EL ECTROM CTROMAGNETI C W AVES AVES
Preface
As you have gone through through the theory part part that consists consists of given fundamental principles, principles, definitions, concepts involved and solved problems. After going through theory part it becomes necessary to solve the unsolved problems based on the concepts given. To To solve this t his purpose we we are providi ng exercise part that comprises of vario us exercises based based on the theory. By solving v arious kinds of problems you can check your grasp on the topic and can determine whether you have been able to find optimum depth in relevant topic or not. Students are advised to solve the questions of exercises (Levels # 1, 2, 3, 4) in the same sequence or as directed by the faculty members, religiously and very carefully. Level # 3 is not for f oundation course students, students, it will be discussed in fresher or target courses. The list of exercises is as following :
Total number of Questions Q uestions in this thi s chapter are : (i) Lev el # 1
. .. .. .. . . . . . .. .. . . . . .. .
31
(ii) Lev el # 2
.......................
18
(iii) Lev el # 3
.......................
28
Total otal no . of questions ..... ....... .... .... .... .... ..... ..... .... .... 77
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LEVEL # 1 Q.6
The S.I unit of displacement current is-
The rate of change of voltage of a parallel plate capacitor if the instantaneous displacement current of 1A is established between the two plates of a 1µF parallel plate capacitor
(A) Henry
(B) Coulomb
(A) 106v/s
(B) 10v/s
(C) Ampere
(D) Farad
(C) 108v/s
(D) 10 –6v/s
Maxwell's concept of EMW displacement current Q.1
Q.2
Displacement current is same as(A) conduction current due to flow of free electrons (B) conduction current due to flow of positive ions
Questions based on
Q.7
The relation between electric field E and magnetic field H in an electromagnetic wave is-
(C) conduction curent due to flow of both positive and negative free charge carriers
Q.3
Properties o f EMW
(D) is not a conduction current but i s caused by time varying electric field
(A) E = H
The maxwell’s equation :
(C) E =
dE B . dl = µ 0 i 0 . dt is a statement of
Q.8
(B) E = µ0
0
(B) Modified Ampere’s law (C) Gauss’s law of electricity
(A) E =
µ0
0 B
(D) Gauss’s law of magnetism (C) E = Q.4
Maxwell’s equation
statement of -
Q.9
µ0
H
B c
(B) E = cB
(D) E =
B c2
(A) Oscillating electric field is along X-axis and oscillating magnetic fi eld is along Yaxis
(B) Faraday’s law of induction (C) Gauss’s law of electricity (D) Gauss’s law of magnetism The charge of a parallel plate capacitor is varying as q = q 0 sin t. Then find the magnitude of displacement current through the capacitor. (Pl ate Area = A, seperation of plates = d) (A) q0 cos(t)
(B) q0 sin
(C) q0 cos
(D)
t
0
An electromagnetic wave is propagating along Y-axis. Then -
(A) Ampere’s law
Q.5
(D) E =
0 H
The relation between electric field E and magnetic field induction B in an electromagnetic waves-
(A) Faraday’s law of induction
B is a E . dl = – dt
H
µ0
q0 A d
t
(B) Oscillating electric field is along Z-axis and oscillating magnetic field is along Xaxis (C) Both oscillating electric and magnetic fields are along Y-axis, but phase difference between them is 90º (D) Both oscillating electric and magnetic fields are mutually perpendicular in arbitrary directions
cost
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Q.10
In electromagnetic wave the phase diff erence between electric and magnetic field vectors E and B is -
Q.11
A E M wave going through a medium is given by E = Eosin (kx – wt) and B = Bosin (kx – wt) then (A) E0k = B0
/2 (D) / 4
(A) 0 (C)
Q.16
(B)
(B) If Electric is in Z direction them magnetic field should be in –y direction. (C) Both ‘A’ and ‘B’ are correct
An el ect rom agneti c wav e goi ng through vaccum is described by E = E0 sin(kx – t) Which is the following is/are independent of the wavelength ? (A) k
(B) k /
(C) k
(D)
(D) Only A is correct Q.17
A plane E M wave of frequency 25 MHz travels in free space in x direction. At a particular point in space and time E = 6.3 jˆ v/m then B at that point is -
Q.12
