Chapter 13: Electromagnetic Waves and Communication System
In December 1901, on a windy hill in Newfoundland, Canada, Guglielmo Marconi sat with a telephone-like receiver pressed to his ear and a kite holding a long wire up into the sky. More than three thousand kilometres away, across the Atlantic Ocean, a transmitting station in Cornwall, England, was sending the same short signal again and again — three dots, the Morse code letter “S”. Marconi reported that he heard it.
Most scientists of the time believed this was impossible. Radio waves, they argued, travel in straight lines. The Earth is a sphere, and a straight line leaving England would sail off above the ocean and shoot into space long before it reached Canada. The bulge of the Earth stood in the way like a wall.
Marconi had no complete theory to explain his result. The explanation came later: high above our heads, at heights of tens to hundreds of kilometres, the atmosphere contains a layer of electrically charged particles. Radio waves of the right frequency strike this layer and are bent back towards the ground, like a ball rebounding from a ceiling. The Atlantic had not been crossed by a straight line at all — the signal had bounced.
That single faint sound in an earphone is the ancestor of every mobile call, television broadcast and satellite link you use today.
Diagram
Fig. 13.1 – Marconi at Signal Hill with a kite-supported aerial, and a radio wave from England curving back to Newfoundland after reflection from the upper atmosphere.
By the end of this chapter, you will be able to answer each of these questions yourself.
13.1 Introduction
Why This Chapter Matters
The age we live in is called the information age, and it rests almost entirely on the physics of electromagnetic waves — usually shortened to EM waves. Television, cellphones and the internet have connected the whole world, and every one of these gadgets uses EM waves as the carrier that transports signals from one place to another.
A “carrier” here simply means a wave that is sent out from one point and picked up at another, with the information ridden on top of it. Whether you are watching a live match on television or receiving a message on your phone, an EM wave has physically crossed the distance between the transmitter and you.
EM Waves Around Us and Beyond
EM waves are not a human invention. Energy from the Sun, without which life on Earth would not be possible, reaches us as EM waves. This energy travels across nearly 150 million km of empty space to get here — space that contains no air, no water, no solid material of any kind, as shown in Fig. 13.2. That fact alone tells us something remarkable about these waves: unlike sound, they do not need a material medium to travel through.
Diagram
Fig. 13.2 – Sunlight travelling across ~150 million km of empty space from the Sun to the Earth, with a small inset comparing sound (needs a medium) and EM waves (do not).
Once you start looking, EM waves turn up everywhere. An ordinary light bulb gives out EM waves. So does the heated engine block of an automobile, an X-ray machine in a hospital, a flash of lightning during a storm, and certain radioactive materials. Stars, other objects in our Milky Way galaxy, and even distant galaxies are all known to emit EM waves.
13.2 EM Wave
The Four Laws Behind Every EM Wave
Everything an EM wave does follows from four basic laws. Together these laws describe how electric and magnetic fields behave, how each is related to the other, and how charges and currents generate them. You have already met all four in earlier chapters; here they are collected in one place, because it is their combination that gives birth to the EM wave.
(1) Gauss’ law for electrostatics. This law is essentially Coulomb’s law written in a different form. It describes the relationship between static electric charges and the electric field they produce. In words, it tells us that a charge at rest sets up an electric field around itself, and fixes exactly how strong that field is.
(2) Gauss’ law for magnetism. This is similar in form to Gauss’ law for electrostatics, but its content is very different. It states that “magnetic monopoles, which are thought to be magnetic charges equivalent to the electric charges, do not exist.” An isolated north pole or an isolated south pole has never been found. Magnetic poles always occur in pairs — cut a bar magnet in half and you get two smaller magnets, each with both poles, not one north piece and one south piece.
(3) Faraday’s law. This law gives the relation between the electromotive force (emf) induced in a circuit and the change in the magnetic flux linked with that circuit. The essential point for us is that a changing magnetic field produces an emf, and therefore an electric field. Note the word “changing” — a steady magnetic field induces nothing.
(4) Ampere’s law. This law gives the relation between the induced magnetic field associated with a loop and the current flowing through that loop. In its original form it says: wherever there is a current, there is a magnetic field encircling it.
Maxwell’s Correction: The Displacement Current
James Clerk Maxwell (1831–1879) noticed a major flaw in Ampere’s law when it was applied to time-dependent fields — that is, to situations where the fields change with time. He realised that a magnetic field can be generated not only by an electric current, but also by a changing electric field.
Therefore, in the year 1861, he added one more term to the equation describing Ampere’s law. This extra term is called the displacement current. It is not a current of moving charges at all; it is the effect of a changing electric field, which produces a magnetic field just as a real current would.
This term is extremely important. The EM waves that come out of these equations would not have been possible in the absence of this term. Without it, a changing electric field would produce nothing, the chain would break, and the wave could never build itself.
As a result of Maxwell’s correction, the set of four equations describing the above four laws is complete. This set is called Maxwell’s equations.
From Equations to Experiment
Maxwell’s equations predicted EM waves on paper. It took more than two decades for someone to make them and catch them in a laboratory.
Diagram
Fig. 13.3 – Timeline strip: Maxwell’s equations (1861–65) → Hertz produces and detects EM waves (1888) → J. C. Bose (1895) → Marconi’s wireless communication (1896).
In exam questions, this section is usually tested in words rather than numbers: you may be asked which law was modified by Maxwell, what the added term is called, why it was needed, or to state any one of the four laws with its conditions. Learn the conditions attached to each law — “over a closed surface,” “over a closed loop” — because dropping them makes the statement wrong.
13.2.1 Sources of EM Waves
According to Maxwell’s theory, “accelerated charges radiate EM waves.” This single sentence is the answer to the question of where every EM wave in the universe comes from. To see why it is true, follow what happens step by step.
Consider a charge oscillating with some frequency — moving back and forth, so that its velocity is constantly changing, which means it is accelerating. A charge always carries an electric field around it. If the charge oscillates, the electric field in the space around it also oscillates.
Now Maxwell’s correction enters. This oscillating electric field produces an oscillating magnetic field. That oscillating magnetic field, by Faraday’s law, is in turn a source of an oscillating electric field. Thus the varying electric and magnetic fields regenerate each other, handing energy back and forth, and the disturbance moves outward into space without needing any wire or medium to travel along.
What an EM Wave Is
Waves that are caused by the acceleration of charged particles, and that consist of electric and magnetic fields vibrating sinusoidally at right angles to each other and to the direction of propagation, are called EM waves or EM radiation.
Figure 13.4 shows an EM wave propagating along the \(z\)-axis. Notice how the two fields sit in mutually perpendicular planes: the time-varying electric field is along the \(x\)-axis, and the time-varying magnetic field is along the \(y\)-axis, while the wave itself moves along \(z\).
Diagram
Fig. 13.4 – EM wave propagating along the z-axis, with the electric field \(\vec{E}_x\) oscillating in the x-direction and the magnetic field \(\vec{B}_y\) oscillating in the y-direction.
Read that figure carefully, because two examiner-favourite facts are hidden in it: the three directions \(\vec{E}\), \(\vec{B}\) and the direction of travel are mutually perpendicular, and the two fields rise and fall together rather than one lagging behind the other.
13.2.2 Characteristics of EM Waves
Now that we know how an EM wave is born, we can list what it is like. The twelve properties below are the working rules of this chapter — almost every question on EM waves is answered by one of them.
Direction, Shape and Phase
1) The electric and magnetic fields, \(\vec{E}\) and \(\vec{B}\), are always perpendicular to each other and also to the direction of propagation of the EM wave. Because the vibrations are at right angles to the direction of travel, EM waves are transverse waves. (In a longitudinal wave, such as sound, the vibration is along the direction of travel — that is the contrast to keep in mind.)
2) The cross product \(\vec{E} \times \vec{B}\) gives the direction in which the EM wave travels. \(\vec{E} \times \vec{B}\) also gives the energy carried by the EM wave.
This is the property you will use again and again in numericals. If you know two of the three directions, the third follows from the right-hand rule for the cross product.
3) The \(\vec{E}\) and \(\vec{B}\) fields vary sinusoidally and are in phase. In phase means they reach their maximum at the same moment and pass through zero at the same moment, as seen in Fig. 13.5. Neither field lags behind the other.
Diagram
Fig. 13.5 – Graph of \(E\) and \(B\) against position for the same EM wave, showing both curves peaking and crossing zero at the same points (in phase).
