Electromagnetic Waves Solved Examples | Physics for JEE Main & Advanced PDF Download

 Page 1


JEE Solved Example on EM Waves 
JEE Mains 
Q1:An electromagnetic wave can be produced, when charge is 
(A) moving with a constant velocity 
(B) moving in a circular orbit 
(C) falling in an electric field 
(D) both B and C 
Ans: (D) 
An electromagnetic wave can be produced by accelerated or oscillating charge. In option (B) and (C), 
the charge is in accelerated state, hence it will be a source of electromagnetic waves. 
 
Q2: If ?? and ?? denote electric and magnetic fields respectively, which of the following is 
dimensionless? 
(A) v?? ?? ?? ?? ?? ?? 
(B) ?? ?? ?? ?? ?? ?? 
(C) ?? ?? ?? ?? (
?? ?? )
?? 
(D) 
?? ?? ?? ?? ?? ?? 
Ans: (A) 
Speed of light, ?? =
1
v?? 0
?? 0
; Also, 
E
B
= ?? 
Therefore, v?? 0
?? 0
?? ?? is dimensionless. 
 
Q3: The electric field of an electromagnetic wave travelling through vacuum is given by the 
equation ?? = ?? ?? ?????? ?(???? - ???? ) . The quantity that is independent of wavelength is 
(A) ???? 
(B) 
?? ?? 
(C) ?? ?? ?? 
(D) ?? 
Ans: (B) 
Here, ?? =
2?? ?? ,?? = 2???? 
?
?? ?? =
2?? /?? 2????
=
1
????
=
1
?? ?(? ?? = ???? ) 
Page 2


JEE Solved Example on EM Waves 
JEE Mains 
Q1:An electromagnetic wave can be produced, when charge is 
(A) moving with a constant velocity 
(B) moving in a circular orbit 
(C) falling in an electric field 
(D) both B and C 
Ans: (D) 
An electromagnetic wave can be produced by accelerated or oscillating charge. In option (B) and (C), 
the charge is in accelerated state, hence it will be a source of electromagnetic waves. 
 
Q2: If ?? and ?? denote electric and magnetic fields respectively, which of the following is 
dimensionless? 
(A) v?? ?? ?? ?? ?? ?? 
(B) ?? ?? ?? ?? ?? ?? 
(C) ?? ?? ?? ?? (
?? ?? )
?? 
(D) 
?? ?? ?? ?? ?? ?? 
Ans: (A) 
Speed of light, ?? =
1
v?? 0
?? 0
; Also, 
E
B
= ?? 
Therefore, v?? 0
?? 0
?? ?? is dimensionless. 
 
Q3: The electric field of an electromagnetic wave travelling through vacuum is given by the 
equation ?? = ?? ?? ?????? ?(???? - ???? ) . The quantity that is independent of wavelength is 
(A) ???? 
(B) 
?? ?? 
(C) ?? ?? ?? 
(D) ?? 
Ans: (B) 
Here, ?? =
2?? ?? ,?? = 2???? 
?
?? ?? =
2?? /?? 2????
=
1
????
=
1
?? ?(? ?? = ???? ) 
where ?? is the speed of electromagnetic wave in vacuum. It is a constant whose value is 
3× 10
8
 m s
-1
. 
 
Q4: Radiations of intensity ?? .?? ?? ?? -?? are striking a metal plate. 
The pressure on the plate is 
(A) ?? .?????? × ????
-?? ?? ?? -?? 
(B) ?? .?????? × ????
-?? ?? ?? -?? 
(C) ?? .?????? × ????
-?? ?? ?? -?? 
(D) ?? .?????? × ????
-?? ?? ?? -?? 
Ans: (A) 
P =
1
?? =
0.5
3× 10
8
= 0.166× 10
-8
 N m
-2
 
 
Q5: Electromagnetic wave consists of periodically oscillating electric and magnetic vectors 
(A)in mutually perpendicular planes but vibrating with a phase difference of ?? 
(B) in mutually perpendicular planes but vibrating with a phase difference of 
?? ?? 
(C) in randomly oriented planes but vibrating in phase 
(D) in mutually perpendicular planes but vibrating in phase. 
Ans: (D) 
Electromagnetic wave consists of periodically oscillating electric and magnetic vectors in mutually 
perpendicular planes but vibrating in phase. 
 