In a plane E.M. wave, the electric field oscillates sinusoidally at a frequency of 2.5 × 1010 Hz and amplutude 480 V/m. The amplitude of oscillating magnetic field will be(A) 1.52 × 10 – 8 Wb/m 2
(A) 2.1 × 10 –8 – kˆ (B) 2.1 × 10 –8 (C) 2.1 kˆ (D) 2.1 × 10 –8
Questions based on
(B) 1.52 × 10 –7 Wb/m 2
kˆ ˆi
Energy density & Intensity
(C) 1.6 × 10 – 6 Wb/m 2 (D) 1.6 × 10 –7 Wb/m 2 Q.13
The energy density of electromagnetic wave in vacuum is given by the relation-
If 0 and µ0 represent the permittivity and permeability of vaccum and and µ represent the permittivity and permeability of medium, then refractive index of the medium is given by(A)
(C)
Q.14
Q.18
0 µ0 µ
(B)
µ0 0
(D)
µ 0 µ0
(A)
(C)
Q.19
E = E0 sin(kx –
Q.15
The ratio of
E0 H0
dimension of – (B) Resi stance
(C) Both
(D) None
(B)
1 1 0E2 + µ0 B2 2 2
B2 1 2 E + (D) 2µ0 2 0
E2 B2 C
1 0E02 2
(B)
E20 2 0
(C)
0 E02
(D)
1 0 E02 4
A lamp radiate s power P0 uniformly in all directions, the amplitude of electric field strength E0 at a distance r from it is-
for a plane E M wave has the
(A) Impedance
B2 2µ0
(A) An el ect rom agneti c wav e goi ng through vacuum is described by-
Q.20
The average value of electric energy density in an electromagnetic wave is (E 0 is peak value)
µ0 0
t) B = B0 sin (kx – t) (A) E0 B0 = k (B) E0 = B0k (C) E0k = B0 (D) none of these
1 E2 . 2 0
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(A) E0 =
P0 20cr 2
P0 (B) E0 = 20cr 2
P0 P0 (C) E 0 = (D) E = 0 40cr 2 80cr ELECTROMAGNETIC WAVES
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Q.21
Q.22
Q.23
Q.24
In an electromagnetic wave, the amplitude of electric field is 1 V/m. The frequency of wave is 5 × 1014 Hz. The wave is propagating along Z-axis. The average energy density of electric field in joul/m 3, will be(A) 2.2 × 10 –12
(B) 4.4 × 10 –12
(C) 6.6 × 10 –12
(D) 8.8 × 10 –12
Q.26
(A) ground waves (C) Q.27
(B) 6.4 × 10 5 W
(C) 4.0 × 10 5 W
(D) 1.6 × 10 5 W
(B) 0.5 w/m 2
(C) 0.1 w/m 2
(D) 0.01 w/m 2
(B) 46.7 w/m 2
(C) 66.5 w/m 2
(D) 86.5 w/m 2
(D) none of above Q.28
The area to be covered for T.V. telecast is doubled, then the height of transmitting antenna (T.V. tower) wilk have to be(A) halved
(B) doubled
(C) quardupled
(D) kept unchanged
The infra-red spectrum lies between(A) radio wave and m icro-wave region (B) the micro-wave and v isible region (C) the visible and ultra violet region (D) the ultra violet and the X-ray region
Q.29
Q.30
Consider an electric charge oscillating with a frequency of 10 MHz. The radiation emitted will have a wavel ength equal to(A) 20 m
(B) 30 m
(C) 40 m
(D) 10 m
The most penetrating radiation out of the following is -
-rays (D) -rays
(A) X-rays
Spectrum & made of propagation of EMW Q.25
The distance upto which T.V. signals can be received depend upon-
(C) radius of the earth and also height of the antenna
On an E M wave, the amplitude of electric and magnetic fields are 100 v/m and 0.265 A/m. the maximum energy flow is(A) 26.5 w/m 2
(D) sky waves
(B) height of the antenna
The intensity of visible radiation at a distance of 1 m from a bulb of 100w which converts only 5% its power into light is(A) 0.4 w/m 2
-rays
(B) X-ray
(A) radius of the earth
The sun delivers 103 w/m 2 of electromagnetic flux to the earth’s surface. The total power that is incident on a roof of dimensions 8m × 20 m will be(A) 2.56 × 104 W
The waves which can travel directly along surface of the earth are known as-
(C) Q.31
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(B)
-rays
Which of the following electromagnetic waves has minimum frequency ? (A) radio wav e
(B) ultasonic wav e
(C) microwav e
(D) audible wav e
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LEVEL # 2 Q.1
Which of the following statements about electromagnetic waves is/are correct -
Q.5
(1) X-rays in vacuum travel faster than light waves in vacuum. (2) The energy of X-ray photon is greater than that of a light photon
A parall el plate capacitor consists of two circular plates each of radius 2 cm, separated by a distance of 0.1 mm. If voltage across the plates is varying at the rate of 5 × 10 13 V/s, then the value of displacement current is-
(3) Light can be polarised but X-ray cannot.
