# Electromagnetic Waves Class 12 notes Physics Chapter 8

Introduction, Maxwell’s Equations, Displacement Current, Conduction Current, Electromagnetic Waves, Ampere Circuital Law, Electromagnetic Spectrum,

## Introduction

In this chapter, we will study regarding displacement current, electromagnetic waves and its various parts and their uses. Electromagnetic waves in the form of visible light enable us to view the world around us. Infrared waves warm our environment. Radio waves carry our favourite TV and radio programs and the list goes on and on.

### History of EMW

• Maxwell: was the first to predict the presence of electromagnetic waves.

• Hertz: produced and detected electromagnetic waves of wavelength 6 m experimentally.

• J.C. Bose: the produced electromagnetic wave of wavelength ranging from 5 mm to 25 mm.

• Marconi: successfully transmitted the EM waves up to a few kilometers. Marconi discovered that if one of the spark gap terminals is connected to an antenna and the other terminal is earthed, the EM waves radiated could go up to several kilometers.

## Maxwell’s Equations

Maxwell’s equations relate electric field E and magnetic field B and their sources which are electric charges and current. In free space, Maxwell’s equations are as follows.

1. \oint\vec{E}.d\vec{S}=\frac{q}{\epsilon_0}

This equation represents Gauss’s law in electrostatics.

2. \oint\vec{B}.d\vec{S}=0

This equation is considered Gauss’s law in magnetism. It states that the net magnetic flux passing through a closed surface is zero.

3. \oint\vec{E}.d\vec{l}=\frac{d\phi}{dt}

This equation is Faraday’s law of electromagnetic induction. This law relates the electric field with changing magnetic flux.

4. \oint\vec{B}.d\vec{l}=\mu_{0}(I_{c}+I_{d})

This equation represents Ampere-Maxwell’s law or a generalized form of Ampere's law.

## Displacement Current

Displacement current is a current which is produced due to the rate of change of electric flux with respect to time. Displacement current is given by

I_{d}=\epsilon_{0}\frac{d\phi_E}{dt}

This current Id passes through the surface A and is known as Maxwell displacement current.

## Electromagnetic Waves

Electromagnetic waves or EM waves are waves that are created as a result of vibrations between an electric field and a magnetic field. In other words, EM waves are composed of oscillating magnetic and electric fields.

### (i). Sources of electromagnetic waves

1. An electric charge at rest produces only an electrostatic field around it.

2. A charge moving with uniform velocity produces both electric and magnetic fields, here magnetic field does not change with time hence it does not produce a time-varying electric field.

3. An accelerating charge produces both an electric field and magnetic field which varies with space and time and forms electromagnetic waves.

4. An accelerating charge emits an electromagnetic wave of the same frequency as the frequency of an accelerating charge.

5. An electron orbiting around its nucleus in a stationary orbit does not emit an electromagnetic wave. It will emit only during the transition from higher energy orbit to lower energy orbit.

6. An electromagnetic wave (X-ray) is produced when a high-speed electron enters a target of high atomic weight.

7. Electromagnetic wave (γ-rays) is produced during the de-excitation of the nucleus in radioactivity.

### (ii). Nature of electromagnetic waves

1. It travels in free space with speed equal to 3 × 108 m/s which is given by c=\frac{1}{sqrt{\mu_{0}\epsilon_{0}}}.

2. These waves do not require a material medium for their propagation.

3. \vec{E} and \vec{B} become maximum at the same place and at the same time, but perpendicular to each other as well as to the direction of propagation. Therefore the phase difference between the two fields is zero. The amplitude of electric and magnetic fields are related to each other as c=\frac{E}{B}. The direction of propagation can be determined by \vec{E}\times\vec{B}.

4. The velocity of an electromagnetic wave in a medium is decided by the electric and magnetic properties of the medium, not by the amplitude of the electric and magnetic field vector.

5. The energy carried by an electromagnetic wave is equally divided between the electric field and the magnetic field. Total average energy density u=\frac{1}{2}\epsilon_{0}E^2=\frac{1}{2}\frac{B^2}{\mu_0}.

6. An electromagnetic wave is not deflected by an electric field as well as a magnetic field because it consists of uncharged particles called photons.

7. Electromagnetic waves carry energy as well as momentum.

## Electromagnetic Spectrum

The orderly distribution of electromagnetic radiations according to their frequency (or wavelength) is called the electromagnetic spectrum. Maxwell predicted the existence of an electromagnetic wave. Electromagnetic wave experimentally discovered by Hertz.

At the end of the nineteenth century, visible light, ultraviolet, infrared, X-rays, and γ-rays had also been discovered. We now know that electromagnetic waves include (i) γ-rays (ii) X-ray (iii) ultraviolet rays (iv) visible light (v) infrared (vi) microwaves (vii) radio waves.

There is no sharp division between one kind of wave and the next. The classification is based roughly on how the waves are produced and/or detected.

### (i). Radio waves

Radio waves are produced by the accelerated motion of charges in conducting wires. They are used in radio and television communication systems. They are generally in the frequency range from 500 kHz to about 1000 MHz. Cellular phones use radio waves to transmit voice communication in the ultrahigh-frequency (UHF) band.

