Displacement Current
While charging a capacitor, Maxwell found an inconsistency in the Ampere’s law.
Maxwell suggested the existence of an additional current, called displacement current, to remove this inconsistency.
This displacement current is due to time-varying electric field and is given by
id = εo (dϕE/dt)
and acts as a source of magnetic field in exactly the same way as conduction current.
Maxwell’s Equations
Electromagnetic Waves
Electromagnetic waves are those waves in which there are sinusoidal variations of electric and magnetic field vectors at right angles to each other as well as at right angles to the direction of wave propagation.
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Sources of electromagnetic waves
Accelerated charges radiate electromagnetic waves. An oscillating charge is an example of accelerating charge. Electromagnetic waves are also produced when fast moving electrons are suddenly stopped by a metallic surface of high atomic number.
Nature of Electromagnetic Waves
Electric and magnetic fields oscillate sinusoidally in space and time in an electromagnetic wave. The oscillating electric and magnetic fields, E and B are perpendicular to each other, and to the direction of propagation of the electromagnetic wave. For a wave of frequency ν, wavelength λ, propagating along z-direction, we have
Note: Eo/Bo = c, where c is velocity of light.
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Speed of Electromagnetic Wave
The speed c of electromagnetic wave in vacuum is related to μ0 and ε0 (the free space permeability and permittivity constants) as follows:
Electromagnetic waves other than light also have the same velocity c in free space.
The speed of light, or of electromagnetic waves in a material medium is given by
where μ is the permeability of the medium and ε its permittivity.
Electromagnetic Spectrum
Different Types of Electromagnetic Waves
Type (Wavelength) | Production | Detection |
Radio (> 0.1 m) | Rapid acceleration and decelerations of electrons in aerials | Receiver’s aerials |
Microwave (0.1m to 1 mm) | Klystron valve or magnetron valve | Point contact diodes |
Infra-red (1 mm to 700 nm) | Vibration of atoms and molecules | Thermopiles Bolometer, Infrared photographic film |
Visible light (700 nm to 400 nm) | 700 nm to 400 nm | Electrons in atoms emit light when they move from one energy level to a lower energy level |
Ultraviolet (400 nm to 1nm) | Inner shell electrons in atoms moving from one energy level to a lower level | Photocells, Photographic film |
X-rays (1nm to 10‒3 nm) | X-ray tubes or inner shell electrons | Photographic film, Geiger tubes, Ionisation chamber |
Gamma rays (< 10‒3 nm) | Radioactive decay of the nucleus |
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.
Microwaves
Microwaves (short-wavelength radio waves), with frequencies in the gigahertz (GHz) range.
They 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.
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Infrared waves
Infrared waves are sometimes referred to as heat waves.
Infrared waves are produced by hot bodies and molecules.
Infrared radiation plays an important role in maintaining the earth’s warmth or average temperature through the greenhouse effect.
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.
Ultraviolet rays
It covers wavelengths ranging from about 4 × 10–7 m (400 nm) down to 6 × 10–10 m (0.6 nm).
Ultraviolet (UV) radiation is produced by special lamps and very hot bodies.
The sun is an important source of ultraviolet light.
Ultraviolet radiations can be focussed into very narrow beams for high precision applications such as LASIK (Laser assisted in situ keratomileusis) eye surgery.
Ultraviolet lamps are used to kill germs in water purifiers
X-rays
It covers wavelengths from about 10‒8 m (10 nm) down to 10‒13 m (10‒4 nm).
One common way to generate X-rays is to bombard a metal target by high energy electrons.
X-rays are used as a diagnostic tool in medicine and as a treatment for certain forms of cancer.
Gamma rays
The wavelengths of Gamma rays are from about 10‒10 m to less than 10‒14 m.
Gamma rays are produced in nuclear reactions and also emitted by radioactive nuclei.
They are used in medicine to destroy cancer cells.
CBSE Class 12 Physics Important Questions Chapter 8 – Electromagnetic Waves
1 Mark Questions
1. The charging current for a capacitor is 0.25A. What is the displacement current across its plates?
Ans. Displacement current remains the same as charging current and is equal to 0.25A.