4) EM waves are produced by accelerated electric charges.
How EM Waves Travel
5) EM waves can travel through free space as well as through solids, liquids and gases. This is unlike sound, which cannot travel through free space at all.
6) In free space, EM waves travel with velocity \(c\), equal to that of light in free space.
\[c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} = 3 \times 10^{8}\ \text{m/s}\]
where \(\mu_0\) (\(4\pi \times 10^{-7}\) T·m/A) is the permeability of free space and \(\varepsilon_0\) (\(8.85 \times 10^{-12}\) C²/Nm²) is the permittivity of free space.
Look closely at what this equation is saying. The speed of light is not an independent fact about light — it is fixed entirely by two electrical and magnetic constants of empty space. This was Maxwell’s most striking result: the number that came out of his equations matched the measured speed of light, which is how physicists realised that light itself is an EM wave.
7) In a given material medium, the velocity (\(v_m\)) of EM waves is given by
\[v_m = \frac{1}{\sqrt{\mu \varepsilon}}\]
where \(\mu\) is the permeability and \(\varepsilon\) is the permittivity of the given medium. Since \(\mu\) and \(\varepsilon\) of any material are larger than \(\mu_0\) and \(\varepsilon_0\), an EM wave always travels slower in a medium than in free space.
Amplitudes, Intensity and Energy
9) The ratio of the amplitudes of the electric and magnetic fields is constant at any point and is equal to the velocity of the EM wave.
\[|\vec{E_0}| = c\,|\vec{B_0}| \quad \text{or} \quad \frac{|\vec{E_0}|}{|\vec{B_0}|} = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} \qquad --- (13.1)\]
Here \(|\vec{E_0}|\) and \(|\vec{B_0}|\) are the amplitudes of \(\vec{E}\) (in V/m) and \(\vec{B}\) (in tesla) respectively.
Because \(c\) is a very large number, \(E_0\) comes out enormously larger than \(B_0\) in numerical value. That does not mean the magnetic part is unimportant — it means only that the two are measured in different units, and Eq. (13.1) is the bridge between them.
10) As the electric field vector (\(\vec{E_0}\)) is more prominent than the magnetic field vector (\(\vec{B_0}\)), it is responsible for the optical effects due to EM waves. For this reason, the electric vector is called the light vector.
11) The intensity of a wave is proportional to the square of its amplitude and is given by the equations
\[I_E = \frac{1}{2}\varepsilon_0 E_0^{2}, \qquad I_B = \frac{1}{2}\frac{B_0^{2}}{\mu_0} \qquad --- (13.2)\]
Here \(I_E\) is the intensity associated with the electric field and \(I_B\) that associated with the magnetic field. Intensity means the energy carried per unit area per unit time, and its SI unit is W/m².
12) The energy of EM waves is distributed equally between the electric and magnetic fields:
\[I_E = I_B\]
Writing the Wave as an Equation
In an EM wave, the magnetic field and the electric field both vary sinusoidally with \(x\). For a wave travelling along the \(x\)-axis having \(\vec{E}\) along the \(y\)-axis and \(\vec{B}\) along the \(z\)-axis, with reference to Chapter 8 we can write \(E_y\) and \(B_z\) as
\[E_y = E_0 \sin(kx - \omega t) \qquad --- (13.2)\]
\[\text{and} \qquad B_z = B_0 \sin(kx - \omega t) \qquad --- (13.3)\]
where \(E_0\) is the amplitude of the electric field \(E_y\) (in V/m) and \(B_0\) is the amplitude of the magnetic field \(B_z\) (in tesla). \(k = \dfrac{2\pi}{\lambda}\) is the propagation constant (SI unit: rad/m) and \(\lambda\) is the wavelength of the wave (in metre). \(\omega = 2\pi \upsilon\) is the angular frequency of oscillations (in rad/s), \(\upsilon\) being the frequency of the wave (in hertz).
The important thing to notice is that the same bracket \((kx - \omega t)\) appears in both equations. That is the mathematical statement of property (3): both the electric and magnetic fields attain their maximum (and minimum) values at the same time and at the same point in space, i.e., \(\vec{E}\) and \(\vec{B}\) oscillate in phase with the same frequency.
13.3 Electromagnetic Spectrum
All EM waves are made in the same way and all of them travel through free space at the same speed \(c\). What separates one from another is only the wavelength (or, equivalently, the frequency). If we line all the known EM waves up in order of wavelength, we get an ordered chart called the EM spectrum, shown in Fig. 13.6.
Diagram
Fig. 13.6 – The electromagnetic spectrum: gamma rays, X-rays, UV, visible light, IR, microwaves and radio waves arranged along a wavelength axis and a frequency axis, with the visible band expanded into its colours.
Notice in Fig. 13.6 that the two scales run in opposite directions. This is not an accident. Since every EM wave in free space obeys
\[c = \upsilon \lambda\]
where \(\upsilon\) is the frequency (in hertz), \(\lambda\) is the wavelength (in metre) and \(c = 3 \times 10^{8}\) m/s, a larger wavelength must mean a smaller frequency, and vice versa. The groups are given separate names, but the spectrum itself is continuous — the boundaries between neighbouring groups are conventions, not walls, and they do overlap slightly.
The properties of the different types of EM waves are given in Table 13.1. Read this table as a map for the sections that follow.
Table 13.1: Properties of different types of EM waves
| Name | Wavelength range in m | Frequency range in Hz | Generated By |
|---|---|---|---|
| Gamma rays | \(6 \times 10^{-13}\) to \(1 \times 10^{-10}\) | \(5 \times 10^{20}\) to \(3 \times 10^{18}\) | a) Transitions of nuclear energy levels b) Radioactive substances |
| X-rays | \(1 \times 10^{-11}\) to \(3 \times 10^{-8}\) | \(3 \times 10^{19}\) to \(1 \times 10^{16}\) | a) Bombardment of high energy electrons (keV) on a high atomic number target (Cu, Mg, Co) b) Energy level transitions of innermost orbital electrons |
| Ultraviolet (UV waves) | \(3 \times 10^{-8}\) to \(4 \times 10^{-7}\) | \(1 \times 10^{16}\) to \(8 \times 10^{14}\) | Rearrangement of orbital electrons of atom between energy levels. As in high voltage gas discharge tube, the Sun and mercury vapour lamp, etc. |
| Visible light | \(4 \times 10^{-7}\) to \(8 \times 10^{-7}\) | \(8 \times 10^{14}\) to \(4 \times 10^{14}\) | Rearrangement of outer orbital electrons in atoms and molecules e.g., gas discharge tube |
| Infrared (IR) radiations | \(8 \times 10^{-7}\) to \(3 \times 10^{-4}\) | \(4 \times 10^{14}\) to \(1 \times 10^{12}\) | Hot objects |
| Microwaves | \(3 \times 10^{-4}\) to \(6 \times 10^{-2}\) | \(1 \times 10^{12}\) to \(5 \times 10^{9}\) | Special electronic devices such as klystron tube |
| Radio waves | \(6 \times 10^{-4}\) to \(1 \times 10^{5}\) | \(5 \times 10^{11}\) to \(8 \times 10^{10}\) | Acceleration of electrons in circuits |
Look down the last column of Table 13.1 and a pattern appears. The waves at the top of the table come from deep inside the atom or from the nucleus itself, where the energy changes are huge. The waves at the bottom come from electrons being pushed about in ordinary circuits, where the energy changes are tiny. The wavelength of an EM wave is, in effect, a fingerprint of the size and violence of the process that made it.
We now briefly describe the different types of EM waves in the order of decreasing wavelength (or increasing frequency) — that is, starting from radio waves at one end and working our way up to gamma rays at the other.
13.3.1 Radio Waves
Radio waves sit at the long-wavelength end of the spectrum, and they are the easiest of all EM waves to make. They are produced by the accelerated motion of charges in a conducting wire — exactly the mechanism described in Section 13.2.1, but arranged deliberately in a circuit.
The frequency of the waves produced by the circuit depends upon the magnitudes of the inductance and the capacitance in it. (Inductance and capacitance are the properties of a coil and of a capacitor respectively; the circuit that combines them will be discussed in the XIIth standard.) The important idea for us is this: by choosing suitable values of the inductance and the capacitance, radio waves of a desired frequency can be produced.
In other words, a radio wave of almost any frequency we want can be manufactured on demand, simply by picking the right coil and the right capacitor, as suggested in Fig. 13.7. That single fact is what made broadcasting possible.