Q.2
(A) 1 and 2
(B) 2 and 3
(C) 1, 2 and 3
(D) 2 only
Q.6
A parall el plate capacitor consists of two circular plates each of radius 12 cm and separated by 5.0 mm. The capacitor is being charged by an external source. The charging current is constant and is equal to 0.15 A. The rate of change of potential difference between the plates will be(A) 1.873 ×
107
(C) 5.56 × 10 3 A
(D) 2.28 × 10 4 A
The transmitting antenna of a radio-station is mounted vertically. At a point 10 km due north of the transmitter the peak electric field is 10 –3 volt/metre. The magnitude of the radiated magnetic field is (A) 3.33 × 10 –10 Tesla (B) 3.33 × 10 –12 Tesla (C) 10 –3 Tesla (D) 3 × 10 5 Tesla
Q.7
(C) 1.873 × 10 9 V/s (D) 1.873 × 10 10 V/s
Q.4
(B) 5.56 × 102 A
V/s
(B) 1.873 × 10 8 V/s
Q.3
(A) 5.50 A
A lam p emits monochromatic green light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amplitude of electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp will be(A) 1.34 V/m
(B) 2.68 V/m
(C) 4.02 V/m
(D) 5.36 V/m
Transmission of T.V. signals from the surface of the moon can be received on earth. But transmitted T.V. signals from Delhi can not be received beyond 110 km distance. The reason is-
Q.8
To double the covering range of a T.V. transmitter tower, its height should be made(A) two times
(B) four times
(C)
(D) 8 times
2 times
In an electromagnetic wave, the direction of the magnetic field induction B is (A) parallel to electric field E (B) perpendicular to electric field E (C) antiparallel to Poynting vector S
(D) random Q.9
(A) there is no atomsphere on the moon (B) strong gravitational effect on T.V. signals
In an electromagnetic wave (A) Power is transmitted along the magnetic field
(C) T.V. signals travel along a straight line, they do not follow the curvature of earth
(B) power is transmitted along the electric field
(D) there is atmosphere around the earth
(C) power is equally transferred along the electric and magnetic fields (D) power is transmitted in a direction perpendicular to both the fields
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Q.10
The ionosphere bends the E.M. waves having the frequencies-
Q.14
(A) less than 40 MHz (B) beyond 40 MHz (C) nothing is certain
Q.15
(D) depends on the moisture present
The energy stored in a 90 cm length of laser beam operating at 10 mw. (A) 3 × 10 8 J
(B) 3 × 10 9 J
(C) 3 × 1011 J
(D) 3 × 10 –11 J
Microwaves are used in RADAR because of its(A) Small wave length
Q.11
The magnetic field in a plane EM wave is given by-
(B) Large wavelength (C) High speed
^
(D) large penetration power
B = (100 µT) sin [(2 × 10 15 s –1)(t – x/c)] j The equation for electric field is-
Q.16
^
(A) E = 100 µN/C sin [(2×1015s –1) (t–x/c)](– k )
(A) A charge moving with constant velocity ^
(B) A charge at rest
(B) E = 3 × 1010 µN/C sin[(2 × 1015 s –1) (t – x/c)](– k ) (C) E = 3 ×
10 10
µN/C sin [(2
×1015 s –1) (t
source of an EM wave is-
(C) A charge moving in a circular orbit
^
– x/c)] k
(D) Charges cannot produce an EM wave
^
(D) E = 100 µN/C sin [(2 × 10 15 s –1)(t – x/c)] k Q.12
Q.17
(A) Impedance
For any E.M. wave if E = 100 V/m and B = 3.33 × 10 –7 T. Then the rate of energy flow per unit area is-
(B) Inductance (C) capacitance (D) Inductance × Capacitance
(A) 3.33 × 10 – 5 J/m 2 (B) 26.5 VA/m 2 (C) 3 × 10 8 J /m 2
Q.18
(D) None of these Q.13
The dimension of E/ H is that of -
A variable frequency AC source is connected to a capacitor. Then on increasing the frequency(A ) Both conduction current and displacement current will increase
Poynting vector P for an EM wave is (A) P = E × B
(B) P = E × H
E (C) P = B
E (D) P = H
(B) Both conduction current and displacement current will decrease (C) conduction current will increase and dis placement current will decrease (D) conduction current will decrease and displacement current will i ncrease.