2. Write the following radiations in a descending order of frequencies: red light, x – rays, microwaves, radio waves
Ans. X – rays, Red light, Microwaves and Radio waves.
3. How does the frequency of a beam of ultraviolet light change, when it goes from air into glass?
Ans. There is no effect on the frequency of ultraviolet light.
4. What is the ratio of speed of gamma rays and radio waves in vacuum?
Ans. One.
5. It is necessary to use satellites for long distance TV transmission. Why?
Ans. Television signals are not reflected back by the layer of atmosphere called ionosphere thus TV signals from air earth station are reflected back to the earth
by means of an artificial satellite
6. What is the role of ozone layer in the atmosphere?
Ans. It absorbs all the harmful ultraviolet radiations thus protecting us from reaching the dangerous effects of uv radiations.
7. What is the nature of waves used in radar?
Ans. Microwaves are used in Radar.
8. What physical quantity is the same for X-rays of wavelength 10-10 m, red light of wavelength 6800 
and radio waves of wavelength 500 m?
Ans. The speed of light (
m/s) in a vacuum is the same for all wavelengths. It is independent of the wavelength in the vacuum.
2 Marks Questions
1. Write the application of Infra-red radiations?
Ans. (1) infra-red radiations are used to take photographs under foggy conditions.
(2) Infra-red radiations are used in revealing the secret writings on the ancient walls.
2. Which constituent radiation of the electromagnetic spectrum is used?
(1) To photograph internal parts of human body.
(2) For air aircraft navigation
Ans. (1) X -Rays
(2) Microwaves
3. Electric field in a plane electromagnetic wave is given by
(a) Write an expression for the magnetic field
(b) What is the magnitude of wavelength and frequency of the wave?
Ans. (a) 
Since magnetic field and electric field are 
to each other
—-(1)
Compare e.g. (1) with standard equation
By = BO sin 
4. IF the earth did not have atmosphere would its average surface temperature be higher or lower than what it is now?
Ans. The infra-red radiations get trapped inside the earth’s atmosphere due to green house effect which makes the earth warm. Therefore average temperature of the earth would have been low.
5. Sky waves are not used in transmitting TV signals, Why? Suggest two methods by which range of TV transmission can be increased?
Ans. Sky waves are not used in transmitting TV signals as they are not reflected by the ionosphere.
Methods of increasing range of TV transmission
(1) Tall antenna
(2) Geostationary satellites
6. “Greater the height of a TV transmitting antenna, greater is its coverage.” Explain.
Ans. Since d = 
If height is increased distance upto which TV coverage can be done will increases.
7. A plane electromagnetic wave travels in vacuum along z-direction. What can you say about the directions of its electric and magnetic field vectors? If the frequency of the wave is 30 MHz, what is its wavelength?
Ans. The electromagnetic wave travels in a vacuum along the z-direction. The electric field (E) and the magnetic field (H) are in the x–y plane. They are mutually perpendicular.
Frequency of the wave, 
= 30 MHz = 
Speed of light in a vacuum, c = 
m/s
Wavelength of a wave is given as:
8. A radio can tune in to any station in the 7.5 MHz to 12 MHz band. What is the corresponding wavelength band?
Ans. A radio can tune to minimum frequency, 
= 7.5 MHz=
Maximum frequency, 
= 12 MHz = 
Speed of light, c = m/s
Corresponding wavelength for can be calculated as:
Corresponding wavelength for v 
can be calculated as:
Thus, the wavelength band of the radio is 40 m to 25 m.
9. A charged particle oscillates about its mean equilibrium position with a frequency of 
Hz. What is the frequency of the electromagnetic waves produced by the oscillator?
Ans. The frequency of an electromagnetic wave produced by the oscillator is the same as that of a charged particle oscillating about its mean position i.e., 
Hz.
10. The amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is 
= 510 nT. What is the amplitude of the electric field part of the wave?
Ans. Amplitude of magnetic field of an electromagnetic wave in a vacuum,
B0 = 510 nT =
Speed of light in a vacuum, c =
Amplitude of electric field of the electromagnetic wave is given by the relation,
E 
=
= 153 N/C
Therefore, the electric field part of the wave is 153 N/C.