Diagram
Fig. 13.7 – A circuit containing an inductor and a capacitor driving a transmitting antenna, with radio waves spreading outward from the antenna rod.
Properties
They have very long wavelengths, ranging from a few centimetres to a few hundreds of kilometres.
The frequency range of the AM band is 530 kHz to 1710 kHz. The frequency of the waves used for TV-transmission ranges from 54 MHz to 890 MHz, while those for the FM radio band range from 88 MHz to 108 MHz.
These three number ranges are worth memorising, because questions often ask you to identify which band a given frequency belongs to. Notice that AM is measured in kilohertz while FM and TV are in megahertz — FM waves are therefore of much higher frequency, and much shorter wavelength, than AM waves. This difference will matter a great deal in Section 13.4, where we see that AM and FM signals cannot even travel to you by the same route.
Uses
Radio waves are used for wireless communication purposes.
They are used for radio broadcasting and for the transmission of TV signals.
Cellular phones use radio waves to transmit voice communication in the ultra high frequency (UHF) band.
13.3.2 Microwaves
Microwaves are the next group as we move up in frequency from radio waves. Their wavelengths are of the order of millimetres to a few centimetres — short enough to be aimed in a narrow beam, yet long enough to pass easily through the atmosphere.
These waves were discovered by H. Hertz in 1888, in the same series of experiments that first confirmed Maxwell’s prediction. Microwaves are produced by oscillator electric circuits containing a capacitor and an inductor — the same L–C arrangement that gives radio waves, but driven at a much higher frequency. They can also be produced by special vacuum tubes, such as the klystron tube listed in Table 13.1.
Properties
They heat certain substances on which they are incident.
They can be detected by crystal detectors.
The first property is the one that shows up in daily life, and it is worth understanding rather than memorising. Certain molecules — water being the important one — respond strongly to a rapidly reversing electric field. The microwave’s electric field flips direction billions of times each second, the water molecules are twisted back and forth trying to follow it, and this molecular jostling is heat.
Uses
Used for the transmission of TV signals.
Used for long distance telephone communication.
Microwave ovens are used for cooking.
Used in radar systems for the location of distant objects like ships, aeroplanes, etc.
They are used in the study of atomic and molecular structure.
The radar application deserves a sentence of explanation. A radar sends out a short pulse of microwaves in a narrow beam, as shown in Fig. 13.8. If the beam strikes an aeroplane or a ship, part of it is reflected back. By measuring the time the echo takes to return and knowing that the wave travels at speed \(c\), the distance of the object is calculated. Microwaves are chosen for this because their short wavelength allows a narrow, well-directed beam, and because they are not seriously absorbed by the atmosphere on the way.
Diagram
Fig. 13.8 – A radar antenna sending a narrow microwave beam towards an aeroplane and receiving the reflected echo back.
13.3.3 Infrared Waves
Infrared waves lie just beyond the red end of the visible band — which is exactly what their name means: “below red” in frequency. They were discovered by William Herschel (1737–1822) in 1800.
Diagram
Fig. 13.9 – Herschel’s experiment: sunlight through a prism forming a spectrum on a table, with thermometers in the coloured bands and one in the dark region beyond red showing the highest reading.
All hot bodies are sources of infrared rays. This follows directly from what we know about sources: in a hot body, the charged particles are in rapid, random, accelerated motion, and accelerated charges radiate. The hotter the body, the more it radiates. About 60% of the solar radiation reaching us is infrared in nature.
Since our eyes cannot detect infrared, special instruments are needed. Thermocouples, thermopiles and bolometers are used to detect infrared rays; each of these works by responding to the small heating produced when the radiation is absorbed.
Properties
When infrared rays are incident on any object, the object gets heated.
These rays are strongly absorbed by glass.
They can penetrate through thick columns of fog, mist and cloud cover.
The second and third properties look like small details, but each has a large consequence. Because glass absorbs infrared while allowing visible light through, the interior of a greenhouse (or a closed car) traps heat: visible sunlight enters freely, warms the objects inside, and those objects re-radiate the energy as infrared, which the glass will not let back out. Because infrared can push through fog and cloud that stop visible light, it can be used to see and photograph through conditions in which the eye is helpless.
Uses
Used in remote sensing.
Used in the diagnosis of superficial tumours and varicose veins.
Used to cure infantile paralysis and to treat sprains, dislocations and fractures.
They are used in solar water heaters and cookers.
Special infrared photographs of the body, called thermograms, can reveal diseased organs, because these parts radiate less heat than the healthy organs.
Infrared binoculars and thermal imaging cameras are used in military applications for night vision.
Used to keep a green house warm.
Used in the remote controls of TV, VCR, etc.
Uses (5) and (6) rest on the same idea from opposite ends. Every object warmer than its surroundings glows in infrared, whether or not any lamp is switched on. A thermal camera therefore needs no illumination at all — it simply reads the infrared each object is already emitting, which is why it works in complete darkness, and why an organ that is running colder than the tissue around it shows up as a distinct patch on a thermogram.
13.3.4 Visible Light
Visible light is the most familiar form of EM waves, for a simple reason: these are the waves that our eyes are built to detect. The wavelength range that the human eye responds to is therefore called the visible light range. It occupies only a very narrow strip of the whole spectrum, roughly from \(4 \times 10^{-7}\) m to \(8 \times 10^{-7}\) m, as Table 13.1 shows.
Visible light is emitted due to atomic excitations. When an atom absorbs energy, one of its outer electrons is lifted to a higher energy level. The electron does not stay there; it falls back, and the energy difference is released as an EM wave. For the outer electrons of most atoms and molecules, that energy difference happens to correspond to visible wavelengths.
Properties
- Different wavelengths give rise to different colours. These are given in Table 13.2 and in Fig. 13.10.
Diagram
Fig. 13.10 – The visible band drawn as a coloured strip from violet at 380 nm to red at 750 nm, with the wavelength scale marked below it.
Table 13.2: Wavelengths of colours in visible light
| Colour | Wavelength |
|---|---|
| violet | 380–450 nm |
| blue | 450–495 nm |
| green | 495–570 nm |
| yellow | 570–590 nm |
| orange | 590–620 nm |
| red | 620–750 nm |
- Visible light emitted or reflected from objects around us provides us information about those objects and hence about the surroundings.
Property (2) is easy to skip over, but it is the reason vision exists at all. Nearly everything you know about the room you are sitting in reached you as EM waves in this narrow band, either given out by a source or bounced off a surface.
13.3.5 Ultraviolet Rays
Just as infrared lies beyond the red end of the visible band, ultraviolet (UV) lies beyond the violet end — shorter in wavelength than violet light and therefore higher in frequency. Ultraviolet rays were discovered by J. Ritter (1776–1810) in 1801.
Diagram
Fig. 13.11 – UV radiation from the Sun arriving at the Earth, with most of it absorbed in the ozone layer and only a small fraction reaching the surface.
That absorbing layer is not a minor detail. UV carries enough energy per wave to damage the large molecules inside living cells, and the ozone layer is the filter that keeps most of it from reaching the ground.
Properties
They produce fluorescence in certain materials, such as ‘phosphors’. (Fluorescence means the material absorbs the invisible UV and re-emits the energy as visible light.)
They cause the photoelectric effect — that is, they can eject electrons from a metal surface.
They cannot pass through glass, but pass through quartz, fluorite, rock salt, etc.
They possess the property of synthesizing vitamin D when the skin is exposed to them.
Uses
Ultraviolet rays destroy germs and bacteria, and hence they are used for sterilizing surgical instruments and for the purification of water.
Used in burglar alarms and security systems.
Used to distinguish real and fake gems.
Used in the analysis of chemical compounds.
Used to detect forgery.
Uses (3) and (5) both rest on property (1). Under a UV lamp, a genuine stone and an imitation, or the original ink of a currency note and a forged mark, fluoresce differently — glowing in different colours or not glowing at all — even though they look identical in ordinary light.
13.3.6 X-rays
The German physicist W. C. Rontgen (1845–1923) discovered X-rays in 1895 while studying cathode rays. Cathode rays are a stream of electrons emitted by the cathode in a vacuum tube. In his honour, X-rays are also called Rontgen rays.
Diagram
Fig. 13.12 – An X-ray tube: electrons emitted by the cathode are accelerated through a high voltage and strike a metal target on the anode, from which X-rays are emitted.
Properties
They are high energy EM waves.
They are not deflected by electric and magnetic fields.