Q6: A radio can tune to any station in ?? .???????? to ?????????? band. The corresponding wavelength 
band is 
(A) ???? ?? to ???? ?? 
(B) ???? ?? to ???? ?? 
(C) ???? ?? to ???? ?? 
(D) ???? ?? to ?? ?? 
Ans: (A) 
Here, ?? 1
= 7.5MHz,?? 2
= 12MHz 
? ??? 1
=
?? ?? 1
=
3 × 10
8
7.5× 10
6
= 40 m and ?? 2
=
?? ?? 2
=
3× 10
8
12× 10
6
= 25 m 
 
 
Page 3


JEE Solved Example on EM Waves 
JEE Mains 
Q1:An electromagnetic wave can be produced, when charge is 
(A) moving with a constant velocity 
(B) moving in a circular orbit 
(C) falling in an electric field 
(D) both B and C 
Ans: (D) 
An electromagnetic wave can be produced by accelerated or oscillating charge. In option (B) and (C), 
the charge is in accelerated state, hence it will be a source of electromagnetic waves. 
 
Q2: If ?? and ?? denote electric and magnetic fields respectively, which of the following is 
dimensionless? 
(A) v?? ?? ?? ?? ?? ?? 
(B) ?? ?? ?? ?? ?? ?? 
(C) ?? ?? ?? ?? (
?? ?? )
?? 
(D) 
?? ?? ?? ?? ?? ?? 
Ans: (A) 
Speed of light, ?? =
1
v?? 0
?? 0
; Also, 
E
B
= ?? 
Therefore, v?? 0
?? 0
?? ?? is dimensionless. 
 
Q3: The electric field of an electromagnetic wave travelling through vacuum is given by the 
equation ?? = ?? ?? ?????? ?(???? - ???? ) . The quantity that is independent of wavelength is 
(A) ???? 
(B) 
?? ?? 
(C) ?? ?? ?? 
(D) ?? 
Ans: (B) 
Here, ?? =
2?? ?? ,?? = 2???? 
?
?? ?? =
2?? /?? 2????
=
1
????
=
1
?? ?(? ?? = ???? ) 
where ?? is the speed of electromagnetic wave in vacuum. It is a constant whose value is 
3× 10
8
 m s
-1
. 
 
Q4: Radiations of intensity ?? .?? ?? ?? -?? are striking a metal plate. 
The pressure on the plate is 
(A) ?? .?????? × ????
-?? ?? ?? -?? 
(B) ?? .?????? × ????
-?? ?? ?? -?? 
(C) ?? .?????? × ????
-?? ?? ?? -?? 
(D) ?? .?????? × ????
-?? ?? ?? -?? 
Ans: (A) 
P =
1
?? =
0.5
3× 10
8
= 0.166× 10
-8
 N m
-2
 
 
Q5: Electromagnetic wave consists of periodically oscillating electric and magnetic vectors 
(A)in mutually perpendicular planes but vibrating with a phase difference of ?? 
(B) in mutually perpendicular planes but vibrating with a phase difference of 
?? ?? 
(C) in randomly oriented planes but vibrating in phase 
(D) in mutually perpendicular planes but vibrating in phase. 
Ans: (D) 
Electromagnetic wave consists of periodically oscillating electric and magnetic vectors in mutually 
perpendicular planes but vibrating in phase. 
 
Q6: A radio can tune to any station in ?? .???????? to ?????????? band. The corresponding wavelength 
band is 
(A) ???? ?? to ???? ?? 
(B) ???? ?? to ???? ?? 
(C) ???? ?? to ???? ?? 
(D) ???? ?? to ?? ?? 
Ans: (A) 
Here, ?? 1
= 7.5MHz,?? 2
= 12MHz 
? ??? 1
=
?? ?? 1
=
3 × 10
8
7.5× 10
6
= 40 m and ?? 2
=
?? ?? 2
=
3× 10
8
12× 10
6
= 25 m 
 
 
Q7: The photon energy in units of ???? for electromagnetic waves of wavelength ?? ???? is 
(A) ?? .?? × ????
-????
 
(B) ?? .?? × ????
????
 
