H C Verma solutions, ELECTROMAGNETIC WAVES, Chapter-40, OBJECTIVE-II, Concepts of Physics, Part-II

Electromagnetic Waves

OBJECTIVE-II

     1.  An electromagnetic wave going through the vacuum is described by

E =Eₒ sin(kx -⍵t).

Which of the following is/are independent of the wavelength?

(a) k

(b) ⍵

(c) k/⍵

(d) k⍵.  

ANSWER: (c).  

EXPLANATION: k =2π/λ, So it depends on the wavelength. Option (a) is incorrect.

  ⍵ =2π𝜈 =2πc/λ

       {Since c =𝜈λ}

So ⍵ also depends on the wavelength. Option (b) is incorrect.

    k/⍵ =(2π/λ)/(2πc/λ) 

          =1/c. 

It is free of wavelength. So option (c) is correct.     

   k⍵ =(2π/𝜆)*(2πc/𝜆)

        =4π²c/𝜆².

It also depends on wavelength. Option (d) is incorrect.

 

     2.  Displacement current goes through the gap between the plates of a capacitor when the charge of the capacitor

(a) increases

(b) decreases

(c) does not change

(d) is zero.        

ANSWER: (a), (b).  

EXPLANATION: Electric field between the plates, E =Q/(εₒA) 

The flux of this field through area A,

φE ={Q/(εₒA)}*A =Q/εₒ

Displacement current is,

iᵨ =εₒ.dφE/dt

   =εₒ.d(Q/εₒ)/dt

   =dQ/dt

  So the displacement current is proportional to the rate of change of the charge accumulated on the capacitor plate. If dQ/dt = zero, then the displacement current is also zero. So options (c) and (d) are incorrect. Options (a) and (b) are correct.

 

     3.  The speed of electromagnetic waves is the same 

(a) for all wavelengths

(b) in all media

(c) for all intensities

(d) for all frequencies.        

ANSWER: (c).  

EXPLANATION: Though the speed of the electromagnetic waves in a vacuum is independent of their wavelength and frequency, it depends on the vacuum wavelength and frequency of the wave in a medium. Hence options (a), (b) and (d) are incorrect. 

    Since the intensity of a wave is defined as the energy crossing per unit area per unit time perpendicular to the direction of propagation of the wave, the speed of the wave does not depend on it. Option (c) is correct. 

   

     4.  Which of the following has zero average value in a plane electromagnetic wave? 

(a) electric field

(b) magnetic field

(c) electric energy

(d) magnetic energy.     

ANSWER: (a), (b).  

EXPLANATION: Since the electric field and the magnetic field in a plane electromagnetic wave are sinusoidal waves, their average value will be zero. Options (a) and (b) are correct. 

  The electric energy density and the magnetic energy density are equal and given as 

uₐᵥ =½εₒEₒ² =(1/2µₒ)Bₒ²

Here εₒ and µₒ are non-zero constants, also Eₒ² and Bₒ² have positive values, hence average electric energy and magnetic energy are not zero. Options (c) and (d) are incorrect.  

 

     5.  The energy contained in a small volume through which an electromagnetic wave is passing oscillates with 

(a) zero frequency

(b) the frequency  of the wave 

(c) half the frequency of the wave

(d) double the frequency of the wave.      

ANSWER: (d).  

EXPLANATION: Total energy per unit volume of the wave, 

u = ½εₒE²+B²/2µₒ

=½εₒEₒ²sin²(⍵t-kx)+(1/2µₒ)Bₒ²sin²(⍵t-kx)

=½εₒEₒ²{1-cos2(⍵t-kx)}+(Bₒ²/2µₒ){1-cos2(⍵t-kx)}

So the oscillation of energy has an angular frequency of 2⍵ i.e. double the frequency of the wave. So option (d) is correct and the rest incorrect. 

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CHAPTER- 40- Electromagnetic Waves

Questions for Short Answer

OBJECTIVE - I

 

CHAPTER- 39- Alternating Current

Questions for Short Answer

OBJECTIVE - I

OBJECTIVE - II

EXERCISES, Q1 to Q10

EXERCISES, Q11 to Q19

 

