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CLUSTER LEVEL PHYSICS WORKSHOP
CLASS-XII
ELECTROMAGNETIC WAVES
One marks questions
The charging current for a capacitor is 0.25 A. what is the displacement current across
its plates?
Displacement current = charging current = 0.25 A.
A variable frequency a.c. source is connected to a capacitor. Will the displacement
current increase or decrease with increase in frequency?
Increase in frequency causes decrease in impedance of the capacitor and consequent
increase in the current. Hence displacement current which equals conduction current
increases with increase in frequency of a.c.
What is the ratio of velocities of light rays of wavelengths 4000 Å and 8000 Å in
vacuum?
Ratio = 1, because light rays of both wavelengths travel with the same velocity of
3x108ms-1 in vacuum.
Name the electromagnetic radiation to which the following wavelengths belong:
(a) 10-2m
(b) 1 Å
(a) Microwaves (b) X-rays.
Arrange the following in the descending order of wavelengths:
 -rays, infrared rays, microwaves, yellow light, radio waves.
Radio waves ˃ infrared rays ˃ red light ˃ yellow light ˃  -rays.
If the wavelength of an electromagnetic radiation is doubled, what will happen to the
energy of photons?
hc
Energy of a photon, E  hv 

When the wavelength of an electromagnetic radiation is doubled, the energy of the
photons is halved.
How does a charge q oscillating at certain frequency produce electromagnetic waves?
Oscillating charge produces sinusoidal variation of electric and magnetic field, which
in turn produces electromagnetic wave.
Identify the following electromagnetic radiation as per the wavelength given below.
(i)
10-12m
(ii) 10-4m
(iii) 106m
(i)
Gamma rays, (ii) Infrared rays, (iii) Radio wave.
Express velocity of propagation of e.m. waves in terms of the peak value of electric &
magnetic fields.
𝐸0
𝐸
= 𝑐 or 𝐵 = 𝑐
𝐵
0
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What is the relation between conduction current and displacement current.
IC = ID
Two marks questions
What is displacement current? Why was this concept introduced?
Displacement current - It is that current which comes into existence, whenever the
electric field and hence the electric flux changes with time. It is equal to 0 times the
rate of change of electric flux through a given surface
d
dE
Id  0 E  0 A
dt
dt
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Maxwell introduced the concept of displacement current for the following
reasons:
(i) To make the Ampere's circuital law logically consistent.
(ii) To satisfy the property of continuity of electric current along any closed path.
A parallel plate capacitor is being charged. Show that the displacement current across
an area in the region between the plates and parallel to it is equal to the conduction
current in the connecting wires.
dq
The conduction current I c 
is not continuous across the capacitor gap as no charge
dt
is transported across this gap.
The displacement current I d is zero outside the capacitor plates and in the gap,
it has the value
d
d
d  q  dq
I d   0 E   0 EA   0   
dt
dt
dt   0  dt
It is exactly the value of the conduction current in the lead wires. Thus the
displacement current satisfies the basic condition that the current is continuous.
The sum I c  I d has the same value along the entire path (both inside and outside
the capacitor plates), although individually the two currents are discontinuous.
What is an electromagnetic wave? Express it graphically
It is the wave radiated by an accelerated charge and which propagates through space
as coupled electric and magnetic fields, oscillating perpendicular to each other and
to the direction of propagation of wave.
The graph showing e m wave is drawn below
A plane electromagnetic wave travels, in vacuum, along the y-direction. Write (i) the
ratio of the magnitudes, and (ii) the directions of its electric and magnetic field
vectors.
E
(i)  c , speed of light.
B
(ii) For an electromagnetic wave travelling along y-direction, its electric and magnetic
 
field vectors are along z-axis and x-axis respectively. The direction of E  B is same
as that of direction of wave propagation and kˆ  iˆ  ˆj.
Name the following constituent radiations of electromagnetic spectrum which :
(i)
Produce intense heating effect.
(ii)
Is absorbed by the ozone layer in the atmosphere.
(iii) Is used for studying crystal structure.
(iv)
Produced during nuclear reactions
(i) Infrared waves.
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(ii) Ultraviolet radiations.
(iii) X-rays.
(iv) Gamma rays
A parallel plate capacitor has circular plates, each of radius 5.0 cm. It is being charged
so that electric field in the gap between its plates rises steadily at the rate of
1012 Vm1 s 1 . What is the displacement current?
d
dE
dE
Displaceme nt current , I d   0 E   0 A
  0 . r 2
dt
dt
dt
12
2
 8.85  10    5  10  1012  0.07 A
Electromagnetic waves travel in a medium at a speed of 2.0 108 ms 1 . The relative
permeability of the medium is 1.0. Find the relative permittivity.
Speed of an e. m.wave in a medium is given by
1
1
v