(C) ?? .?? × ????
-????
 
(D) ?? .?? × ????
-?? 
Ans: (D) 
As ?? =
h?? ?? =
6.6×10
-34
×3×10
8
2×10
-2
= 9.9× 10
-24
 J =
9.9×10
-24
1.6×10
-19
eV= 6.2× 10
-5
eV 
 
 
Q8: A plane electromagnetic wave is incident on a material surface. The wave delivers moment ?? 
and energy E. Then 
(A) ?? ? ?? ,?? ? ?? 
(B) ?? = ?? ,?? = ?? 
(C) ?? = ?? ,?? ? ?? 
(D) ?? ? ?? ,?? = ?? 
Ans: (A) 
When plane electromagnetic wave is incident on a material surface, the wave delivers some 
momentum and energy to the surface and hence ?? ? 0 and E ? 0. 
 
Q9: The charge on a parallel plate capacitor varies as ?? = ?? ?? ?????? ??? ?? ???? . The plates are very large 
and close together (area = ?? , separation = ?? ). The displacement current through the capacitor is 
(A) ?? ?? ?? ?? ? ?????? ??? ? ?? 
(B) -?? ?? ?? ???? ?????? ??? ?????? 
(C) ?? ?? ?? ?? ?????? ??? ? ?? 
(D) ?? ?? ???? ?????? ??? ?????? 
Ans: (B) 
Displacement current, I
D
= conduction current, I
C
 
? ?
????
????
=
?? ????
[?? 0
cos?2?????? ] = -?? 0
2?? ? sin?2?????? 
 
 
 
 
Page 4


JEE Solved Example on EM Waves 
JEE Mains 
Q1:An electromagnetic wave can be produced, when charge is 
(A) moving with a constant velocity 
(B) moving in a circular orbit 
(C) falling in an electric field 
(D) both B and C 
Ans: (D) 
An electromagnetic wave can be produced by accelerated or oscillating charge. In option (B) and (C), 
the charge is in accelerated state, hence it will be a source of electromagnetic waves. 
 
Q2: If ?? and ?? denote electric and magnetic fields respectively, which of the following is 
dimensionless? 
(A) v?? ?? ?? ?? ?? ?? 
(B) ?? ?? ?? ?? ?? ?? 
(C) ?? ?? ?? ?? (
?? ?? )
?? 
(D) 
?? ?? ?? ?? ?? ?? 
Ans: (A) 
Speed of light, ?? =
1
v?? 0
?? 0
; Also, 
E
B
= ?? 
Therefore, v?? 0
?? 0
?? ?? is dimensionless. 
 
Q3: The electric field of an electromagnetic wave travelling through vacuum is given by the 
equation ?? = ?? ?? ?????? ?(???? - ???? ) . The quantity that is independent of wavelength is 
(A) ???? 
(B) 
?? ?? 
(C) ?? ?? ?? 
(D) ?? 
Ans: (B) 
Here, ?? =
2?? ?? ,?? = 2???? 
?
?? ?? =
2?? /?? 2????
=
1
????
=
1
?? ?(? ?? = ???? ) 
where ?? is the speed of electromagnetic wave in vacuum. It is a constant whose value is 
3× 10
8
 m s
-1
. 
 
Q4: Radiations of intensity ?? .?? ?? ?? -?? are striking a metal plate. 
The pressure on the plate is 
(A) ?? .?????? × ????
-?? ?? ?? -?? 
(B) ?? .?????? × ????
-?? ?? ?? -?? 
(C) ?? .?????? × ????
-?? ?? ?? -?? 
(D) ?? .?????? × ????
-?? ?? ?? -?? 
Ans: (A) 
P =
1
?? =
0.5
3× 10
8
= 0.166× 10
-8
 N m
-2
 
 
Q5: Electromagnetic wave consists of periodically oscillating electric and magnetic vectors 
(A)in mutually perpendicular planes but vibrating with a phase difference of ?? 
(B) in mutually perpendicular planes but vibrating with a phase difference of 
?? ?? 
(C) in randomly oriented planes but vibrating in phase 
(D) in mutually perpendicular planes but vibrating in phase. 
Ans: (D) 
Electromagnetic wave consists of periodically oscillating electric and magnetic vectors in mutually 
perpendicular planes but vibrating in phase. 
 