CHAPTER- 38- Electromagnetic Induction

Questions for Short Answer

OBJECTIVE - I

OBJECTIVE - II

EXERCISE - Q1 to Q10

EXERCISES - Q11 to Q20

EXERCISES - Q21 to Q30

EXERCISES - Q31 to Q40

EXERCISES - Q41 to Q50

EXERCISES - Q51 to Q60

EXERCISES - Q61 to Q70

EXERCISES - Q71 to Q80

EXERCISES - Q81 to Q90

EXERCISES - Q91 to Q98

CHAPTER- 37- Magnetic Properties of Matter

Questions for Short Answer

OBJECTIVE - I

OBJECTIVE - II

EXERCISES

CHAPTER- 36- Permanent Magnets

Questions for Short Answer

OBJECTIVE - I

OBJECTIVE - II

EXERCISES - Q1 to Q10

EXERCISES - Q11 to Q20

EXERCISES - Q21 to Q25

CHAPTER- 35- Magnetic Field due to a Current

Questions for Short Answer

OBJECTIVE - I

OBJECTIVE - II

EXERCISES -Q1 to Q10

EXERCISES Q11 to Q20

EXERCISES -Q21 to Q30

EXERCISES -Q31 to Q40

EXERCISES -Q41 to Q50

EXERCISES -Q51 to Q61

CHAPTER- 34- Magnetic Field

Questions for Short Answer

OBJECTIVE - I

OBJECTIVE - II

EXERCISES - Q1 to Q10

EXERCISES -Q11 to Q20

EXERCISES -Q21 to Q30

EXERCISES -Q31 to Q40

EXERCISES -Q41 to Q50

EXERCISES -Q51 to Q61

CHAPTER- 33- Thermal and Chemical Effects of Electric Current

Questions for Short Answer

OBJECTIVE - I

OBJECTIVE - II

EXERCISES - Q1 to Q12

EXERCISES - Q13 to Q24

 

CHAPTER- 32- Electric Current in Conductors

Questions for Short Answer

OBJECTIVE - I

OBJECTIVE - II

EXERCISES - Q1 to Q10

EXERCISES - Q11 to Q20

EXERCISES - Q21 to Q30

EXERCISES - Q31 to Q40

EXERCISES - Q41 to Q50

EXERCISES - Q51 to Q60

EXERCISES - Q61 to Q70

EXERCISES - Q71 to Q80

EXERCISES - Q81 to Q84 

CHAPTER- 31- Capacitors

Questions for Short Answer

OBJECTIVE - I

 