3 Marks Questions
1. In a plane electromagnetic wave, the electric field oscillates sinusoid ally with a frequency of 
and amplitude 48V/m.
(a) What is the wavelength of the em. wave?
(b) Calculate the amplitude of the oscillating magnetic field.
(c) Calculate average energy density of the electromagnetic field of the wave?
Ans. (a) V =
EO = 48 V/m
(b) EO = cBO
(c) Energy density
2. Find the wavelength of electromagnetic waves of frequency 
in free space. Give two applications of the type of wave.
Ans. V = 
These are infra-red radiations
Applications
(1) It keeps the earth warm.
(2) Infra-red lamps are used to treat muscular strains.
3. A plane monochromatic wave lies in the visible region. It is represented by the sinusoidal variation with time by the following components of electric field
Ex = 0, Ey = 4 sin 
Ez = 0
Where 
And 
is the wavelength of light.
(a) What is the direction of propagation of the wave?
(b) What is its amplitude?
(c) Compute the component of magnetic field?
Ans. (a) The direction of propagation of wave is along + x – axis.
(b) Amplitude = 4 units
(c) Component of magnetic of field
4. Write the characteristics of em waves? Write the expression for velocity of electromagnetic waves in terms of permittivity and permeability of the medium?
Ans. Characteristics of em waves
(1) It travels in free space with speed of light 
(2) Electromagnetic waves are transverse in nature.
Velocity of em waves in vacuum C
= 
5. The electric field of a plane electromagnetic wave in vacuum is represented by.
Ex = 0, Ey = 0.5 cos 
and Ez = 0
(a) What is the direction of propagation of electromagnetic wave?
(b) Determine the wavelength of the wave?
(c) Compute the component of associated magnetic field?
Ans. (a) The equation Ey = 0.5 cos
Represents wave is propagating along + x – axis
(b) Comparing equation with the standard one
Ey = EO cos w 
(c) Associated magnetic field is 
to electric field and the direction of propagation. Since wave is propagating along x – axis, electric field is along, y – axis
Thus, magnetic field is along z – axis
6. Find the wavelength of electromagnetic waves of frequency 
in free space. Give its two applications.
Ans.
These are Gamma Rays.
Applications
(1) These rays are used to get information regarding atomic structure.
(2) They have very high penetrating power so they are used for detection purpose
7. (1) State the condition under which a microwave oven heats up food items containing water molecules most efficiently?
(2) Name the radiations which are next to these radiations in em. Spectrum having (a) Shorter wavelength (b) Longer wavelength
Ans. (1) Frequency of the microwaves must be equal to the resonant frequency of the water molecules present in the food item.
(2) (a) visible light
(b) Microwaves
8. The terminology of different parts of the electromagnetic spectrum is given in the text. Use the formula E = 
(for energy of a quantum of radiation: photon) and obtain the photon energy in units of eV for different parts of the electromagnetic spectrum. In what way are the different scales of photon energies that you obtain related to the sources of electromagnetic radiation?
Ans. Energy of a photon is given as:
Where,
h = Planck’s constant =
c = Speed of light = 
m/s
= Wavelength of radiation
The given table lists the photon energies for different parts of an electromagnetic spectrum for different .
| (m) | E (eV) |
| 103 |  |
| 1 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
The photon energies for the different parts of the spectrum of a source indicate the spacing of the relevant energy levels of the source.
9. About 5% of the power of a 100 W light bulb is converted to visible radiation. What is the average intensity of visible radiation
(a) at a distance of 1 m from the bulb?
(b) at a distance of 10 m?
Assume that the radiation is emitted isotropic ally and neglect reflection.
Ans. Power rating of bulb, P = 100 W
It is given that about 5% of its power is converted into visible radiation.
Power of visible radiation,
Hence, the power of visible radiation is 5W.
(a) Distance of a point from the bulb, d = 1 m Hence, intensity of radiation at that point is given as:
(b) Distance of a point from the bulb, 
= 10 m Hence, intensity of radiation at that point is given as:
10. Use the formula 
T= 0.29 cm K to obtain the characteristic temperature ranges for different parts of the electromagnetic spectrum. What do the numbers that you obtain tell you?