X-rays ionize the gases through which they pass.
They have high penetrating power.
Their overdose can kill living plant and animal tissues and hence they are harmful.
Property (2) is worth pausing on, because it is a favourite of examiners. Cathode rays are deflected by electric and magnetic fields, since they are made of electrons and electrons carry charge. X-rays, being EM waves, carry no charge at all. A field has nothing to grip, so the beam travels straight on. If a question asks you to distinguish X-rays from cathode rays, this is the cleanest test.
Uses
Useful in the study of the structure of crystals.
X-ray photographs are useful to detect bone fracture. X-rays have many other medical uses such as the CT scan.
X-rays are used to detect flaws or cracks in metals.
These are used for the detection of explosives, opium, etc.
Uses (2), (3) and (4) are all the same physics in different settings: an X-ray beam is sent through an object that visible light cannot enter, and the pattern of what gets absorbed and what passes through builds a picture of the inside — a fracture in a bone, a hidden crack in a weld, or the contents of a sealed piece of luggage.
13.3.7 Gamma Rays (γ-rays)
Gamma rays occupy the extreme high-frequency, short-wavelength end of the spectrum. They were discovered by P. Villard (1860–1934) in 1900.
Diagram
Fig. 13.13 – A radioactive nucleus emitting a γ-ray, with a strip comparing penetrating power: a thin sheet stops the least penetrating radiation, while γ-rays require a thick lead block.
Properties
They are the highest energy EM waves (energy range keV – GeV).
They are highly penetrating.
They have a small ionising power.
They kill living cells.
Properties (2) and (3) sit together and must not be confused. Being uncharged, a gamma ray does not tug at the electrons of every atom it passes; it interacts only occasionally. So along any given centimetre of its path it knocks out relatively few electrons — a small ionising power — but for the same reason it is not easily stopped, and it travels deep into matter before it is finally absorbed. Weak interaction per collision, but enormous range: that is the gamma ray in one line.
Uses
Used as insecticide disinfection for wheat and flour.
Used for food preservation.
Used in radiotherapy for the treatment of cancer and tumour.
They are used to produce nuclear reactions.
Uses (1) and (2) are the same idea applied to food: the gamma beam kills the insects, moulds and bacteria present in stored grain or packaged food, so the food keeps for far longer. The radiation passes through and does not remain in the food afterwards.
13.4 Propagation of EM Waves
You must have seen a TV antenna used to receive TV signals, either from a transmitting tower or from a satellite. In communication using radio waves, an antenna in the transmitter radiates the EM waves; these waves travel through space and reach the receiving antenna at the other end.
The wave, however, does not arrive with the strength it left. As the EM wave travels away from the transmitter, the strength of the wave keeps on decreasing. Part of the reason is simple geometry: the wave spreads out over an ever-larger area as it moves away, so the energy falling on any one antenna gets smaller and smaller. Part of the reason is the Earth itself and the air above it, which absorb, reflect and bend the wave along the way.
Several factors influence the propagation of EM waves and the path they follow. It is also important to understand the composition of the Earth’s atmosphere, as it plays a vital role in the propagation of EM waves. The different layers of the Earth’s atmosphere are shown in Fig. 13.14.
Diagram
Fig. 13.14 – The Earth surrounded by its atmospheric layers, drawn as shells: Troposphere (up to about 20 km), Stratosphere (up to about 50 km), Mesosphere (up to about 85 km), Thermosphere (up to about 690 km) and Exosphere (up to about 10000 km).
Notice in Fig. 13.14 how thin the lowest layers are compared with the size of the Earth, and how far the upper layers extend. Each layer differs in density, in temperature, and — crucially for us — in how many free electrons and ions it contains. A radio wave that meets a layer of ordinary neutral air behaves quite differently from one that meets a layer full of charged particles, and it is this difference that decides the route a signal can take.
Because of this, a wave leaving a transmitting antenna does not have just one way of reaching the receiver. It may crawl along the surface of the Earth, or fly in a straight line through the lower atmosphere, or be turned back towards the ground by the charged upper atmosphere. These are the three different modes of propagation, and which one a wave uses depends chiefly on its frequency.
The different modes of propagation of EM waves are described below and are shown together in Fig. 13.15.
Diagram
Fig. 13.15 – Propagation of EM waves: a transmitting antenna sending a surface wave along the ground, a space wave to a receiving aerial in line of sight, a sky wave reflected from the ionosphere, and a path via a communication satellite.
Study Fig. 13.15 carefully before reading further, because the three sub-sections that follow simply take one arrow of this figure at a time. In each case, ask yourself two questions: what is the wave bouncing off (or hugging), and what range of frequency is able to do that?
13.4.1 Ground (Surface) Wave
The simplest route a radio wave can take is to stay near the ground and follow it.
When a radio wave from a transmitting antenna propagates near the surface of the Earth so as to reach the receiving antenna, the wave propagation is called ground wave or surface wave propagation.
In this mode, radio waves travel close to the surface of the Earth and move along its curved surface from transmitter to receiver, as shown in Fig. 13.16. This is worth noticing: the wave does not shoot off in a straight line and leave the Earth behind. It bends with the ground, staying in contact with it all the way.
Diagram
Fig. 13.16 – A ground wave travelling from a transmitting antenna along the curved surface of the Earth to a receiving antenna, with small arrows into the ground showing energy being absorbed.
Why the Range Is Small
Staying in contact with the Earth comes at a price. The radio waves induce currents in the ground beneath them, and these currents carry away energy from the wave — the wave loses its energy by absorption. Every kilometre of ground the wave hugs takes another bite out of its strength.
Therefore, the signal cannot be transmitted over large distances by this mode. The wave simply dies out.
Radio waves having a frequency less than 2 MHz (that is, in the medium frequency band) are transmitted by ground wave propagation. This is suitable for local broadcasting only. For TV or FM signals, which are very high frequency, ground wave propagation cannot be used.
There is a physical reason behind that 2 MHz limit, and it is worth seeing rather than memorising. A low-frequency wave has a long wavelength — recall from Section 13.3.1 that an AM wave at 1000 kHz is about 300 m long. A wave that long is far larger than most obstacles and than the curvature it must follow over a short stretch, so it bends around the Earth and around buildings and hills quite readily. A high-frequency FM or TV wave is only a few metres long or less; it behaves far more like a straight ray of light, refuses to bend around the horizon, and in addition is absorbed by the ground much more heavily. So the higher the frequency, the worse the ground wave performs.
13.4.2 Space Wave
The second route a wave can take is essentially a straight one.
When the radio waves from the transmitting antenna reach the receiving antenna either directly along a straight line (line of sight), or after reflection from the ground or from a satellite, or after reflection from the troposphere, the wave propagation is called space wave propagation. The radio waves reflected from the troposphere are called tropospheric waves.
Radio waves with a frequency greater than 30 MHz can pass through the ionosphere (60 km – 1000 km) after suffering a small deviation. In other words, these high-frequency waves are not turned back by the upper atmosphere; they punch straight through it and escape. Hence, these waves cannot be transmitted over long distances by space wave propagation except by using a satellite. Also, for TV signals, which have a high frequency, transmission over long distance is not possible by means of space wave propagation.
Range and the Height of the Antenna
The maximum distance over which a signal can reach is called its range. Since a space wave travels in a straight line, and the Earth is curved, the wave eventually skims off past the horizon — and beyond that point, nothing is received.
This gives a very practical conclusion: for larger TV coverage, the height of the transmitting antenna should be as large as possible. Raising the antenna pushes the horizon further away. This is the reason why transmitting and receiving antennas are mounted on top of high-rise buildings.
Range is the straight line distance from the point of transmission (the top of the antenna) to the point on the Earth where the wave will hit while travelling along a straight line. Range is shown by \(d\) in Fig. 13.17.
Diagram
Fig. 13.17 – Range of the signal (not to scale): transmitting antenna AA′ of height \(h\) at A, the straight-line path \(d\) to the point B on the Earth’s surface, a receiving antenna of height \(h'\) at C with its own distance \(d'\), and the Earth of radius \(R\) with centre O.