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LEVEL # 3 Q.1
Which one statement is incorrect about
Q.6
Which one statement is incorrect – 1
electromagnetic wave
(A) Speed of light in free space =
(A) E B gives always direction of propagation
1
(B) E is always perpendicular to B
(B) Speed of light in medium =
(C) Transverse in nature
E0 (C) B 0
(D) E is always parallel to B Q.7 Q.2
0 0
In an electromagnetic wave, the amplitude of electric field is 10 V/m. The frequency of wave is 5 × 1014 Hz, the wave is propagating along
Bo (D) E = C 0
C
A pl ane el ectrom agnetic wav e of freq uency 25MHz travels in free space along the x – direction. At a particular point in space and time E 6.3 jˆ V/m. What is B at this point.
z – axis, then total average energy density of
(A) 2.1 ×10 – 9 T (C) 1.2 × 10 – 11 T
E.M.wave is –
(B) 2.1 × 10 – 8 T (D) 2.1 × 10 – 11 T
(A) 2.21 ×10 –10 J/m 3 (B) 4.42 × 10 –10 J/m 3
Q.8
Displacement current is – (A) continuous when electric field is changing in the circuit (B) continuous when magnetic field is changing in the circuit (C) continuous in both types of fields (D) continuous through wires and resistance only.
Q.9
In a plane electromagnetic wave propagating in space has an electric field of am plitude 9 × 103 V/m, then the amplitude of the magnetic field is – (A) 2.7 × 10 12T (B) 9.0 × 10 – 3 T (C) 3.0 × 10 – 4 T (D) 3.0 × 10 – 5 T
Q.10
A radiowave has a maximum magnetic field induction of 10 – 4 T on arrival at a receiving antenna. The maximum electric field intensity of such a wave is – (A) zero (B) 3 ×104 V/m (C) 5.8 × 10 – 9 V/m (D) 3.3 × 10 – 13 V/m
Q.11
A capacitor is having a capacity of 2pF. Electric field across the capacitor is changing with a value of 1012 V/s. The displacement current is (A) 2A (B) 3A (C) 6A (D) 9A
(C) 1.11 × 10 –10 J/m 3 (D) None
Q.3
Instantaneous displacement current of 2.0 A is set up in the space between two parallel plates of 1 F capacitor, then rate of change in potential difference across capacitor is –
Q.4
(A) 3 ×106 v/s
(B) 4 × 106 v/s
(C) 2 ×106 v/s
(D) none of these
The T.V. transmission tower in Delhi has a height of 240 m. The distance upto which the broadcast can be received, (taking the radius of earth to be 6.4 × 10 6m)
Q.5
(A) 100 Km
(B) 60 Km
(C) 55 Km
(D) 50 Km
Which of the following have zero average value in a plane electromagnetic wave. (A) electric energy (B) magnetic field (C) magnetic & electric energy both (D) none of these
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Q.12
A TV tower has a height of 100m. The average population density around the tower is 1000 per km2. The radius of the earth is 6.4 × 106 m. The population covered by the tower is (A) 2 × 106
(B) 3 × 106
10 6
10 6
(C) 4 ×
(D) 6 ×
Q.18
Which of the following are not electromagnetic waves ?
