ELECTROMAGNETIC WAVES: MAXWELL'S THEORY, TYPES, CHARACTERISTICS - PHYSICAL - 2024

The electromagnetic waves are transverse waves that correspond to fields caused by accelerated electric charges. The 19th century was the century of great advances in electricity and magnetism, but until the first half of it, scientists were still unaware of the relationship between the two phenomena, believing them independent of each other.

It was the Scottish physicist James Clerk Maxwell (1831-1879) who proved to the world that electricity and magnetism were but two sides of the same coin. Both phenomena are closely related.

A thunderstorm. Source: Pixabay.

Maxwell theory

Maxwell unified the theory of electricity and magnetism in 4 elegant and concise equations, the predictions of which were soon confirmed:

What evidence did Maxwell have to develop his electromagnetic theory?

It was already a fact that electric currents (moving charges) produce magnetic fields, and in turn a variable magnetic field originates electric currents in conductive circuits, which would imply that a variable magnetic field induces an electric field.

Could the reverse phenomenon be possible? Would variable electric fields be capable of generating magnetic fields in turn?

Maxwell, a disciple of Michael Faraday, was convinced of the existence of symmetries in nature. Both electrical and magnetic phenomena also had to adhere to these principles.

According to this researcher, oscillating fields would generate disturbances in the same way that a stone thrown into a pond generates waves. These disturbances are nothing more than oscillating electric and magnetic fields, which Maxwell precisely called electromagnetic waves.

Maxwell predictions

Maxwell's equations predicted the existence of electromagnetic waves with propagation speed equal to the speed of light. The prediction was confirmed shortly after by the German physicist Heinrich Hertz (1857 - 1894), who managed to generate these waves in his laboratory using an LC circuit. This occurred shortly after Maxwell's death.

To verify the correctness of the theory, Hertz had to build a detector device that allowed him to find the wavelength and frequency, data from which he could calculate the speed of electromagnetic radio waves, coinciding with the speed of light..

Maxwell's work had been received with skepticism by the scientific community at the time. Perhaps it was partly because Maxwell was a brilliant mathematician and had presented his theory with all the formality of the case, which many failed to understand.

However, Hertz's experiment was brilliant and compelling. Their results were well received and doubts about the veracity of Maxwell's predictions were cleared.

Displacement current

The current of displacement is the creation of Maxwell, arising from a deep analysis of Ampere's law, which states that:

A battery charges a capacitor. The surfaces S (solid line) and S 'and the contour C are shown to apply Ampere's law. Source: modified from Pixabay.

Therefore, the term to the right in Ampere's law, involving the current, is not null and neither is the member to the left. Immediate conclusion: there is a magnetic field.

Is there a magnetic field at S '?

However, there is no current that crosses or crosses the curved surface S ', which has the same contour C, since this surface encompasses part of what is in the space between the plates of the condenser, which we can assume is air or another substance non-conductive.

In that region there is no conductive material through which any current flows. It should be remembered that for a current to flow, the circuit must be closed. Since the current is zero, the integral on the left in Ampere's law is 0. There is no magnetic field then, is there?

There is definitely a contradiction. S 'is also limited by curve C and the existence of the magnetic field must not depend on the surface to which C limits.

Maxwell resolved the contradiction by introducing the concept of displacement current i _D.

Displacement current

While the capacitor is charging, a variable electric field exists between the plates and current flows through the conductor. When the capacitor charges, the current in the conductor ceases and a constant electric field is established between the plates.

Then Maxwell deduced that, associated with the variable electric field, there must be a current that he called a displacement current i _D, a current that does not involve movement of charge. For the surface S 'it is valid:

Electric current is not a vector, although it has magnitude and meaning. It is more appropriate to relate the fields to a quantity that is vector: the current density J, whose magnitude is the quotient between the current and the area through which it passes. The units of current density in the International System are amperes / m ².

In terms of this vector, the displacement current density is:

In this way, when Ampere's law is applied to the contour C and the surface S is used, i _C is the current through it. On the other hand, i _C does not pass through S ', but i _D does.

Exercise resolved

Speed ​​in a given medium

In a given medium, it is possible to show that the speed of electromagnetic waves is given by the expression:

In which ε and μ are the respective permittivity and permeability of the medium in question.

Amount of movement

An electromagnetic radiation with energy U has an associated momentum p whose magnitude is: p = U / c.

Types of electromagnetic waves

Electromagnetic waves have a very wide range of wavelengths and frequencies. They are grouped in what is known as the electromagnetic spectrum, which has been divided into regions, which are named below, starting with the longest wavelengths:

Radio waves

Located at the highest wavelength and lowest frequency end, they range from a few to a billion Hertz. They are those that are used to transmit a signal with information of various kinds and are captured by the antennas. Television, radio, mobiles, planets, stars and other celestial bodies broadcast them and they can be captured.