Let the height of the transmitting antenna (AA′), situated at A, be \(h\). B represents the point on the surface of the Earth at which the space wave hits the Earth. Since the straight-line path A′B just grazes the Earth at B, the radius OB is perpendicular to it, and therefore the triangle OA′B is a right angled triangle. From ∆OA′B we can write
\[OA'^{2} = A'B^{2} + OB^{2}\]
Now OA′ is the distance from the centre of the Earth to the top of the antenna, which is the Earth’s radius plus the antenna height; A′B is the range \(d\); and OB is the Earth’s radius \(R\). Substituting these,
\[(R + h)^{2} = d^{2} + R^{2}\]
Expanding the left-hand side,
\[\text{or} \qquad R^{2} + h^{2} + 2Rh = d^{2} + R^{2}\]
The \(R^2\) terms cancel from both sides, leaving \(h^2 + 2Rh = d^2\). As \(h \ll R\) — the tallest tower is a few hundred metres, while the Earth’s radius is about 6400 km, so \(h^2\) is utterly negligible beside \(2Rh\) — we can ignore \(h^{2}\) and write
\[d \cong \sqrt{2Rh}\]
Here \(d\) is the range (in metre), \(R\) is the radius of the Earth (in metre) and \(h\) is the height of the transmitting antenna above the Earth’s surface (in metre).
The range can be increased by mounting the receiver at a height \(h'\), say at a point C on the surface of the Earth. The range then increases to \(d + d'\), where \(d'\) is \(\sqrt{2Rh'}\). This is because the receiving antenna, being raised, can also “see” over the horizon by its own amount, and the two horizons meet somewhere in between. Thus
\[\text{Total range} = d + d' = \sqrt{2Rh} + \sqrt{2Rh'}\]
where \(h\) is the height of the transmitting antenna and \(h'\) is the height of the receiving antenna, both in metre.
13.4.3 Sky Wave Propagation
The third route is the one that took a signal across the Atlantic. Instead of hugging the ground or shooting off past the horizon, the wave goes upward — and comes back down.
When radio waves from a transmitting antenna reach the receiving antenna after reflection in the ionosphere, the wave propagation is called sky wave propagation.
The ionosphere, as we saw in Fig. 13.14, is the region of the upper atmosphere (roughly 60 km to 1000 km) that contains free electrons and ions, produced when solar radiation strips electrons from the gas molecules there. A layer full of free charges behaves quite differently from ordinary air: a radio wave of suitable frequency entering it is bent more and more until it is turned back towards the ground, exactly like a ball rebounding from a ceiling.
The sky waves include waves of frequency between 3 MHz and 30 MHz. These waves can suffer multiple reflections between the ionosphere and the Earth, as shown in Fig. 13.18 — bouncing down to the ground, up again to the ionosphere, and down once more. Therefore, they can be transmitted over large distances, far beyond the horizon.
Diagram
Fig. 13.18 – A sky wave from a transmitter making multiple hops between the ionosphere and the Earth’s surface, with the skip distance marked as the gap around the transmitter in which no sky wave is received.
Two Limits: Critical Frequency and Skip Distance
The ionosphere will not reflect just any wave sent up to it. There is a ceiling on the frequency it can turn back.
Critical frequency: It is the maximum value of the frequency of a radio wave which can be reflected back to the Earth from the ionosphere when the waves are directed normally to the ionosphere.
Note the condition carefully: “directed normally to the ionosphere.” A wave that strikes the layer at a slant can be reflected even if its frequency is above the critical frequency, because a glancing hit is turned back more easily than a head-on one. This single fact leads to the next idea.
Suppose a transmitter sends up a wave of fixed frequency greater than the critical frequency. Rays going straight up escape; rays going up at a slant are reflected. Rays leaving at a very steep angle escape as well, and only those leaving beyond a certain angle come back — so they land at some distance from the transmitter, leaving a ring of ground around it in which no sky wave lands at all.
Skip distance (zone): It is the shortest distance from a transmitter, measured along the surface of the Earth, at which a sky wave of fixed frequency (if greater than the critical frequency) will be returned to the Earth, so that no sky waves can be received within the skip distance.
13.5 Introduction to Communication System
Communication is the exchange of information. Since ancient times it has been practised in various ways — through speaking, writing, singing, using body language, and so on. In every one of these, something that exists in one mind is coded into a form that can travel (a sound, a mark on paper, a gesture) and is then decoded at the other end.
What limited all the ancient methods was distance. A shout carries a few hundred metres; a letter carries far, but takes days. After the discovery of electricity in the late 19th century, human communication systems changed dramatically, because for the first time information could be made to travel at the speed of an electrical signal.
Modern communication is based upon the discoveries and inventions by a number of scientists like J. C. Bose (1858–1937), S. F. B. Morse (1791–1872), G. Marconi (1874–1937) and Alexander Graham Bell (1847–1922) in the 19th and 20th centuries.
From Analogue Wires to a Digital World
In the 20th century, we could send messages over large distances using analogue signals, cables and radio waves. With the advancements of digitization technologies, we can now communicate with the entire world almost in real time.
That phrase “almost in real time” is worth dwelling on. A message sent to another continent today arrives in a fraction of a second, because the carrier of that message is an EM wave travelling at \(3 \times 10^{8}\) m/s. Everything we studied in the first half of this chapter — how EM waves are made, how they are grouped by frequency, how they travel through and around the atmosphere — is the physical foundation on which every one of these systems is built.
The ability to communicate is an important feature of modern life. We can speak directly to others all around the world and generate a vast amount of information every day.
Here we will briefly discuss how communication systems work.
Diagram
Fig. 13.19 – A single strip showing information going from a source, through a sending stage, across a distance, to a receiving stage and finally to a user, with the same strip labelled underneath for a telephone call, a TV broadcast and an internet message.
13.5.1 Elements of a Communication System
There are three basic (essential) elements of every communication system:
- Transmitter,
- Communication channel, and
- Receiver.
“Essential” is the important word here. Remove any one of the three and no communication takes place at all, no matter how advanced the technology. The complete arrangement is shown as a block diagram in Fig. 13.20.
Diagram
Fig. 13.20 – Block diagram of the basic elements of a communication system: Information source → message signal → Transmitter → transmitted signal → Channel (with Noise entering it) → received signal → Receiver → message signal → User of information.
In a communication system, as shown in Fig. 13.20, the transmitter is located at one place and the receiver at another place. Between them lies the channel.
The communication channel is a passage through which signals transfer in between a transmitter and a receiver. This channel may be in the form of wires or cables, or may also be wireless, depending on the type of communication system.
Trace the diagram from left to right and give each arrow a name. The information source produces the message; the transmitter converts it into a transmitted signal fit for the channel; the channel carries it, weakening it along the way; the receiver rebuilds the original message from what arrives; and the user finally receives the information. Notice the one arrow that points into the system rather than along it — noise, which enters at the channel and was never part of the message.
Two Modes of Communication
There are two basic modes of communication: (i) point to point communication and (ii) broadcast.
In point to point communication mode, communication takes place over a link between a single transmitter and a receiver. Telephony is the standard example — one caller, one listener, one link.
In the broadcast mode, there are a large number of receivers corresponding to the single transmitter. Radio and Television transmission are the examples: one station transmits, and thousands of sets receive the same signal at the same instant.
13.5.2 Commonly Used Terms in Electronic Communication System
The following terms are useful to understand any communication system. Learn them as a working vocabulary — every one of them reappears in the next section and in examination questions.
1) Signal
The information converted into electrical form that is suitable for transmission is called a signal. In a radio station, music and speech are converted into electrical form by a microphone for transmission into space. This electrical form of sound is the signal.
The point to grasp is that a wire or an antenna cannot carry music; it can only carry a varying voltage or current. So the first job in any communication system is to turn the information into electricity.
A signal can be analog or digital, as shown in Fig. 13.21.
Diagram
Fig. 13.21 – (a) An analog signal: a smooth, continuously varying voltage against time, swinging between +5 V and −5 V. (b) A digital signal: a square wave against time, jumping between only two levels, +5 V and 0 V.
(i) Analog signal: A continuously varying signal (voltage or current) is called an analog signal. Since a wave is a fundamental analog signal, sound and picture signals in TV are analog in nature (Fig. 13.21 a).
(ii) Digital signal: A signal (voltage or current) that can have only two discrete values is called a digital signal. For example, a square wave is a digital signal. It has two values, viz., +5 V and 0 V (Fig. 13.21 b).
2) Transmitter
A transmitter converts the signal produced by a source of information into a form suitable for transmission through a channel and subsequent reception.
3) Transducer
A device that converts one form of energy into another form of energy is called a transducer. For example, a microphone converts sound energy into electrical energy; therefore a microphone is a transducer. Similarly, a loudspeaker is a transducer which converts electrical energy into sound energy.