 r 0  r  0
1
1
0 0
r r
2 

c
r r
c2
r r
hence relative permittivity,
(3  108 ) 2
r 

 2.25
 r 2 1.0  (2  108 ) 2
To which regions of the electromagnetic spectrum the following wavelengths belong?
2000 Ǻ,5000 Ǻ’ 10000 Ǻ and 1.0Ǻ
2000 Ǻ - ultraviolet rays
5000 Ǻ - visible light
10000 Ǻ - infrared rays and
1.0Ǻ - X rays
Which constituent radiations of electromagnetic spectrum is used
(i)
In radar,
(ii)
To photograph internal parts of a human body
(iii) For taking photographs during nights and foggy conditions
(iv)
In water purification
(i)
Microwaves, (ii) X rays, (iii)Infrared rays and (iv) UV rays
Find the wavelength of electromagnetic wave of frequency 4X109Hz in free space.
Give its two applications.
𝑐
3
𝜆 = 𝜈 =3X108/ 4X109 = 40 = 0.075m
This wavelength corresponds to microwaves and is used (i) microwave oven and
(ii) radar
Three marks questions
Mention the various properties of electromagnetic waves.
c2
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These are as follows:
1. The electromagnetic waves are produced by accelerated charges and do not
require any material medium for their propagation.


2. The directions of oscillations of E and B fields are perpendicular to each other
as well as perpendicular to the direction of propagation of the wave. So the
electromagnetic waves are transverse in nature.


3. The oscillations of E and B fields are in same phase.
4. All electromagnetic waves travel in free space with the same speed,
1
c
 3  10 8 ms 1
 0 0
In a material medium, the electromagnetic waves travel with the speed,
1
c
c
v

 , where n is the refractive index of the medium.