Microwave oven

Located in the ultra-high (UHF), super-high (SHF) and extremely high (EHF) frequencies, they range between 1 GHz and 300 GHz. Unlike the previous ones that can measure up to a mile (1.6 km), microwaves They range from a few centimeters to 33 cm.

Given their position in the spectrum, between 100,000 and 400,000 nm, they are used to transmit data on frequencies that are not interfered with by radio waves. For this reason, they are applied in radar technology, cell phones, kitchen ovens, and computer solutions.

Its oscillation is the product of a device known as a magnetron, which is a kind of resonant cavity that has 2 disk magnets at the ends. The electromagnetic field is generated by the acceleration of the electrons from the cathode.

Infrared rays

These heat waves are emitted by thermal bodies, some types of lasers, and light-emitting diodes. Although they tend to overlap with radio waves and microwaves, their range is between 0.7 and 100 micrometers.

The entities most often produce heat that can be detected by night goggles and the skin. They are often used for remote controls and special communication systems.

Visible light

In the referential division of the spectrum we find perceptible light, which has a wavelength between 0.4 and 0.8 micrometers. What we distinguish are the colors of the rainbow, where the lowest frequency is characterized by red and the highest by violet.

Its length values ​​are measured in nanometers and Angstrom, it represents a very small part of the entire spectrum and this range includes the largest amount of radiation emitted by the sun and stars. In addition, it is the product of the acceleration of electrons in energy transits.

Our perception of things is based on visible radiation that falls on an object and then on the eyes. The brain then interprets the frequencies that give rise to the color and details present in things.

Ultraviolet rays

These ripples are in the range of 4 and 400 nm, they are generated by the sun and other processes that emit large amounts of heat. Long-term exposure to these short waves can cause burns and certain types of cancer in living things.

Since they are the product of jumps of electrons in excited molecules and atoms, their energy is involved in chemical reactions and they are used in medicine to sterilize. They are responsible for the ionosphere since the ozone layer prevents its damaging effects on the earth.

X-rays

This designation is due to the fact that they are invisible electromagnetic waves capable of passing through opaque bodies and producing photographic prints. Located between 10 and 0.01 nm (30 to 30,000 PHz), they are the result of electrons jumping from orbits in heavy atoms.

These rays can be emitted by the sun's corona, pulsars, supernovae, and black holes due to their large amount of energy. Their prolonged exposure causes cancer and they are used in the medical field to obtain images of bone structures.

Gamma rays

Located at the extreme left of the spectrum, they are the waves that have the highest frequency and usually occur in black holes, supernovae, pulsars and neutron stars. They can also be the result of fission, nuclear explosions and lightning.

Since they are generated by stabilization processes in the atomic nucleus after radioactive emissions, they are lethal. Their wavelength is subatomic, allowing them to pass through atoms. They are still absorbed by the Earth's atmosphere.

Applications of the different electromagnetic waves

Electromagnetic waves have the same reflection and reflection properties as mechanical waves. And along with the energy they propagate, they can also carry information.

Because of this, different types of electromagnetic waves have been applied to a large number of different tasks. Here we will see some of the most common.

Electromagnetic spectrum and some of its applications. Source: Tatoute and Phrood

Radio waves

Shortly after being discovered, Guglielmo Marconi proved that they could be an excellent communication tool. Since their discovery by Hertz, wireless communications with radio frequencies such as AM and FM radio, television, cell phones, and much more, have become increasingly widespread throughout the world.

Microwave oven

They can be used to heat food, because water is a dipole molecule that is capable of responding to oscillating electric fields. Food contains water molecules, which when exposed to these fields, begin to oscillate and collide with each other. The resulting effect is warming.

They can also be used in telecommunications, due to their ability to travel in the atmosphere with less interference than other waves of greater wavelength.

Infrared waves

The most characteristic application of infrared is night vision devices. They are also used in communication between devices and in spectroscopic techniques for the study of stars, interstellar gas clouds, and exoplanets.

They can also create body temperature maps, which are used to identify some types of tumors whose temperature is higher than that of the surrounding tissues.

Visible light

Visible light makes up a large part of the spectrum emitted by the Sun, to which the retina responds.

Ultraviolet rays

Ultraviolet rays have enough energy to interact with matter significantly, so continuous exposure to this radiation causes premature aging and increases the risk of developing skin cancer.

X-rays and gamma rays

X-rays and gamma rays have even more energy and are therefore capable of penetrating soft tissues, hence, almost from the moment of their discovery, they have been used to diagnose fractures and examine the interior of the body in search of diseases..

X-rays and gamma rays are used not only as a diagnostic tool, but as a therapeutic tool for the destruction of tumors.

References

1. Giancoli, D. (2006). Physics: Principles with Applications. Sixth Edition. Prentice Hall. 628-637.
2. Rex, A. (2011). Fundamentals of Physics. Pearson. 503-512.
3. Sears, F. (2015). University Physics with Modern Physics. 14th Edition. Pearson. 1053-1057.