Q.14
The shortest wavelength is for (A) -rays
(B) X-rays
(C) ultraviolet rays
(D) microwaves
(D) X-rays.
rays are respectively a, b and c. Then :
Q.20
(A) a < b, b < c
(B) a > b, b > c
(C) a > b, b > a
(D) a < b, b > c
A plane electromagnetic wave of frequency
(B) does not emit electromagnetic wave
40 MHz travels in free space in the x-direction.
(C) produces a gravitational field
At some point and at some instant, the electric field E has its maximum val ue of 750 N/C in
(D) None of these
y-direction. The wavelength of the wave is—
The electromagnetic radiations are in descending order of wavelength in the following sequence (A) infra-red waves, radio waves, X-rays, visible light rays
Q.21
(A) 3.5 m
(B) 5.5 m
(C) 7.5 m
(D) 9.5 m
In Q. 20, the magnitude and direction of
(B) Radio-waves, infra-red waves, visible light rays, X-rays
magnetic field will be—
(C) Radio waves, visible light rays, infra-red waves, X-rays
(B) 2.5 T in Y-direction
(A) 2.5 T in X-direction (C) 2.5 T in Z-direction
(D) X-rays, visible light rays, infra-red wave, radiowaves.
Q.16
(C) -rays
An accelerated charge (A) emits an electromagnetic wave
Q.15
(B) gamma rays
The frequencies of X-rays, -rays and ultraviolet
Q.19 Q.13
(A) cosmic rays
X-rays and -rays are both electromagnetic waves, which one of the f ollowing statements is true
(D) None of these Q.22
The waves related to tele-communication are—
(A) in general, X-rays hav e larger wavelength than that of -rays (B) X-rays have smaller wavelength than that of -rays
Q.23
(A) infra red
(B) visible light
(C) microwaves
(D) ultraviolet rays
A flood light is covered with a filter that transmits red light. The electric field of the emerging
(C) -rays have smaller frequency than that of X-rays
beam is represented by a sinusoidal plane
(D) wavelength and frequency of X-rays are both larger than those of -rays
Ex = 36 sin (1.20 × 10 7 z – 3.6 × 1015 t) V/m
wave
The average intensity of the beam will be— Q.17
The maximum distance upto which TV transmission from a TV tower of height h can be received is proportional to (A) h1/2
(B) h
(C) h3
(D) h2
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(A) 0.86 W/m 2
(B) 1.72 W/m 2
(C) 3.44 W/m 2
(D) 6.88 W/m 2
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Statements t ype question : Each of the questions gi ven below consist of Statement – I and Statement – II. Use the following Key to choose the appropriate answer. (A) If both Statement- I and Statement- II are true, and Statement - II is the correct explanation of Statement– I. (B) If both Statement - I and Statement - II are true but Statement - II is not the correct explanation of Statement – I. (C) If Statement - I is tru e but Statement - II is false. (D) If Statement - I is false bu t Statement - II is true. Q.24
Q.26
Statement I : If earth did not have atmosphere, its average surface temperature would be lower than what it is now. Statement II : Green house effect of the atmosphere would be absent.
Q.27
Statement I : Gamma rays are more energetic than X-rays. Statement II : Gamma rays are of nuclear origin but X- rays are produced due to sudden deceleration of high energy electrons while falling on a metal of high atomic number.
Q.28
Statement I : A changing electric field produces a magnetic fi eld.
Statement I : Microwaves have less energy than optical waves. Statement II : Microwaves move faster than optical waves.
Statement II : A changing magnetic field produces an electric field. Q.25
Statement I : Light can travel in vacuum but sound cannot do so. Statement II : Light is an electromagnetic wave and sound is a mechanical wave.
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ANSWER KEY LEVEL # 1 Ques.
1
2
3
4
5
6
7
8
9
10
11
Ans.
C
D
B
B
C
A
C
B
B
A
B
Ques.
12
13
14
15
16
17
18
19
20
21
22
Ans.
C
B
C
C
C
B
D
D
B
A
D
Ques.
23
24
25
26
27
28
29
30
31
Ans.
A
A
B
A
C
B
C
D
A
LEVEL # 2 Qu e s.
1
2
3
4
5
6
7
8
9
10
A n s.
D
C
B
C
C
B
B
B
D
B
Qu e s.
11
12
13
14
15
16
17
18
A n s.
B
B
A
D
A
C
A
B
LEVEL # 3 Qu e s.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Ans.
D
B
C
C
B
D
B
A
D
B
A
C
A
A
B
A
A
C
D
C
Qu e s.
21
22
23
24
25
26
27
28
Ans.
C
C
B
B
A
A
B
C
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