Note that the two examples work in opposite directions. One transducer stands at the beginning of the system, turning the message into electricity; another stands at the end, turning electricity back into a message a human can sense.
4) Receiver
The receiver receives the message signal at the channel output, reconstructs it in a recognizable form of the original message, and delivers it to the user of information.
5) Noise
A random unwanted signal is called noise. The source generating the noise may be located inside or outside the system. Efforts should be made to minimise the noise level in a communication system.
6) Attenuation
The loss of strength of the signal while propagating through the channel is known as attenuation. It occurs because the channel distorts, reflects and refracts the signals as they pass through it.
Attenuation and noise are the two enemies of every communication system, and they work together against you: the message keeps getting weaker while the unwanted noise stays. The remedies for attenuation are the next two terms.
7) Amplification
Amplification is the process of raising the strength of a signal, using an electronic circuit called an amplifier.
8) Range
The maximum (largest) distance between a source and a destination up to which the signal can be received with sufficient strength is termed as range.
This is the same range we calculated in Section 13.4.2 for a space wave, seen now from the point of view of the communication engineer rather than the geometry of the Earth.
9) Bandwidth
The bandwidth of an electronic circuit is the range of frequencies over which it operates efficiently.
10) Modulation
The signals in a communication system (e.g. music, speech, etc.) are low frequency signals and cannot be transmitted over large distances. In order to transmit the signal to large distances, it is superimposed on a high frequency wave, called a carrier wave. This process is called modulation. Modulation is done at the transmitter and is an important part of a communication system.
11) Demodulation
The process of regaining the signal from a modulated wave is called demodulation. This is the reverse process of modulation, and it is carried out at the receiver — the carrier has done its job of transporting the message and is now discarded.
12) Repeater
A repeater is a combination of a transmitter and a receiver. The receiver receives the signal from the transmitter, amplifies it, and transmits it to the next repeater. Repeaters are used to increase the range of a communication system. These are shown in Fig. 13.22.
Diagram
Fig. 13.22 – Use of repeater stations to increase the range of communication: a transmitting tower, followed by two repeater towers on the Earth’s surface, each receiving the weakened wave and sending it on.
13.6 Modulation
As mentioned earlier, an audio signal has low frequency (< 20 kHz). Low frequency signals cannot be transmitted over large distances. Because of this, a high frequency wave, called a carrier wave, is used. Some characteristic (e.g. amplitude, frequency or phase) of this wave is changed in accordance with the amplitude of the signal. This process is known as modulation.
Why a Carrier Is Needed at All
Two separate difficulties are solved by the carrier, and it is worth keeping them apart in your mind.
The first is that a low frequency signal simply cannot be radiated efficiently. Recall from Section 13.5.2 that an antenna must be at least \(\lambda/4\) long to radiate a wave well. A 15 kHz audio signal has so long a wavelength that this works out to about 5 km of antenna — plainly impossible. Ride the same information on a carrier of, say, 1 MHz, and the required antenna shrinks to a few tens of metres.
The second difficulty is interference between stations. Modulation also helps avoid the mixing up of signals from different transmitters, as different carrier wave frequencies can be allotted to different transmitters. Without the use of these waves, the audio signals, if transmitted directly by different transmitters, would have got mixed up — every station would be sending out waves in the same low frequency range, and a receiver would have no way of separating them.
The Three Kinds of Modulation
Modulation can be done by modifying the (i) amplitude (amplitude modulation), (ii) frequency (frequency modulation), and (iii) phase (phase modulation) of the carrier wave, in proportion to the amplitude or intensity of the signal wave, keeping the other two properties the same.
Read that last clause carefully — it is the whole idea. A wave has three things that can be varied: how tall it is, how fast it oscillates, and where in its cycle it is. In any one scheme of modulation, exactly one of these is made to follow the message, and the other two are left alone.
Figure 13.23 (a) shows a carrier wave and (b) shows the signal. The carrier wave is a high frequency wave, while the signal is a low frequency wave. Amplitude modulation, frequency modulation and phase modulation of carrier waves are shown in Fig. 13.23 (c), (d) and (e) respectively.
Diagram
Fig. 13.23 – (a) Carrier wave, (b) signal, (c) AM, (d) FM and (e) PM, drawn one below the other as displacement versus time.
Compare the three lower traces in Fig. 13.23. In (c), the height of the carrier swells and shrinks with the signal, while its spacing stays uniform. In (d), the height stays constant but the waves bunch together and spread apart as the signal rises and falls. In (e), the shift is in where the cycle begins.
Comparing AM, FM and PM
Amplitude modulation (AM) is simple to implement and has a large range. It is also cheaper. Its disadvantages are that (i) it is not very efficient as far as power usage is concerned, (ii) it is prone to noise, and (iii) the reproduced signal may not exactly match the original signal. In spite of this, these are used for commercial broadcasting in the long, medium and short wave bands.
There is a physical reason why AM is prone to noise, and it follows from everything in Section 13.5.2. Noise picked up along the way adds itself to the amplitude of the arriving wave — and in AM, the amplitude is precisely where the information is stored. The noise is therefore indistinguishable from the message.
Frequency modulation (FM) is more complex as compared to amplitude modulation, and therefore is more difficult to implement. However, its main advantage is that it reproduces the original signal closely and is less susceptible to noise. This modulation is used for high quality broadcast transmission.
13.7 Summary
EM Waves and Maxwell’s Equations
Four basic laws describe electric and magnetic fields and their generation by charges and currents: Gauss’ law for electrostatics, Gauss’ law for magnetism, Faraday’s law, and Ampere’s law. Together, after Maxwell’s correction, they are called Maxwell’s equations.
Gauss’ law for magnetism states that magnetic monopoles do not exist; magnetic poles always occur in pairs, and the magnetic flux through any closed surface is zero.
In 1861, Maxwell found that Ampere’s law was incomplete for time-varying fields, and added the displacement current term: a magnetic field is produced not only by a current but also by a changing electric field. Without this term, EM waves would not be possible.
Maxwell’s equations for charges and currents in vacuum:
\[\int \vec{E} \cdot d\vec{S} = \frac{Q_{in}}{\varepsilon_0} \qquad \text{(Gauss' law; integral over a closed surface } S\text{)}\]
\[\int \vec{B} \cdot d\vec{S} = 0 \qquad \text{(Gauss' law for magnetism; closed surface } S\text{)}\]
\[\int \vec{E} \cdot d\vec{l} = -\frac{d\phi_m}{dt} \qquad \text{(Faraday's law with Lenz's law; closed loop)}\]
\[\int \vec{B} \cdot d\vec{l} = \mu_0 I + \varepsilon_0 \mu_0 \frac{d\phi_E}{dt} \qquad \text{(Ampere–Maxwell law; closed loop)}\]
- Historical landmarks: Hertz produced and detected EM waves in 1888 and showed reflection, refraction and interference; J. C. Bose produced EM waves of wavelength 5 mm to 25 nm in 1895; Marconi pioneered wireless communication from 1896 and received the Nobel Prize in 1909.
Sources and Nature of EM Waves
Accelerated charges radiate EM waves. An oscillating charge produces an oscillating electric field, which produces an oscillating magnetic field, which regenerates the electric field — and the disturbance travels outward.
A charge at rest has only an electric field. A charge moving with constant velocity produces a steady magnetic field and cannot radiate. Only an accelerated charge radiates. An oscillating charge emits an EM wave of the same frequency as its oscillation.
EM waves are waves caused by the acceleration of charged particles, in which \(\vec{E}\) and \(\vec{B}\) vibrate sinusoidally at right angles to each other and to the direction of propagation.
Characteristics of EM Waves
- \(\vec{E}\) and \(\vec{B}\) are perpendicular to each other and to the direction of propagation → EM waves are transverse.
- \(\vec{E} \times \vec{B}\) gives the direction of propagation and also the energy carried by the wave.
- \(\vec{E}\) and \(\vec{B}\) vary sinusoidally and are in phase.
- EM waves are produced by accelerated charges, and can travel through free space as well as through solids, liquids and gases.
- In free space:
\[c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} = 3 \times 10^{8}\ \text{m/s}\]
with \(\mu_0 = 4\pi \times 10^{-7}\) T·m/A and \(\varepsilon_0 = 8.85 \times 10^{-12}\) C²/Nm².
- In a material medium of permeability \(\mu\) and permittivity \(\varepsilon\):
\[v_m = \frac{1}{\sqrt{\mu \varepsilon}}\]
- EM waves obey the principle of superposition.