Q6: A radio can tune to any station in ?? .???????? to ?????????? band. The corresponding wavelength 
band is 
(A) ???? ?? to ???? ?? 
(B) ???? ?? to ???? ?? 
(C) ???? ?? to ???? ?? 
(D) ???? ?? to ?? ?? 
Ans: (A) 
Here, ?? 1
= 7.5MHz,?? 2
= 12MHz 
? ??? 1
=
?? ?? 1
=
3 × 10
8
7.5× 10
6
= 40 m and ?? 2
=
?? ?? 2
=
3× 10
8
12× 10
6
= 25 m 
 
 
Q7: The photon energy in units of ???? for electromagnetic waves of wavelength ?? ???? is 
(A) ?? .?? × ????
-????
 
(B) ?? .?? × ????
????
 
(C) ?? .?? × ????
-????
 
(D) ?? .?? × ????
-?? 
Ans: (D) 
As ?? =
h?? ?? =
6.6×10
-34
×3×10
8
2×10
-2
= 9.9× 10
-24
 J =
9.9×10
-24
1.6×10
-19
eV= 6.2× 10
-5
eV 
 
 
Q8: A plane electromagnetic wave is incident on a material surface. The wave delivers moment ?? 
and energy E. Then 
(A) ?? ? ?? ,?? ? ?? 
(B) ?? = ?? ,?? = ?? 
(C) ?? = ?? ,?? ? ?? 
(D) ?? ? ?? ,?? = ?? 
Ans: (A) 
When plane electromagnetic wave is incident on a material surface, the wave delivers some 
momentum and energy to the surface and hence ?? ? 0 and E ? 0. 
 
Q9: The charge on a parallel plate capacitor varies as ?? = ?? ?? ?????? ??? ?? ???? . The plates are very large 
and close together (area = ?? , separation = ?? ). The displacement current through the capacitor is 
(A) ?? ?? ?? ?? ? ?????? ??? ? ?? 
(B) -?? ?? ?? ???? ?????? ??? ?????? 
(C) ?? ?? ?? ?? ?????? ??? ? ?? 
(D) ?? ?? ???? ?????? ??? ?????? 
Ans: (B) 
Displacement current, I
D
= conduction current, I
C
 
? ?
????
????
=
?? ????
[?? 0
cos?2?????? ] = -?? 0
2?? ? sin?2?????? 
 
 
 
 
Q10: If ?? ?? be the peremeability and ?? ?? be the permittivity of a medium, then its refractive index is 
given by 
(A) 
?? v?? ?? ?? ?? 
(B) 
?? ?? ?? ?? ?? 
(C) v?? ?? ?? ?? 
(D) ?? ?? ?? ?? 
Ans: (C) 
Refractive index of medium is =
?? ?? where ?? =
1
v?? 0
?? 0
 and ?? =
1
v?? 0
?? 0
?? 0
,?? ?? ? ??? =
1/v?? 0
?? 0
1/v?? 0
?? 0
?? 1
,?? ?? =
v
?? 1
,?? ?? 
Given ?? ?? = ?? 0
 and ?? ?? = ?? 0
 then ?? = v?? ?? ?? 0
 
 
Q11: An electromagnetic wave of frequency ?? = ???????? passes from vacuum into a dielectric 
medium with permittivity ?? = 4. Then 
(A) wavelength and frequency both become half. 
(B) wavelength is doubled and frequency remains unchanged. 
(C) wavelength and frequency both remain unchanged. 
(D) wavelength is halved and frequency remains unchanged. 
Ans: (D) 
The frequency of electromagnetic wave remains unchanged but the wavelength of electromagnetic 
wave changes when it passes from one medium to another. 
?? =
1
v?? 0
?? 0
? ? ?? ?
1
v?? 0
 and ?? ?
1
v?? ? ?
?? ?? = v
?? ?? 0
=
v
4
1
= 2;
?? ?? =
????
?? ?? '
=
?? ?? '
= 2 or ?? '
=
?? 2
 
 
 
 
 
 
 
 
 
Page 5


JEE Solved Example on EM Waves 
JEE Mains 
Q1:An electromagnetic wave can be produced, when charge is 
(A) moving with a constant velocity 
(B) moving in a circular orbit 
(C) falling in an electric field 
(D) both B and C 
Ans: (D) 
An electromagnetic wave can be produced by accelerated or oscillating charge. In option (B) and (C), 
the charge is in accelerated state, hence it will be a source of electromagnetic waves. 
 
