Tuesday, June 28, 2022

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

Electromagnetic Waves


OBJECTIVE-I


     1.  A magnetic field can be produced by

(a) moving charge

(b) a changing electric field

(c) none of them

(d) both of them    


ANSWER: (d).  


EXPLANATION: A magnetic field can be produced both by a moving charge and a changing electric field. The current by the moving charge is called conduction current and due to the changing electric field is called the displacement current. Option (d) is correct.   





     2.  A compass needle is placed in the gap of a parallel plate capacitor. The capacitor is connected to a battery through resistance. The compass needle

(a) does not deflect

(b) deflects for a very short time and then comes back to the original position

(c) deflects and remains deflected as long as the battery is connected

(d) deflects and gradually comes to the original position in a time that is large compared to the time constant.    

ANSWER: (d).  


EXPLANATION: When the capacitor is connected to a battery, the plates start to be charged. During this charging, there is a changing electric field between the plates. This results in a magnetic field between the plates. So the compass needle deflects. Up to the time constant 𝝉 =CR, the plates are charged up to 63%. For the rest of 37% of charging, the time taken is many times longer than 𝝉. So the rate of charging of the plates (and hence the rate of change of electric field between the plates) up to the time t =𝝉 is comparatively faster than the rest of the charging time. Since the magnetic field between the plates depends upon the rate of change of the electric field (which is highest initially), the magnetic field created initially is maximum and then it decreases. So the compass needle deflects initially to maximum and then gradually comes to the original position (when the plates are fully charged and the rate of the change is almost zero). The time taken to come to the original position is many times more than the time constant, as discussed above. Hence option (d) is correct. 

 




     3.  Dimensions of 1/(µₒεₒ) is

(a) L/T 

(b) T/L

(c) L²/T²

(d) T²/L²  

ANSWER: (c).  


EXPLANATION: The speed of an electromagnetic wave is given as,  

c =1/√(εₒµₒ)

→1/(εₒµₒ) =c²

Since the dimensions of speed c are LT⁻¹, the dimensions of 

1/(εₒµₒ) =(LT⁻¹)² =L²/T².

Hence option (c) is correct.

      




     4.  Electromagnetic waves are produced by 

(a) a static charge

(b) a moving charge

(c) an accelerating charge

(d) chargeless particles.    

ANSWER: (c).  


EXPLANATION: Electromagnetic waves are produced by an accelerated charge because an accelerated charge produces a changing electric field and a changing magnetic field which constitutes the wave.

Hence option (c) is correct.   


  




     5.  An electromagnetic wave going through a vacuum is described by 

E =Eₒ sin(kx-⍵t); B =Bₒsin(kx-⍵t)

Then

(a) Eₒk =Bₒ⍵

(b) EₒBₒ =⍵k

(c) Eₒ⍵ =Bₒk

(d) none of these 

ANSWER: (a).  


EXPLANATION: Since Eₒ/Bₒ =c

and ⍵/k =c, where k is the wave number.

Thus, ⍵/k =Eₒ/Bₒ

→Eₒk =Bₒ⍵.

Option (a) is correct.

 

 




     6.  An electric field E and a magnetic field B exist in a region. The fields are not perpendicular to each other. 

(a) This is not possible.

(b) No electromagnetic wave is passing through the region.

(c) An electromagnetic wave may be passing through the region.

(d) An electromagnetic wave is certainly passing through the region.  

ANSWER: (c).  


EXPLANATION: An electric field E and a magnetic field B may exist independently in a region at any angle. Hence option (a) is not correct.

    The mutually perpendicular and varying electric and magnetic fields of an electromagnetic wave are linked to each other and they are not affected by the electric and magnetic fields of other sources. Hence an electromagnetic wave can pass unaffected in such external fields. So in the given condition, an electromagnetic wave may be passing through the region. Option (c) is correct. Options (b) and (d) are not binding and hence not correct.   


  




     7.  Consider the following two statements regarding a linearly polarized, plane electromagnetic wave: 

(A) The electric field and the magnetic field have equal average values.

(B) The electric energy and the magnetic energy have equal average values.


(a) Both A and B are true.

(b) A is false but B is true

(c) B is false but A is true

(d) Both A and B are false.     

ANSWER: (a).  


EXPLANATION: The electric and magnetic fields are sinusoidal waves in an electromagnetic wave. In a single time period, the average value of the sinusoidal wave is zero. If we take the average value over a long time, the value of the average field will be the same Hence both the electric and magnetic fields have an equal average value equal to zero. Statement A is true. 