- Ratio of the amplitudes:
\[|\vec{E_0}| = c\,|\vec{B_0}| \quad \text{or} \quad \frac{|\vec{E_0}|}{|\vec{B_0}|} = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} \qquad --- (13.1)\]
- \(\vec{E_0}\) is more prominent than \(\vec{B_0}\) and is responsible for optical effects; the electric vector is therefore called the light vector.
- Intensity is proportional to the square of the amplitude:
\[I_E = \frac{1}{2}\varepsilon_0 E_0^{2}, \qquad I_B = \frac{1}{2}\frac{B_0^{2}}{\mu_0} \qquad --- (13.2)\]
- The energy of an EM wave is shared equally between the electric and magnetic fields: \(I_E = I_B\).
- For a wave along the \(x\)-axis with \(\vec{E}\) along \(y\) and \(\vec{B}\) along \(z\):
\[E_y = E_0 \sin(kx - \omega t) \qquad --- (13.2)\] \[B_z = B_0 \sin(kx - \omega t) \qquad --- (13.3)\]
where \(k = \dfrac{2\pi}{\lambda}\) is the propagation constant and \(\omega = 2\pi\upsilon\) is the angular frequency. Both fields peak at the same time and place.
EM Spectrum
The EM spectrum is the orderly arrangement of EM waves according to wavelength (or frequency) in distinct groups with different properties. All obey \(c = \upsilon\lambda\), so larger wavelength means smaller frequency.
In order of decreasing wavelength (increasing frequency):
- Radio waves — produced by accelerated charges in a conducting wire; frequency set by the inductance and capacitance of the circuit. Wavelengths from a few cm to a few hundred km. AM band 530 kHz–1710 kHz; TV transmission 54 MHz–890 MHz; FM band 88 MHz–108 MHz. Used for wireless communication, broadcasting, TV, and cellphones (UHF band).
- Microwaves — discovered by Hertz (1888); produced by L–C oscillator circuits and special vacuum tubes (klystron). They heat certain substances and are detected by crystal detectors. Used in TV transmission, long distance telephony, microwave ovens, radar, and the study of atomic and molecular structure.
- Infrared waves — discovered by William Herschel (1800); all hot bodies emit them; about 60% of solar radiation is infrared. Detected by thermocouples, thermopiles and bolometers. They heat objects, are strongly absorbed by glass, and penetrate fog, mist and cloud. Used in remote sensing, medical diagnosis and therapy, solar heaters and cookers, thermograms, night vision, greenhouses and TV remote controls.
- Visible light — detected by the human eye; emitted due to atomic excitations. Different wavelengths give different colours (violet 380–450 nm to red 620–750 nm).
- Ultraviolet rays — discovered by J. Ritter (1801); from mercury vapour lamps, sparks, arc lamps and the Sun (mostly absorbed by the ozone layer). They cause fluorescence and the photoelectric effect, cannot pass through glass but pass through quartz, and synthesize vitamin D. Used for sterilization and water purification, burglar alarms, testing gems, chemical analysis and detecting forgery.
- X-rays — discovered by W. C. Rontgen (1895); produced when cathode rays are suddenly stopped by an obstacle. High energy, not deflected by electric or magnetic fields, ionize gases, highly penetrating, harmful in overdose. Used in crystal studies, medical imaging and CT scans, detecting flaws in metals, and detecting explosives.
- Gamma rays — discovered by P. Villard (1900); emitted from the nuclei of radioactive elements such as uranium and radium. Highest energy (keV–GeV), highly penetrating, small ionising power, kill living cells. Used for disinfecting wheat and flour, food preservation, radiotherapy and producing nuclear reactions.
- Ultraviolet, X-rays and gamma rays are ionizing radiations — they strip electrons from atoms along their path.
Propagation of EM Waves
The strength of a wave decreases as it travels away from the transmitter. The Earth’s atmosphere (troposphere, stratosphere, mesosphere, thermosphere, exosphere) plays a vital role in propagation.
Ground (surface) wave: the wave travels close to the Earth’s surface, following its curvature. It induces currents in the ground and loses energy by absorption, so the range is small. Used for frequencies below 2 MHz (medium frequency band); suitable for local broadcasting only. Cannot be used for TV or FM.
Space wave: the wave reaches the receiver directly (line of sight), or after reflection from the ground, a satellite, or the troposphere (tropospheric waves). Waves above 30 MHz pass through the ionosphere (60 km–1000 km) and so need a satellite for long-distance transmission.
Range of a space wave from an antenna of height \(h\) on an Earth of radius \(R\):
\[d \cong \sqrt{2Rh}\]
obtained from \((R+h)^2 = d^2 + R^2\) by neglecting \(h^2\) since \(h \ll R\).
- If the receiving antenna is also raised to a height \(h'\):
\[\text{Total range} = d + d' = \sqrt{2Rh} + \sqrt{2Rh'}\]
Since \(d \propto \sqrt{h}\), transmitting antennas are mounted as high as possible.
Sky wave: the wave is reflected back to the Earth by the ionosphere, and can make multiple hops between the ionosphere and the ground, so it travels over large distances. Sky waves lie between 3 MHz and 30 MHz.
Critical frequency: the maximum frequency of a radio wave that can be reflected back to the Earth from the ionosphere when the wave is directed normally to the ionosphere.
Skip distance (zone): the shortest distance from a transmitter, along the Earth’s surface, at which a sky wave of a fixed frequency (greater than the critical frequency) returns to the Earth; no sky waves are received within this distance.
Communication System
Communication is the exchange of information. A communication system is a set-up used for the transmission and reception of information from one place to another.
Three essential elements: transmitter, communication channel, receiver. The channel may be wires, cables or wireless.
Two modes: point to point (one transmitter, one receiver, e.g. telephony) and broadcast (one transmitter, many receivers, e.g. radio and TV).
Key terms:
- Signal — information in electrical form. Analog: continuously varying. Digital: only two discrete values (e.g. +5 V and 0 V).
- Transducer — converts one form of energy into another (microphone, loudspeaker).
- Noise — random unwanted signal, from inside or outside the system.
- Attenuation — loss of signal strength while propagating through the channel.
- Amplification — raising the strength of a signal using an amplifier.
- Range — largest distance up to which the signal is received with sufficient strength.
- Bandwidth — range of frequencies over which a circuit operates efficiently.
- Modulation / Demodulation — superimposing the signal on a carrier wave / recovering it back.
- Repeater — a receiver plus transmitter that amplifies and re-transmits a signal to increase range.
- An antenna must be at least \(\lambda/4\) long for efficient transmission and reception.
Modulation
An audio signal has low frequency (< 20 kHz) and cannot be transmitted over large distances. It is superimposed on a high frequency carrier wave. This also prevents the signals of different transmitters from mixing, since each transmitter is allotted a different carrier frequency.
Modulation changes one characteristic of the carrier — amplitude (AM), frequency (FM) or phase (PM) — in proportion to the amplitude of the signal, keeping the other two unchanged.
AM: simple, cheap, large range; but power-inefficient, prone to noise, and the reproduced signal may not exactly match the original. Used for commercial broadcasting in the long, medium and short wave bands.
FM: more complex and harder to implement, but reproduces the original signal closely and is less susceptible to noise. Used for high quality broadcast transmission.
PM: easier than FM; used in determining the velocity of a moving target, which cannot be done using frequency modulation.
13.8 Check Your Concepts
Maxwell added the displacement current term to Ampere’s law. Explain why an EM wave could not exist at all if this term were absent.
A charge moves with a constant velocity in a straight line. It produces both an electric field and a magnetic field, and yet it radiates no EM wave. Why not? What must change before it radiates?
Gauss’ law for magnetism states that the magnetic flux through any closed surface is zero, while the electric flux through a closed surface need not be zero. What physical difference between electricity and magnetism does this express?
An EM wave travels along the \(+z\) direction with its electric field along the \(+x\) direction. Determine the direction of its magnetic field, giving your reasoning.
The electric field vector of an EM wave is called the “light vector”. Why is the magnetic field vector not given this name, even though the energy of the wave is shared equally between the two fields?
When light passes from air into glass its speed decreases. State what happens to its frequency and to its wavelength, and justify your answer using \(c = \upsilon\lambda\) together with \(v_m = 1/\sqrt{\mu\varepsilon}\).
Gamma rays are said to have high penetrating power but small ionising power. Explain how both statements can be true at the same time.