OBJECTIVE - II

EXERCISES - Q1 to Q10

EXERCISES - Q11 to Q20

EXERCISES - Q21 to Q30

EXERCISES - Q31 to Q40

EXERCISES - Q41 to Q50

EXERCISES - Q51 to Q60

EXERCISES - Q61 to Q68

CHAPTER- 30- Gauss's Law

Questions for Short Answer

OBJECTIVE - I

OBJECTIVE - II

EXERCISES - Q1 - Q10

EXERCISES - Q11 - Q20

EXERCISES - Q21 - Q24

CHAPTER- 29- Electric Field and Potential

Questions for Short Answer

OBJECTIVE-I

OBJECTIVE -II

EXERCISES - Q1 - Q10

EXERCISES - Q11 - Q20

EXERCISES - Q21 - Q30

EXERCISES - Q31 - Q40

EXERCISES - Q41 - Q50

EXERCISES - Q51 - Q60 

EXERCISES - Q61 - Q70

EXERCISES - Q71 - Q75 

CHAPTER- 28- Heat Transfer

Questions for Short Answer

OBJECTIVE -I

OBJECTIVE - II

EXERCISES - Q1 to Q10

EXERCISES - Q11 to Q20

EXERCISES - Q21 to Q30

EXERCISES - Q31 to Q40

EXERCISES - Q41 to Q50

EXERCISES - Q51 to Q55

CHAPTER- 27-Specific Heat Capacities of Gases

Questions for Short Answer

OBJECTIVE - I

OBJECTIVE -II

EXERCISES - Q1 - Q10

EXERCISES - Q11 - Q20

EXERCISES - Q21 - Q30

EXERCISES - Q31 - Q35

CHAPTER- 26-Laws of Thermodynamics

Questions for Short Answer

OBJECTIVE - I

OBJECTIVE - II

EXERCISES - Q1 to Q10

EXERCISES - Q11 to Q22

CHAPTER- 25-CALORIMETRY

Questions for Short Answer

OBJECTIVE-I

OBJECTIVE-II

EXERCISES - Q1 to Q10

EXERCISES - Q-11 to Q-18

CHAPTER- 24-Kinetic Theory of Gases

Questions for Short Answer

OBJECTIVE - I

OBJECTIVE - II

EXERCISES- Q1 to 10

EXERCISES- Q11 to 20

EXERCISES- Q21 to 30

EXERCISES- Q31 to Q40

EXERCISES- Q41 to Q50

EXERCISES- Q51 to Q62

CHAPTER- 23 - Heat and Temperature

Questions for Short Answer

OBJECTIVE - I

OBJECTIVE - II

EXERCISES - Q-1 TO Q-10

EXERCISES - Q-11 TO Q-20

EXERCISES - Q-21 TO Q-34

CHAPTER- 22 - Photometry

Questions for Short Answer

OBJECTIVE - I

OBJECTIVE - II

EXERCISES

CHAPTER- 21 - Speed of Light

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES

CHAPTER- 20 - Dispersion and Spectra

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES

CHAPTER- 19 - Optical Instruments

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES - Q 1 to Q 12

EXERCISES - Q 13 to Q 24

CHAPTER- 18 - Geometrical Optics

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES - Q 1 to Q10

EXERCISES- Q11 to Q20

EXERCISES- Q21 to Q30

EXERCISES- Q31 to Q40

EXERCISES- Q41 to Q50

EXERCISES- Q51 to Q60

EXERCISES- Q61 to Q70

EXERCISES- Q71 TO 79

CHAPTER- 17 - Light Waves

Questions for Short Answers

OBJECTIVE - I

OBJECTIVE - II

EXERCISES - Q1-Q10

EXERCISES - Q11-Q20

EXERCISES - Q21-Q30

EXERCISES - Q31-Q41

CHAPTER- 16 - Sound Waves

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES - Q-1 TO Q-10

EXERCISES - Q-11 TO Q-20

EXERCISES -Q-21 TO Q-30

EXERCISES -Q-31 TO Q-40

EXERCISES -Q-41 TO Q-50

EXERCISES -Q-51 TO Q-60

EXERCISES -Q-61 TO Q-70

EXERCISES - Q-71 TO Q-80

EXERCISES - Q-81 TO Q-89

CHAPTER- 15 - Wave Motion and Waves on a String

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES - Q-1 TO Q-10

EXERCISES - Q-11 TO Q-20

EXERCISES - Q-21 TO Q-30

EXERCISES - Q-31 TO Q-40

EXERCISES - Q-41 TO Q-50

EXERCISES - Q-51 TO Q-57

CHAPTER- 14 - Fluid Mechanics

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES- Q-1 TO Q-10

EXERCISES- Q-11 TO Q-20

EXERCISES- Q-21 TO Q-32

CHAPTER- 13 - Fluid Mechanics

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES Q-1 TO Q-10

EXERCISES- Q11 TO Q20

EXERCISES Q-21 TO Q30

EXERCISES Q-31 TO Q35

CHAPTER- 12 - Simple Harmonic Motion

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES- Q1 TO Q10

EXERCISES- Q11 TO Q20

EXERCISES- Q21 TO Q30

EXERCISES- Q31 TO Q40

EXERCISES- Q41 TO Q50

EXERCISES- Q51 TO Q58 (2-Extra Questions)

CHAPTER- 11 - Gravitation

Questions for Short Answers

OBJECTIVE - I

OBJECTIVE - II

EXERCISES - Q_1 to Q_10

EXERCISES -Q-11 TO Q-20

EXERCISES -Q 21 TO 30

EXERCISES -Q 31 TO 39

CHAPTER- 10 - Rotational Mechanics

Questions for Short Answers

OBJECTIVE - I

OBJECTIVE - II

EXERCISES - Q-1 TO Q-15

EXERCISES - Q-16 TO Q-30

EXERCISES Q-31 TO Q-45

EXERCISES Q-46 TO Q-60

EXERCISES Q-61 TO Q-75

EXERCISES Q-76 TO Q-86

CHAPTER- 9 - Center of Mass, Linear Momentum, Collision

Questions for Short Answers

Objective - I

Objective - II

EXERCISES Q-1 TO Q-10

EXERCISES Q-11TO Q-20

EXERCISES Q-21 TO Q-30

EXERCISES Q-31 TO Q-42

EXERCISES Q-43 TO Q-54

CHAPTER- 8 - Work and Energy

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Click here for → Exercises (1-10)

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CHAPTER- 7 - Circular Motion

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CHAPTER- 6 - Friction

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For more practice on problems on friction solve these- "New Questions on Friction".

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CHAPTER- 5 - Newton's Laws of Motion

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Click here for→Newton's Laws of Motion,Exercises(Q.No. 13 to 27)

Click here for→Newton's Laws of Motion,Exercises(Q.No. 28 to 42)

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CHAPTER- 4 - The Forces

The Forces-

"Questions for short Answers"    

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Click here for "The Forces" - OBJECTIVE-II

Click here for "The Forces" - Exercises

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CHAPTER- 3 - Kinematics - Rest and Motion

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CHAPTER- 2 - "Physics and Mathematics"

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Exercises (20-35)

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