# Wave model for electromagnetic radiation

Around 1860 Maxwell developed four equations that basically synthesize the behavior of electrical and magnetic phenomena. Maxwell

Maxwell's equations suggest that the electric field and the magnetic field propagate concurrently. Thus, this set of equations allows us to make some inferences, among them:

• a time-varying electric field induces the appearance of a magnetic field;
• A time-varying magnetic field induces the appearance of an electric field.

Therefore, if an electric field and a magnetic field are generated, both variables in time, one will be able to support the existence of the other, so that both coexistence and propagation will be perfectly possible. When propagating, these two fields constitute the electromagnetic radiationlike radio waves, visible light, microwaves, x-rays, etc.

Because of their undulatory behavior, electromagnetic radiation is also calledelectromagnetic waves (OEM). Heinrich Hertz experimentally proved in 1887 the existence of OEMs by generating and detecting radio waves in his laboratory. Heinrich Hertz

According to Maxwell's theory for electromagnetism, OEMs are produced by fast-moving electric charges. An example of the application of this principle is radio transmitting antennas, which generate their waves from oscillating electrons. When performing a frequency movef, an electron (or an electrically charged particle) emits an OEM whose frequency is alsof.

In the figure below, we can see a simplified representation of how an electromagnetic pulse propagates - a flat OEM. In addition to being time-varying, the electric and magnetic fields are perpendicular to each other and to the direction of propagation.

An OEM does not need a material medium to propagate (such as mechanical waves, for example). Therefore, there is a possibility that it propagates in a vacuum. The propagation velocity of electromagnetic waves in a vacuum was calculated by Maxwell even before he knew light was an OEM. The mathematical expression that gives us the value of this velocity,ç, is given by: Where:

ε0= 8.85x10-12 F / m (vacuum electrical permittivity);

μ0= 4πx10-7 T.m / A (magnetic vacuum permeability);

c = 2.99792x108 m / s (speed of light).

The above results apply to both vacuum and air, and coincide with the experimentally obtained light velocity in air. Based on this, Maxwell concluded that visible light was also an OEM.

Importantly, OEMs do not interact with the electrical and magnetic fields they pass through. In this way, the light does not deviate when passing near an electrified body or a magnetic pole. 