X-rays are not deflected by electric and magnetic fields, whereas cathode rays are. Explain the reason, and state how this fact could be used to distinguish the two in the laboratory.
Why must a UV lamp be made with a quartz envelope rather than an ordinary glass one?
A thermal imaging camera can photograph a person in complete darkness, with no lamp of any kind switched on. Explain how this is possible.
Why are γ-ray, X-ray and ultraviolet telescopes placed aboard satellites, while radio telescopes and optical telescopes can be built on the ground? Why, in addition, are optical telescopes usually placed at high altitudes?
A medium-wave AM station remains audible inside a deep valley, while an FM station is lost there. Account for this difference in terms of the mode of propagation and the wavelength involved.
Show, without doing any calculation, that the range of a TV tower increases only as the square root of its height. What practical difficulty does this create for anyone who wishes to double the coverage of an existing tower?
A short-wave listener 150 km from a transmitter cannot receive its signal at all, while another listener 1500 km away receives it clearly. Name the phenomenon responsible and explain it.
What is meant by the critical frequency of the ionosphere? Why is the condition “when the waves are directed normally to the ionosphere” an essential part of the definition?
Distinguish between point to point communication and broadcast mode, giving one example of each. Is a mobile phone conversation a broadcast simply because thousands of phones lie within range of the same tower? Justify your answer.
Distinguish between attenuation and noise. Explain why a repeater is able to overcome one of these but not the other completely.
A digital signal takes only two values, while an analog signal takes every value in its range. Explain why the digital signal is less easily corrupted by noise during transmission.
Both amplitude modulation and frequency modulation carry the same message on the same kind of carrier wave. Explain why FM reception is far less noisy than AM reception.
Two reasons are usually given for the necessity of modulation: the impracticable length of the antenna, and the mixing up of signals from different stations. Explain each reason in your own words, and state which of the two would still be a problem if only one transmitter existed in the whole world.
State two characteristics of an EM wave.
Why are microwaves used in radar?
What are EM waves?
How are EM waves produced?
Can we produce a pure electric or magnetic wave in space? Why?
Does an ordinary electric lamp emit EM waves?
Why do light waves travel in vacuum whereas sound waves cannot?
What are ultraviolet rays? Give two uses.
What are radio waves? Give two of their uses.
Name the most harmful radiation entering the Earth’s atmosphere from outer space.
Give reasons for the following:
- Long distance radio broadcast uses short wave bands.
- Satellites are used for long distance TV transmission.
Name the three basic units of any communication system.
What is a carrier wave?
Why are high frequency carrier waves used for the transmission of audio signals?
What is modulation?
What is meant by amplitude modulation?
What is meant by bandwidth?
What is demodulation?
What type of modulation is required for television broadcast?
How does the effective power radiated by an antenna vary with wavelength?
Why should broadcasting programs use different frequencies?
Explain the necessity of a carrier wave in communication.
13.9 Practice with Numericals
An EM wave in vacuum has an electric field amplitude of 90 V/m. Calculate the amplitude of its magnetic field. (Take \(c = 3 \times 10^{8}\) m/s.)
The magnetic field amplitude of an EM wave in vacuum is \(2.0 \times 10^{-8}\) T. Calculate the amplitude of the electric field and state its SI unit.
A radio station broadcasts at a frequency of 105 MHz. Calculate the wavelength of the wave emitted and state which radio band it belongs to.
Calculate the frequency of an EM wave of wavelength 450 nm, and name the colour of visible light to which it corresponds, using Table 13.2.
An EM wave of wavelength \(5 \times 10^{-3}\) m travels in free space. Calculate its frequency and name the region of the EM spectrum in which it lies.
An EM wave travelling in vacuum has an electric field given by \(E_y = 30 \sin(2\pi \times 10^{8}\,t - kx)\) V/m, with all quantities in SI units. Find (a) the amplitude of the magnetic field, and (b) the frequency and the wavelength of the wave.
Two beams of blue light of the same colour have amplitudes in the ratio 3 : 1. Calculate the ratio of their intensities.
The amplitude of the electric field of an EM wave in vacuum is 40 V/m. Calculate the intensity \(I_E\) associated with the electric field, taking \(\varepsilon_0 = 8.85 \times 10^{-12}\) C²/Nm². State the value of \(I_B\) for the same wave, with reason.
An EM wave travelling along the \(x\)-axis has a magnetic field \(\vec{B} = \hat{k}\ 2 \times 10^{-4} \sin(\omega t - kx)\) T. Calculate the peak value of the electric force acting on a charge of 4 µC placed in the path of the wave. (Take \(c = 3 \times 10^{8}\) m/s.)
A TV transmitting antenna is 245 m tall. Calculate the range of the signal and the area covered by the transmission. (Radius of the Earth \(= 6.4 \times 10^{6}\) m.)
A transmitting antenna of height 45 m and a receiving antenna of height 80 m are used for line of sight communication. Calculate the maximum distance between them for satisfactory transmission. (Radius of the Earth \(= 6.4 \times 10^{6}\) m.)
A radar is mounted on a hill 320 m high. Calculate the maximum distance at which it can detect a ship on the surface of the sea. (Radius of the Earth \(= 6.4 \times 10^{6}\) m.)
A TV tower of height 100 m covers a certain area. To what height must the tower be raised so that the area covered becomes three times as large? (Radius of the Earth \(= 6.4 \times 10^{6}\) m.)
An audio signal of frequency 12 kHz is to be radiated directly from an antenna. Calculate the minimum antenna length (\(\lambda/4\)) required. If the same signal is instead transmitted on a carrier wave of frequency 2 MHz, calculate the new minimum antenna length. (Take \(c = 3 \times 10^{8}\) m/s.)
An EM wave of frequency 60 MHz enters a medium for which \(\mu = \mu_0\) and \(\varepsilon = 4\varepsilon_0\). Calculate the speed of the wave in the medium and its wavelength there, remembering that the frequency does not change on entering the medium. (Take \(c = 3 \times 10^{8}\) m/s.)
Calculate the frequency in MHz of a radio wave of wavelength 250 m. Remember that the speed of all EM waves in vacuum is \(3.0 \times 10^{8}\) m/s.
Calculate the wavelength in nm of an X-ray wave of frequency \(2.0 \times 10^{18}\) Hz.
The speed of light is \(3 \times 10^{8}\) m/s. Calculate the frequency of red light of wavelength \(6.5 \times 10^{-7}\) m.
Calculate the wavelength of a microwave of frequency 8.0 GHz.
In an EM wave the electric field oscillates sinusoidally at a frequency of \(2 \times 10^{10}\) Hz. What is the wavelength of the wave?
The amplitude of the magnetic field part of a harmonic EM wave in vacuum is \(B_0 = 5 \times 10^{-7}\) T. What is the amplitude of the electric field part of the wave?
A TV tower has a height of 200 m. How much population is covered by TV transmission if the average population density around the tower is 1000/km²? (Radius of the Earth \(= 6.4 \times 10^{6}\) m)
The height of a TV tower is 600 m at a given place. Calculate its coverage range if the radius of the Earth is 6400 km. What should be the height to get double the coverage area?
A transmitting antenna at the top of a tower has a height of 32 m and that of the receiving antenna is 50 m. What is the maximum distance between them for satisfactory communication in line of sight mode? Given the radius of the Earth is \(6.4 \times 10^{6}\) m.
13.10 Objective Questions
- The EM wave emitted by the Sun and responsible for heating the Earth’s atmosphere due to the green house effect is
- Infra-red radiation
- X ray
- Microwave
- Visible light
- Earth’s atmosphere is richest in
- UV
- IR
- X-ray
- Microwaves
- How does the frequency of a beam of ultraviolet light change when it travels from air into glass?
- No change
- increases
- decreases
- remains same
- The direction of an EM wave is given by
- \(\vec{E} \times \vec{B}\)
- \(\vec{E} \cdot \vec{B}\)
- along \(\vec{E}\)
- along \(\vec{B}\)
- The maximum distance up to which TV transmission from a TV tower of height \(h\) can be received is proportional to
- \(h^{1/2}\)
- \(h\)
- \(h^{3/2}\)
- \(h^{2}\)
- The waves used by artificial satellites for communication purposes are
- Microwave
- AM radio waves
- FM radio waves
- X-rays
- If a TV telecast is to cover a radius of 640 km, what should be the height of the transmitting antenna?
- 32000 m
- 53000 m
- 42000 m
- 55000 m