 develops the basics of THz communication. The design of such communication systems requires, among other things, precise knowledge of the transmission channel. In the working group 2.21, the wave propagation in interior spaces is investigated with regard to attenuation, reflection, diffraction and scattering. In addition, measurements of digital signal parameters are carried out during transmission attempts in the THz frequency range.

Fig .: Experimental setup for indoor dispersion measurements.

## Successful research on wave propagation

"The decision of the DFG shows that interdisciplinary mathematical research at KIT is excellently positioned," says Professor Oliver Kraft, KIT Vice President for Research. "I congratulate the participating scientists on this recognition of their research achievements and look forward to the coming results of their work."

Both the SFB 1173 “Wave Phenomena” and the SFB / Transregio 165 “Waves to Weather” are included in the work of the KIT Center MathSEE (Mathematics in Sciences, Engineering, and Economics), which brings together theoretical-mathematical and application-oriented research.

An SFB is a research program designed to last up to twelve years (usually three times four years) in which scientists work on challenging topics across the boundaries of disciplines, institutes and faculties.

An SFB / Transregio is a supra-regional SFB supported by several universities. Both types of program contribute to the development of a scientific profile and to the promotion of young researchers.

The SFB 1173 "Wave Phenomena: Analysis and Numerics" will receive funding of over ten million euros for the next four years. More than 80 KIT researchers are involved in the Collaborative Research Center. There are also other groups at the Universities of Stuttgart and Tübingen and at the Technical University of Vienna.

The scientists from mathematics as well as physics and electrical engineering conduct interdisciplinary research on the fundamental properties of acoustic, electromagnetic and elastic waves. The basic mathematical research is supplemented by application-related studies in the fields of optics and photonics, biomedical engineering and geophysics.

Waves are omnipresent in nature, for example in the form of electromagnetic waves, which are essential for modern communication, or in the form of acoustic waves, which are used for seismic measurements of the nature of the ground. "The propagation of waves can be described extremely elegantly with mathematical methods and raises many fascinating and so far unsolved questions," says the spokeswoman for the SFB 1173, Professor Marlis Hochbruck.

"Answering these pressing questions is the aim of our Collaborative Research Center and is of great importance for scientific and technical progress, both in basic research and in applications."

In addition to gaining scientific knowledge, the contribution of the CRC “Wave Phenomena” also includes promoting young scientists. Young researchers who write their doctoral theses within the Collaborative Research Center benefit from the interdisciplinary environment, the cooperation with renowned scientists and the exchange with internationally outstanding guests. With the continuation of the funding, the DFG honors the success of the SFB to date and proves the international visibility of KIT in the field of research into wave phenomena.

In the SFB / Transregio 165 “Waves to Weather” (W2W) scientists from KIT, the Ludwig Maximilians University (LMU) Munich work as coordinators, the University of Mainz, the Technical University (TUM) Munich and the German Center for Air work - and space travel (DLR) in Munich and the University of Heidelberg together to enable a new generation of weather forecasts. W2W is focused on identifying the limits of predictability, especially of undulating air movements, in different situations and creating the best possible physical prognosis.

Further press contact: Kosta Schinarakis, editor / press officer, phone: +49 721 608-21165, fax: +49 721 608-43658, email: [email protected]

As “The Research University in the Helmholtz Association”, KIT creates and imparts knowledge for society and the environment. The aim is to make significant contributions to global challenges in the fields of energy, mobility and information. To this end, around 9,300 employees work together on a broad disciplinary basis in the natural, engineering, economics, humanities and social sciences. The KIT prepares its 25,100 students for responsible tasks in society, business and science through a research-oriented university course. The innovation activity at KIT bridges the gap between knowledge and application for social benefit, economic prosperity and the preservation of our natural foundations of life.

## Electromagnetic waves

All charge carriers that are accelerated or decelerated emit electromagnetic fields that spread through space. The strengths of the electric and magnetic fields change periodically both spatially and temporally and therefore have the properties of waves. They are called electromagnetic waves.

#### Magnets

#Magnet #Permanent magnet #Elementary magnet #Magnetic field

#### Properties of waves

#Sine #cosine #frequency #wavelength #period

All charge carriers that are accelerated or decelerated emit electromagnetic fields that spread through space. The strengths of the electric and magnetic fields change periodically both spatially and temporally and therefore have the properties of waves. They are called electromagnetic waves (Fig. 1).

## On the theory of the birefringence of electromagnetic waves in an ionized gas under the influence of a constant magnetic field (ionosphere)

1. The complex refractive index and the waveform of electromagnetic waves in a homogeneous ionized gas in a constant magnetic field are easily calculated. A relationship is established between the earlier calculations by K. Försterling and the author and the formulas by Appleton, Goldstein and Hartree. 2. Within the ionized gas, the electric field strength and the electrons oscillate with an elliptical waveform in planes that are rotated out of the wave planes perpendicular to the direction of propagation (longitudinal component). The rotation takes place around an axis which is perpendicular to the plane determined by the direction of propagation and the constant magnetic field, and is greater for the electron path than for the electric field strength. The longitudinal component of the electric field strength is proportional to the longitudinal displacement of the electrons. It disappears when it propagates in the direction of the constant magnetic field and when the wave emerges from the ionized gas.