Ans. A body at a particular temperature produces a continuous spectrum of wavelengths. In case of a black body, the wavelength corresponding to maximum intensity of radiation is given according to Planck’s law. It can be given by the relation,
Where, = maximum wavelength
T = temperature
Thus, the temperature for different wavelengths can be obtained as:
For =
;
For =
;
For = 
cm;
and so on.
The numbers obtained tell us that temperature ranges are required for obtaining radiations in different parts of an electromagnetic spectrum. As the wavelength decreases, the corresponding temperature increases
5 Marks Questions
1. Given below are some famous numbers associated with electromagnetic radiations in different contexts in physics. State the part of the electromagnetic spectrum to which each belongs.
(a) 21 cm (wavelength emitted by atomic hydrogen in interstellar space).
(b) 1057 MHz (frequency of radiation arising from two close energy levels in hydrogen; known as Lamb shift).
(c) 2.7 K [temperature associated with the isotropic radiation filling all space-thought to be a relic of the ‘big-bang’ origin of the universe].
(d) 5890 
– 5896 [double lines of sodium]
(e) 14.4 keV [energy of a particular transition in 57Fe nucleus associated with a famous high resolution spectroscopic method
(Mossbauer spectroscopy)].
Ans. (a) Radio waves; it belongs to the short wavelength end of the electromagnetic spectrum.
(b) Radio waves; it belongs to the short wavelength end.
(c) Temperature, 
is given by Planck’s law as:
This wavelength corresponds to microwaves.
(d) This is the yellow light of the visible spectrum.
(e) Transition energy is given by the relation,
E = 
Where,
h = Planck’s constant =
= Frequency of radiation
Energy, E = 14.4 K eV
This corresponds to X-rays.
2. Answer the following questions:
(a) Long distance radio broadcasts use short-wave bands. Why?
(b) It is necessary to use satellites for long distance TV transmission. Why?
(c) Optical and radio telescopes are built on the ground but X-ray astronomy is possible only from satellites orbiting the earth. Why?
(d) The small ozone layer on top of the stratosphere is crucial for human survival. Why?
(e) If the earth did not have an atmosphere, would its average surface temperature be higher or lower than what it is now?
(f) Some scientists have predicted that a global nuclear war on the earth would be followed by a severe ‘nuclear winter’ with a devastating effect on life on earth. What might be the basis of this prediction?
Ans. (a) Long distance radio broadcasts use shortwave bands because only these bands can be refracted by the ionosphere.
(b) It is necessary to use satellites for long distance TV transmissions because television signals are of high frequencies and high energies. Thus, these signals are not reflected by the ionosphere. Hence, satellites are helpful in reflecting TV signals. Also, they help in long distance TV transmissions.
(c) With reference to X-ray astronomy, X-rays are absorbed by the atmosphere. However, visible and radio waves can penetrate it. Hence, optical and radio telescopes are built on the ground, while X-ray astronomy is possible only with the help of satellites orbiting the Earth.
(d) The small ozone layer on the top of the atmosphere is crucial for human survival because it absorbs harmful ultraviolet radiations present in sunlight and prevents it from reaching the Earth’s surface.
(e) In the absence of an atmosphere, there would be no greenhouse effect on the surface of the Earth. As a result, the temperature of the Earth would decrease rapidly, making it chilly and difficult for human survival.
(f) A global nuclear war on the surface of the Earth would have disastrous consequences. Post-nuclear war, the Earth will experience severe winter as the war will produce clouds of smoke that would cover maximum parts of the sky, thereby preventing solar light form reaching the atmosphere. Also, it will lead to the depletion of the ozone layer.
3. Suppose that the electric field part of an electromagnetic wave in vacuum is E = {(3.1 N/C) cos [(1.8 rad/m) y + (
rad/s)t]}
.
(a) What is the direction of propagation?
(b) What is the wavelength
?
(c) What is the frequency
?
(d) What is the amplitude of the magnetic field part of the wave?
(e) Write an expression for the magnetic field part of the wave.
Ans. (a) From the given electric field vector, it can be inferred that the electric field is directed along the negative x direction. Hence, the direction of motion is along the negative y direction i.e., 
.
