# What is the speed of the electromagnetic field

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### Qualitative considerations on the propagation of electromagnetic waves

Up to now we have dealt almost exclusively with the generation of electromagnetic waves in the form of the Hertzian dipole, now we focus in particular on the propagation or propagation of these waves. The electromagnetic waves emitted by the dipole travel at the speed of light. At a sufficiently distant point, which is then referred to as the far field, the waves pass this point with negligible curvature as a plane wave. 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 each other, but each of them can nevertheless form its own wave in the sense of an electrical or a magnetic component. In the far field, these two waves are in the same phase and vibrate at the same frequency. The electric and magnetic waves, i.e. the electric field and the magnetic field, are perpendicular to each other and at the same time always perpendicular to the direction of propagation. The electromagnetic wave is therefore necessarily a transverse wave. Electric field, magnetic field and the speed of propagation form a three-dimensional, right-angled coordinate system, pointing in -direction, in -direction, and in -direction (right-handed 3-finger rule: = extended thumb up, = index finger to the left, = extended remaining Finger forward, coordinate systems).

Since both fields of the electromagnetic wave are sinusoidal, we can now formulate the following sine functions of place and time:

with the amplitudes and, the angular frequency and the circular wave number. The following applies to the propagation speed of the wave.

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 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, an arrow is drawn for the strength of the electric field in the direction of the -axis and an arrow for the strength of the magnetic field in the direction of the -axis. 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.

A certain point on the axis in the direction of the speed of propagation results in a flat surface in the plane with the vectors of the electric and magnetic fields. The cross product is perpendicular to this plane in the direction of the propagation speed of the wave. If the electromagnetic wave now passes such a point, you can infinitesimally mark a small slice of thickness with the vectors and in the plane, which is constantly changing in phase.

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

This process takes place continuously; in this regard, one speaks of Faraday's and Maxwell's law of induction. 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 propagation depends on the substance, but is always lower than the speed of propagation in a vacuum and approximately in air. The so-called speed of light is independent of the reference system, as Einstein's special theory of relativity has shown.