r r n
E0
c
B0
6. The electromagnetic waves carry energy as they travel through space and this
energy is shared equally by the electric and magnetic fields. The average
energy density of an e.m. wave is
B2 
1
u  u E  u B   0 E02  0 
2
0 
7. Electromagnetic waves are not deflected by electric and magnetic fields.
8. Electromagnetic waves show the properties of reflection, refraction,
interference, diffraction and polarization.
5. The amplitude ratio of the electric and magnetic fields is
Q.2
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Mention the wavelength range, frequency range and source of production of Radio
Wave, Microwave, Infrared Rays and Visible light, give the important properties and
uses of each part.
Radio waves – These are the e. m. waves of longest wavelength and minimum
frequency.
Wavelength range - 600m to 0.1 m
Frequency range 500 KHz to 100 MHz.
Source Accelerated motion of charges in conducting wires or
oscillating circuits.
Uses: (i) In radio and television communication systems.
(ii) In radioastronomy.
Microwaves - They are the e. m. waves having wavelength next smaller to
radiowaves. Due to their shorter wavelength, they can travel as a beam.
Wavelength range 0.3 m to 10 3 m
10 9 Hz to1012 Hz
Frequency range Source Oscillating currents in special vacuum tubes like
Klystrons and Magnetrons.
Uses: (i) In radar systems for aircraft navigation.
(ii)In long-distance communication systems via geostationary satellites.
(iii) In microwave ovens.
Infrared rays – These rays produce heating effect, so they are also known as
heat waves or thermal radiation.
5  10 3 m to 10 6 m
Wavelength range 1011 Hz to 5  1014 Hz
Frequency range Source Hot bodies and molecules.
Uses:
(i) In the remote control of a TV or VCR.
(ii) In green houses to keep the plants warm.
(iii) In haze photography because infrared waves are less scattered than
visible light by atmospheric particles.
(iv) Infrared lamps in the treatment of muscular complaints.
(v) In reading the secret writings on the ancient walls
(vi) In knowing the molecular structure.
Visible light - It is very small part of the e.m. spectrum towards which the
human retina is sensitive.
8  10 7 m to 4  10 7 m
Wavelength range 4  1014 Hz to 7  1014 Hz
Frequency range Source Radiated by excited atoms in ionized gas and
incandescent bodies.
Uses: (i) It provides us the sensation of vision.
(ii) It can cause photo-chemical reactions.
Q.3
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Giving the wavelength range, frequency range and source of production of Ultra violet
Rays, X-Rays and Gamma Rays, give the important properties and uses of each part.
Ultraviolet rays - This region of the e.m. spectrum has wavelengths just
shorter than visible light.
3.5  10 7 m to 1.5  10 7 m
Wavelength range
1016 Hz to 1017 Hz
Frequency range Source High voltage gas discharge tubes
Uses: (i) In food preservation.
(ii) In the study of invisible writings, forged documents and finger
prints.
(iii) In the study of molecular structure.
X-rays - These e.m. waves have wavelengths just shorter than ultraviolet light.
As X-rays can pass through many forms of matter, so they have many useful
medical and industrial applications.
Wavelength range
10-8m to 10-11m
1018 Hz to 10 20 Hz
Frequency range
Source
Sudden deceleration of fast moving electrons
by a metal target.
Uses: (i) In medical diagnosis because X-rays can pass through flesh but not
through bones.
(ii)In the study of crystals structure.
(iii) In engineering for detecting faults, cracks, flaws and holes in the
finished metal products.
(iv) In detective departments to detect explosives, diamond, gold etc.
(v) In radiotherapy to cure untraceable skin diseases and malignant
growths.
Gamma rays - These are e.m. radiations of highest frequency range and
lowest wavelength range. These are most penetrating e.m. waves.
10 14 m to 1010 m
Wavelength range
-
Frequency range
1018 Hz to 10 22 Hz
Source
Radioactive nuclei and nuclear reactions.
Uses: (i) In radiotherapy for the treatment of malignant tumours.
(ii) In the manufacture of polyethylene from ethylene.
(iii) To preserve food stuffs for a long time.
(iv) To study the structure of atomic nuclei.
Q.4
Electromagnetic waves with wavelength
(i)
1 are used to treat muscular strain.
(ii)
2 are used by a FM radio station for broadcasting.
3 are used to detect fracture in bones.
(iii)
(iv)
4 areabsorbed by the ozone layer of the atmosphere.
Identify and name the part of electromagnetic spectrum to which these
radiations belong. Arrange these wavelengths in decreasing order of
magnitude.
Ans.
(i )
1  Infra red radiations
ii  2  radiwaves
iii  3  X  rays
iv  4  Ultraviolet rays
The wavelengths in decreasing order of magnitude are: 2  1  4  3 .
Q.5
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When can a charge act as a source of electromagnetic waves? How are the directions,
of the electric and magnetic field vectors, in an electromagnetic wave, related to each
other and to the direction of propagation of the wave?
Which physical quantity, if any, has the same value for waves belonging to the
different parts of the electromagnetic spectrum?
Only an accelerated charge can act as a source of electromagnetic waves.
The directions of electric and magnetic field vectors are perpendicular to each other as
well as to direction of propagation of the wave.
The wave speed in vacuum has the same value for all the waves.
Q.6
The
Ans.
Given
magnetic field in a plane electromagnetic wave
By  2 10 7 sin 0.5 103 x  1.5 1011 t tesla.
(a) What is the wavelength and frequency of the wave?
(b) Write an expression for the electric field.



is

By  2 10 7 sin 0.5 103 x  1.5 1011 t tesla
 x

On comparing with the standard equation, BY  B0 sin 2   vt 

 
2
We get ,
 0.5 103



2
2  3.14

 1.26 10  2 m
3
0.5 10
0.5 103
given
by
Also, 2 v  1.5  1011
1.5  1011 1.5  1011

v

 23.9  10 9 Hz  23.9 GHz.
2
2  3.14
8
(b) E0  cB0  3  10  2  10 7  60 Vm 1 .
The electric field is perpendicular to the direction of propagation (x-axis) and
the direction of magnetic field (y-axis). So the expression for electric field is
E z  E 0 sin 0.5  10 3 x  1.5  1011 t Vm 1