### (ii). Microwaves

Microwaves, with frequencies in the gigahertz (GHz) range, are produced by special vacuum tubes (called klystrons, magnetrons, and Gunn diodes). Due to their short wavelengths, they are suitable for the radar systems used in aircraft navigation. Radar also provides the basis for the speed guns used to time fastballs, tennis serves, and automobiles. Microwave ovens are an interesting domestic application of these waves.

### (iii). Infrared waves

Infrared waves are produced by hot bodies and molecules. This band lies adjacent to the low-frequency or long-wavelength end of the visible spectrum. Infrared waves are sometimes referred to as heat waves. This is because water molecules present in most materials readily absorb infrared waves.

Infrared lamps are used in physical therapy. Infrared radiation also plays an important role in maintaining the earth’s warmth or average temperature through the greenhouse effect. Infrared detectors are used in Earth satellites, both for military purposes and to observe the growth of crops.

#### # Greenhouse Effect

The greenhouse effect is a natural process that warms the Earth’s surface. When the Sun’s energy reaches the Earth’s atmosphere, some of it is reflected back to space and the rest is absorbed and re-radiated by greenhouse gases. Greenhouse gases include water vapor, carbon dioxide, methane, nitrous oxide, ozone, and some artificial chemicals such as chlorofluorocarbons (CFCs).

The absorbed energy warms the atmosphere and the surface of the Earth. This process maintains the Earth’s temperature at around 33 degrees Celsius warmer than it would otherwise be, allowing life on Earth to exist.

### (iv). Visible rays

It is the part of the spectrum that is detected by the human eye. It runs from about 4 × 1014 Hz to about 7 × 1014 Hz or a wavelength range of about 700 – 400 nm. Visible light emitted or reflected from objects around us provides us information about the world.

Our eyes are sensitive to this range of wavelengths. Different animals are sensitive to different ranges of wavelengths. For example, snakes can detect infrared waves, and the ‘visible’ range of many insects extends well into the ultraviolet.

### (v). Ultraviolet rays

Ultraviolet (UV) radiation is produced by special lamps and very hot bodies. The sun is an important source of ultraviolet light. But fortunately, most of it is absorbed in the ozone layer in the atmosphere at an altitude of about 40 – 50 km. UV light in large quantities has harmful effects on humans.

Welders wear special glass goggles or face masks with glass windows to protect their eyes from the large amount of UV produced by welding arcs. Due to its shorter wavelengths, UV radiations can be focussed into very narrow beams for high-precision applications such as LASIK (Laser-assisted in situ keratomileusis) eye surgery. UV lamps are used to kill germs in water purifiers.

### (vi). X-rays

Its frequency order is 1016 Hz to 1021 Hz. Its wavelength lies between 10 nm to 10-4 nm. It is produced in a tube called a modern X-ray tube. It is detected by photographic film, Geiger tubes and an ionization chamber.

X-rays are used as a diagnostic tool in medicine and as a treatment for certain forms of cancer. In engineering, it is used for detecting faults, cracks, flaws, and holes. It is used for detecting pearls in oysters, defects in rubber tires, and golds.

### (vii). Gamma rays

They lie in the upper-frequency range of the electromagnetic spectrum and have wavelengths from about 10-10 m to less than 10-14 m. This high-frequency radiation is produced in nuclear reactions and is also emitted by radioactive nuclei. They are used in medicine to destroy cancer cells.

 Different Types of Electromagnetic Waves

## Summary

• Maxwell developed Ampere’s circuital law, but later in the process of charging a capacitor, Maxwell found this equation incomplete. To make Ampere’s law complete, Maxwell gave the concept of displacement current and modified Ampere’s circuital law.

• Putting Gauss’s law, Faraday’s law of EMW, and modified Ampere’s law together Maxwell observed symmetry between electric and magnetic fields. These laws together are called Maxwell’s four equations, solutions of which predicted the presence of EM waves.

• Displacement current exists where the electric field changes with time.

• During the charging of a capacitor, the conduction current in the wire and displacement current in the gap is exactly equal.

• Sinusoidal EM waves are analogous to sinusoidal transverse mechanical waves on a stretched string.

• The vector product E x B always points in the direction of propagation.

• All EM waves travel with same speed c = 1 / √μ0ε0 in vacuum c = 299792458 m/s in vacuum.

• All EM waves are transverse in nature hence they can be polarized because polarization is the sure check of the transverse nature of a wave.

• Average energy in an electric field and that in the magnetic field in an EM wave is the same.

• The momentum carried by the EM wave is given by the Energy / Speed of light.

• Hertz’s experiment confirmed that accelerating charges produce EM waves.

• Complete Electromagnetic spectrum (also called Maxwell’s rainbow) in decreasing order of frequency are cosmic rays, γ-rays, X-rays, UV-radiation, visible radiation, infrared radiation, microwaves, and radio waves.

• Amplitude modulated medium waves (MW) also called ground waves are confined to the troposphere. They are vertically polarized. The frequency ranges from (500 to 1600 kHz).

• Amplitude modulated short waves (SW), also called sky waves are reflected by the ionosphere. Frequency ranges from 1500 kHz to 40 MHz

• Frequency-modulated waves of TV signals penetrate the entire atmosphere and are not reflected by the ionosphere so they require direct transmission.

• X-ray astronomy is possible only from satellites outside the earth’s atmosphere because the atmosphere absorbs the X-rays.