Q2: If ?? and ?? denote electric and magnetic fields respectively, which of the following is 
dimensionless? 
(A) v?? ?? ?? ?? ?? ?? 
(B) ?? ?? ?? ?? ?? ?? 
(C) ?? ?? ?? ?? (
?? ?? )
?? 
(D) 
?? ?? ?? ?? ?? ?? 
Ans: (A) 
Speed of light, ?? =
1
v?? 0
?? 0
; Also, 
E
B
= ?? 
Therefore, v?? 0
?? 0
?? ?? is dimensionless. 
 
Q3: The electric field of an electromagnetic wave travelling through vacuum is given by the 
equation ?? = ?? ?? ?????? ?(???? - ???? ) . The quantity that is independent of wavelength is 
(A) ???? 
(B) 
?? ?? 
(C) ?? ?? ?? 
(D) ?? 
Ans: (B) 
Here, ?? =
2?? ?? ,?? = 2???? 
?
?? ?? =
2?? /?? 2????
=
1
????
=
1
?? ?(? ?? = ???? ) 
where ?? is the speed of electromagnetic wave in vacuum. It is a constant whose value is 
3× 10
8
 m s
-1
. 
 
Q4: Radiations of intensity ?? .?? ?? ?? -?? are striking a metal plate. 
The pressure on the plate is 
(A) ?? .?????? × ????
-?? ?? ?? -?? 
(B) ?? .?????? × ????
-?? ?? ?? -?? 
(C) ?? .?????? × ????
-?? ?? ?? -?? 
(D) ?? .?????? × ????
-?? ?? ?? -?? 
Ans: (A) 
P =
1
?? =
0.5
3× 10
8
= 0.166× 10
-8
 N m
-2
 
 
Q5: Electromagnetic wave consists of periodically oscillating electric and magnetic vectors 
(A)in mutually perpendicular planes but vibrating with a phase difference of ?? 
(B) in mutually perpendicular planes but vibrating with a phase difference of 
?? ?? 
(C) in randomly oriented planes but vibrating in phase 
(D) in mutually perpendicular planes but vibrating in phase. 
Ans: (D) 
Electromagnetic wave consists of periodically oscillating electric and magnetic vectors in mutually 
perpendicular planes but vibrating in phase. 
 
Q6: A radio can tune to any station in ?? .???????? to ?????????? band. The corresponding wavelength 
band is 
(A) ???? ?? to ???? ?? 
(B) ???? ?? to ???? ?? 
(C) ???? ?? to ???? ?? 
(D) ???? ?? to ?? ?? 
Ans: (A) 
Here, ?? 1
= 7.5MHz,?? 2
= 12MHz 
? ??? 1
=
?? ?? 1
=
3 × 10
8
7.5× 10
6
= 40 m and ?? 2
=
?? ?? 2
=
3× 10
8
12× 10
6
= 25 m 
 
 
Q7: The photon energy in units of ???? for electromagnetic waves of wavelength ?? ???? is 
(A) ?? .?? × ????
-????
 
(B) ?? .?? × ????
????
 
(C) ?? .?? × ????
-????
 
(D) ?? .?? × ????
-?? 
Ans: (D) 
As ?? =
h?? ?? =
6.6×10
-34
×3×10
8
2×10
-2
= 9.9× 10
-24
 J =
9.9×10
-24
1.6×10
-19
eV= 6.2× 10
-5
eV 
 
 
Q8: A plane electromagnetic wave is incident on a material surface. The wave delivers moment ?? 
and energy E. Then 
(A) ?? ? ?? ,?? ? ?? 
(B) ?? = ?? ,?? = ?? 
(C) ?? = ?? ,?? ? ?? 
(D) ?? ? ?? ,?? = ?? 
Ans: (A) 
When plane electromagnetic wave is incident on a material surface, the wave delivers some 
momentum and energy to the surface and hence ?? ? 0 and E ? 0. 
 
