Electromagnetic waves
A charge at rest does not radiate, and neither does one moving at constant velocity. An accelerated charge does, and an alternating current in a conductor is exactly that: all of antenna engineering comes from there.
01What an electromagnetic wave looks like
From Maxwell’s equations in vacuum comes a wave with a very rigid structure: the two fields are perpendicular to each other and both perpendicular to the direction of propagation. It is transverse, needs no medium and its two fields oscillate in phase.
That \( E = cB \) explains why people almost always talk about the electric field and almost never about the magnetic one: in SI units the number for \( B \) is three hundred million times smaller, and on a charge the electric force dominates completely except at relativistic speeds.
An electromagnetic wave also carries momentum, so when it strikes a surface it exerts radiation pressure: \( P = I/c \) if it is absorbed and double that if it is reflected. With sunlight in Earth orbit —1361 W/m²— that is about 4.5 micropascals, nothing for a person and enough to move a solar sail of square kilometers, or to slowly shift the orbit of a satellite if it is not compensated.
02What radiates and what does not
A stationary charge has a field but does not radiate. One moving at constant velocity does not either. An accelerated charge radiates, and from that comes all of antenna engineering: an alternating current in a conductor is charge accelerating back and forth.
| Zone | Distance | How the field falls off | What happens |
|---|---|---|---|
| Reactive near field | Less than \( \lambda/2\pi \) | As \( 1/r^3 \) | The energy goes back and forth: nothing is radiated |
| Far field | More than \( 2D^2/\lambda \) | As \( 1/r \) | The energy leaves and never comes back |
The first row is the one that explains why a 50 Hz installation does not radiate: with a wavelength of 6000 km, everything one could possibly wire is in the near field, and there the energy oscillates between the conductor and space without escaping. It is also the principle of wireless charging and of a transformer: near-field coupling, not radiation.
A transmitter, two antennas and a distance. The free-space loss, the field at the receiver and how much margin is left over its sensitivity are calculated. Try changing the frequency without touching anything else.
03Energy and photons
The wave description is enough for almost everything in this unit, but when the frequency rises a lot the other side appears: energy travels in packets.
| Material | \( E_g \) | LED \( \lambda \) | Color |
|---|---|---|---|
| GaAs | 1.42 eV | 873 nm | Infrared: remote controls |
| GaAsP | 1.9 eV | 653 nm | Red |
| GaP | 2.2 eV | 564 nm | Green |
| InGaN | 2.7 eV | 459 nm | Blue |
The table is the unit on chemical bonds seen from the viewpoint of optics: the color of an LED is its band gap. And silicon, at 1.12 eV, emits at 1107 nm, in the infrared, but it also has an indirect band gap and so is a terrible emitter: other compounds are used to make light. As a detector, on the other hand, it works very well up to those 1100 nm, and that is the reason a silicon photodiode sees nothing beyond.
04In the lab
With a low-power transmitter and a field-strength meter, record the received signal at increasing distances in an open space. Plot in dB against the logarithm of the distance and verify the slope of 20 dB per decade.
Compare the signal received with a whip antenna and with a pointed directional one, at the same distance. Calculate the difference in dB and compare it with the stated gain.
With a simple spectrometer, measure the emission wavelength of LEDs of different colors. Calculate the photon energy and compare it with the tabulated band gap of the semiconductor of each one.
05Common mistakes
- Believing that the magnetic field of a wave is negligible. It is not: it is \( E/c \), small in number and essential to the phenomenon.
- Thinking that free-space loss is absorption. It is geometry: the same power spread over a larger sphere.
- Assuming that an antenna amplifies. Gain is directivity: it concentrates what there is, it does not add power.
- Measuring a radiated field in the near field. There \( 1/r \) does not hold and the measurement does not mean what it seems to.
- Forgetting that the Friis equation gets worse with frequency. At equal gain, 5 GHz reaches less far than 2.4.
- Confusing transmitter power with EIRP. The latter already includes the gain of the antenna.
06Self-assessment
What is the relation between \( E \) and \( B \) in a wave?
\( E = cB \), and the two oscillate in phase, perpendicular to each other and to the propagation.
What radiates and what does not?
An accelerated charge radiates. A stationary one, or one at constant velocity, does not.
What is the impedance of vacuum?
377 ohms. It relates the electric field to the magnetic one in a plane wave.
Why does a 50 Hz installation not radiate?
Because with a wavelength of 6000 km everything is in the near field, where the energy goes back and forth without escaping.
What energy does a 620 nm photon have?
Two electronvolts: \( 1240/620 \).
Why does a silicon photodiode not see beyond 1100 nm?
Because there the photon no longer has the energy of its 1.12 eV band gap and does not generate an electron-hole pair.
07Further reading
- Raymond A. Serway and John W. Jewett. Physics for Scientists and Engineers with Modern Physics. 10th ed. (Spanish edition, “Física para ciencias e ingeniería”), Cengage, 2019. Electromagnetic waves, the Poynting vector, radiation pressure and the spectrum.
- John D. Kraus and Ronald J. Marhefka. Antennas. 3rd ed., McGraw-Hill, 2001. From the accelerated charge to the real antenna, with field zones, gain and radiation patterns.
- Eugene Hecht. Optics. 5th ed. (Spanish edition, “Óptica”), Pearson, 2017. The treatment of the electromagnetic wave from the viewpoint of optics, which is the continuation of the last three units.