    In an electromagnetic wave, the average electric field energy density over a long time is

Ue =¼εₒEₒ²

and average magnetic field energy density over a long time is

Ub ={1/(4µₒ)}*Bₒ²

Since Eₒ =cBₒ, and µₒεₒ =1/c²

Ub =(εₒc²/4)*(Eₒ/c)² =¼εₒEₒ² =Ue 

So average electric and magnetic field energy value is equal. Statement B is also true.

Hence option (a) is correct.  


      




     8.  A free electron is placed in the path of a plane electromagnetic wave. The electron will start  moving 

(a) along the electric field

(b) along the magnetic field

(c) along the direction of propagation of the wave

(d) In a  plane containing the magnetic field and the direction of propagation. 

ANSWER: (a).  


EXPLANATION: When a free electron is placed in the path of an electromagnetic wave, it will only be affected by the electric field. A charge at rest is unaffected by a magnetic field. So the electron will start moving along the electric field. Option (a) is correct. 


    




     9.  A plane electromagnetic wave is incident on a material surface. The wave delivers momentum p and energy E.

(a) p =0, E ≠0.

(b) p ≠0, E =0.

(c) p ≠0, E ≠0.

(d) p =0, E =0. 

ANSWER: (c)  


EXPLANATION: The relation between momentum p and energy E is 

p =E/c, where c is the speed of light. 

Clearly, options (a) and (b) are incorrect. 

Also, an electromagnetic wave always carries energy, hence it has some non-zero momentum from the above relation. Thus option (d) is not correct. 

Only option (c) is correct.    


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Links to the Chapters




CHAPTER- 40- Electromagnetic Waves


CHAPTER- 34- Magnetic Field

CHAPTER- 29- Electric Field and Potential











CHAPTER- 28- Heat Transfer

OBJECTIVE -I







EXERCISES - Q51 to Q55


CHAPTER- 27-Specific Heat Capacities of Gases

CHAPTER- 26-Laws of Thermodynamics


CHAPTER- 25-CALORIMETRY

Questions for Short Answer

OBJECTIVE-I

OBJECTIVE-II


EXERCISES - Q-11 to Q-18


CHAPTER- 24-Kinetic Theory of Gases







CHAPTER- 23 - Heat and Temperature






CHAPTER- 17 - Light Waves




CHAPTER- 14 - Fluid Mechanics



CHAPTER- 13 - Fluid Mechanics


CHAPTER- 12 - Simple Harmonic Motion








CHAPTER- 11 - Gravitation




CHAPTER- 10 - Rotational Mechanics




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


CHAPTER- 8 - Work and Energy

Click here for → Question for Short Answers

Click here for → OBJECTIVE-I

Click here for → OBJECTIVE-II

Click here for → Exercises (1-10)

Click here for → Exercises (11-20)

Click here for → Exercises (21-30)

Click here for → Exercises (31-42)

Click here for → Exercise(43-54)

CHAPTER- 7 - Circular Motion

Click here for → Questions for Short Answer 

Click here for → OBJECTIVE-I

Click here for → OBJECTIVE-II

Click here for → EXERCISES (1-10)

Click here for → EXERCISES (11-20)

Click here for → EXERCISES (21-30)

CHAPTER- 6 - Friction

Click here for → Questions for Short Answer

Click here for → OBJECTIVE-I

Click here for → Friction - OBJECTIVE-II

Click here for → EXERCISES (1-10)

Click here for → Exercises (11-20)

Click here for → EXERCISES (21-31)

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

---------------------------------------------------------------------------------

CHAPTER- 5 - Newton's Laws of Motion


Click here for → QUESTIONS FOR SHORT ANSWER

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

-------------------------------------------------------------------------------

CHAPTER- 4 - The Forces

The Forces-

"Questions for short Answers"    


Click here for "The Forces" - OBJECTIVE-I


Click here for "The Forces" - OBJECTIVE-II


Click here for "The Forces" - Exercises


--------------------------------------------------------------------------------------------------------------

CHAPTER- 3 - Kinematics - Rest and Motion

Click here for "Questions for short Answers"


Click here for "OBJECTIVE-I"


Click here for EXERCISES (Question number 1 to 10)


Click here for EXERCISES (Question number 11 to 20)


Click here for EXERCISES (Question number 21 to 30)


Click here for EXERCISES (Question number 31 to 40)


Click here for EXERCISES (Question number 41 to 52)


CHAPTER- 2 - "Physics and Mathematics"

Click here for "Questions for Short Answers"


Click here for "OBJECTIVE-II"

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