Q9: The charge on a parallel plate capacitor varies as ?? = ?? ?? ?????? ??? ?? ???? . The plates are very large 
and close together (area = ?? , separation = ?? ). The displacement current through the capacitor is 
(A) ?? ?? ?? ?? ? ?????? ??? ? ?? 
(B) -?? ?? ?? ???? ?????? ??? ?????? 
(C) ?? ?? ?? ?? ?????? ??? ? ?? 
(D) ?? ?? ???? ?????? ??? ?????? 
Ans: (B) 
Displacement current, I
D
= conduction current, I
C
 
? ?
????
????
=
?? ????
[?? 0
cos?2?????? ] = -?? 0
2?? ? sin?2?????? 
 
 
 
 
Q10: If ?? ?? be the peremeability and ?? ?? be the permittivity of a medium, then its refractive index is 
given by 
(A) 
?? v?? ?? ?? ?? 
(B) 
?? ?? ?? ?? ?? 
(C) v?? ?? ?? ?? 
(D) ?? ?? ?? ?? 
Ans: (C) 
Refractive index of medium is =
?? ?? where ?? =
1
v?? 0
?? 0
 and ?? =
1
v?? 0
?? 0
?? 0
,?? ?? ? ??? =
1/v?? 0
?? 0
1/v?? 0
?? 0
?? 1
,?? ?? =
v
?? 1
,?? ?? 
Given ?? ?? = ?? 0
 and ?? ?? = ?? 0
 then ?? = v?? ?? ?? 0
 
 
Q11: An electromagnetic wave of frequency ?? = ???????? passes from vacuum into a dielectric 
medium with permittivity ?? = 4. Then 
(A) wavelength and frequency both become half. 
(B) wavelength is doubled and frequency remains unchanged. 
(C) wavelength and frequency both remain unchanged. 
(D) wavelength is halved and frequency remains unchanged. 
Ans: (D) 
The frequency of electromagnetic wave remains unchanged but the wavelength of electromagnetic 
wave changes when it passes from one medium to another. 
?? =
1
v?? 0
?? 0
? ? ?? ?
1
v?? 0
 and ?? ?
1
v?? ? ?
?? ?? = v
?? ?? 0
=
v
4
1
= 2;
?? ?? =
????
?? ?? '
=
?? ?? '
= 2 or ?? '
=
?? 2
 
 
 
 
 
 
 
 
 
Q12: Light with an energy flux of ???? ?? ????
-?? falls on a nonreflecting surface at normal incidence. 
If the surface has an area of ???? ????
?? , the average force exerted on the surface during a 30 minute 
time span is 
(A) ?? .?? × ????
-?? ?? 
(B) ?? .?? × ????
-?? ?? 
(C) ?? .?? × ????
?? ?? 
(D) ?? .?? × ????
?? ?? 
 
Ans: (B) 
The total energy falling on the surface is U = 18× 20× (30 × 60)= 6.48× 10
5
 J 
Therefore, the total momentum delivered (for complete absorption is) 
?? =
U
?? =
6.48× 10
5
3× 10
8
= 2.16× 10
-3
 kg m s
-1
. 
The average force exerted on the surface is 
F =
?? ?? =
2.16× 10
-3
0.18× 10
4
= 1.2× 10
-6
 N 
 
Q13: Which of the following electromagnetic wave play an important role in maintaining the 
earth's warmth or average temperature through the greenhouse effect? 
(A) Visible rays 
(B) Infrared waves 
(C) Gamma rays 
(D) Ultraviolet rays 
 
Ans: (B) 
Infrared radiation plays an important role in maintaining the earth's warmth through greenhouse 
effect. Incoming visible light when passes relatively easily through the atmosphere is absorbed by the 
earth's surface and radiated as infrared (longer wavelength) radiation. This radiation is trapped by 
greenhouse gases such as carbon dioxide and water vapour. In this way an average temperature is 
maintained. 
Q14: Maxwell in his famous equations of electromagnetism introduced the concept of 
(A) ac current 
(B) displacement current 
(C) impedance 
(D) reactance 
Ans: (B) 
 
Q15: The ultra high frequency band of radiowaves in electromagnetic wave is used as in 
(A)television waves 
(B) cellular phone communication