(b) It is given that,
…(i)
The general equation for the electric field vector in the positive x direction can be written as:
…(2)
On comparing equations (1) and (2), we get
Electric field amplitude, 
= 3.1 N/C
Angular frequency, 
Wave number, k = 1.8 rad/m
Wavelength, 
= 3.490 m
(c) Frequency of wave is given as:
(d) Magnetic field strength is given as:
Where,
c = Speed of light =
(e) On observing the given vector field, it can be observed that the magnetic field vector is directed along the negative z direction. Hence, the general equation for the magnetic field vector is written as:
4. In a plane electromagnetic wave, the electric field oscillates sinusoid ally at a frequency of 
and amplitude 48 V
.
(a) What is the wavelength of the wave?
(b) What is the amplitude of the oscillating magnetic field?
(c) Show that the average energy density of the E field equals the average energy density of the B field. [c =
]
Ans. Frequency of the electromagnetic wave, 
Electric field amplitude, 
Speed of light, c =
(a) Wavelength of a wave is given as:
(b) Magnetic field strength is given as:
(c) Energy density of the electric field is given as:
And, energy density of the magnetic field is given as:
Where,
∈0 = Permittivity of free space
= Permeability of free space
We have the relation connecting E and B as:
E = cB … (1)
Where,
… (2)
Putting equation (2) in equation (1), we get
Squaring both sides, we get
5. Suppose that the electric field amplitude of an electromagnetic wave is 
= 120 N/C and that its frequency is 
= 50.0 MHz. (a) Determine,
(b) Find expressions for E and B.
Ans. Electric field amplitude, 
= 120 N/C
Frequency of source, = 50.0 MHz = 
Speed of light, c = 
m/s
(a) Magnitude of magnetic field strength is given as:
Angular frequency of source is given as:
=
Propagation constant is given as:
Wavelength of wave is given as:
(b) Suppose the wave is propagating in the positive x direction. Then, the electric field vector will be in the positive y direction and the magnetic field vector will be in the positive z direction. This is because all three vectors are mutually perpendicular.
Equation of electric field vector is given as:
And, magnetic field vector is given as:
6. A parallel plate capacitor (Fig. 8.7) made of circular plates each of radius R = 6.0 cm has a capacitance C = 100 pF. The capacitor is connected to a 230 V ac supply with a (angular) frequency of 300 rad
.
(a) What is the rms value of the conduction current?
(b) Is the conduction current equal to the displacement current?
(c) Determine the amplitude of B at a point 3.0 cm from the axis between the plates.
Ans. Radius of each circular plate,
R = 6.0 cm = 0.06 m
Capacitance of a parallel plate capacitor,
C = 100 pF =
Supply voltage, V = 230 V
Angular frequency, 
= 300 rad 
(a) Rms value of conduction current, I 
Where,
XC = Capacitive reactance
=
= 6.9 
Hence, the rms value of conduction current is 6.9 
(b) Yes, conduction current is equal to displacement current.
(c) Magnetic field is given as:
B 
Where,
= Free space permeability 
I0 = Maximum value of current =
r = Distance between the plates from the axis = 3.0 cm = 0.03 m
= 
Hence, the magnetic field at that point is 
7. Figure 8.6 shows a capacitor made of two circular plates each of radius 12 cm, and separated by 5.0 cm. The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to 0.15 A.
(a) Calculate the capacitance and the rate of charge of potential difference between the plates.
(b) Obtain the displacement current across the plates.
(c) Is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor? Explain.
Ans. Radius of each circular plate,
r = 12 cm = 0.12 m
Distance between the plates,
d = 5 cm = 0.05 m
Charging current,
I = 0.15 A
Permittivity of free space,
=
(a) Capacitance between the two plates is given by the relation,
C 
Where,
A = Area of each plate 
Charge on each plate, q = CV
Where,
V = Potential difference across the plates
Differentiation on both sides with respect to time (t) gives:
Therefore, the change in potential difference between the plates is 
V/s.
(b) The displacement current across the plates is the same as the conduction current. Hence, the displacement current, id is 0.15 A.
(c) Yes
Kirchhoff’s first rule is valid at each plate of the capacitor provided that we take the sum of conduction and displacement for current.