Sunday, January 16, 2022

H C Verma solutions, ELECTROMAGNETIC INDUCTION, Chapter-38, Questions for Short Answer, Concepts of Physics, Part-II

Electromagnetic Induction


Questions for Short Answer


    1.  A metallic loop is placed in a non-uniform magnetic field. Will an emf be induced in the loop?  


ANSWER: Since there is no change of flux with time, no emf will be induced in the loop.    





    2.  An inductor is connected to a battery through a switch. Explain why the emf induced in the inductor is much larger when the switch is opened as compared to the emf induced when the switch is closed.  


ANSWER: When the switch is closed, the current takes some time to grow. In fact, in one time constant, it grows to 63% of the full current. But when the switch is opened, there is no other path for the current to flow and it suddenly drops to zero in fractions of a second. Thus the rate of change of the current in the circuit is much higher when the switch is opened. So the emf induced in the inductor, in this case, is much larger than in the case when the switch is closed.    




    3.  The coil of a moving-coil galvanometer keeps on oscillating for a long time if it is deflected and released. If the ends of the coil are connected together, the oscillation stops at once. Explain.   


ANSWER: When the coil is released after deflection, it oscillates due to the mechanical energy stored in the suspended wire. During oscillations, the flux of the magnetic field through the coil produced by the poles of the permanent magnets changes, and an emf is developed between the ends of the coil. But no current flows as the ends are not connected. As soon as we connect the ends of the coil, a current begins to flow due to this induced emf and according to Lenz's law, this induced current will produce flux in the coil that will oppose the movement of the coil. So the oscillation stops at once.      




    4.  A short magnet is moved along the axis of a conducting loop. Show that the loop repels the magnet if the magnet is approaching the loop and attracts the magnet if it is going away from the loop.  


ANSWER: When the short magnet is away from the loop on its axis, the magnetic flux through the loop is small compared to the case when it is near to it. So whether we take the magnet closer on the axis of the loop or take it away, there is a change in flux through the loop. This change of flux through the loop will produce an induced current in it. According to Lenz's law, "the direction of the induced current is such that it opposes the change that has induced it". Since the induced current here is due to the movement of the short magnet, it will oppose the movement of the magnet. Thus when the magnet is approaching the loop, it will be repelled by the loop and will be attracted by the loop when going away from it.     




    5.  Two circular loops are placed coaxially but separated by a distance. A battery is suddenly connected to one of the loops establishing a current in it. Will there be a current induced in the other loop? If yes, when does the current start, and when does it end? Do the loops attract each other or do they repel?  


ANSWER: Initially there is no current in either of the loops and no magnetic fields. When the battery is suddenly connected in one of the loops, a current is established in this loop, and magnetic flux through it is also established. But the current and the magnetic flux so produced take a very small amount of time to reach this value from zero. In this small time, there is a change of magnetic flux through the loop. This flux change is also through the second loop that is placed coaxially. This change of the flux through the other loop will also induce a current in this loop. 

      The induced current in the second loop remains for a very short time. It starts as soon as the battery is connected in the first loop and a current begins to grow and ends just when the current reaches a constant value in the first loop. 

     According to Lenz's law, the induced current will oppose the change that has induced it, so the direction of the induced current in the second loop will be such that it will produce a flux that is opposite to the flux produced by the first one. So the loops repel each other in this short time.              




    6.  The battery discussed in the previous question is suddenly disconnected. Is a current induced in the other loop? If yes, when does it start, and when does it end? Do the loops attract each other or repel?   


ANSWER: Originally there is a current established in the first loop. When the battery is suddenly disconnected, the current in the loop becomes zero in a very short time. So there is a change of current from say 'i', to zero. Thus there is a change of magnetic flux through this loop. Since the second loop is coaxially placed parallel to the first one, the magnetic flux through the second loop also changes in that very short time. So this change of flux through the second loop induces a current in it. 

       This induced current in the second loop starts just when the battery is disconnected and ends when the current in the first loop just becomes zero. The current remains only for this very short interval of time. 

      According to Lenz's law, this induced current will oppose the change that has induced it. So the induced current will try to keep the magnetic flux stable as it was when the battery was connected. With the disconnection of the battery, the flux starts reducing, so the induced current in the other loop will produce a magnetic flux in the same direction. Thus the direction of the induced current will be the same as it was in the first loop and the loops will attract each other.


         




    7.  If the magnetic field outside a copper box is suddenly changed what happens to the magnetic field inside the box? Such low-resistivity metals are used to form enclosures that shield objects inside them against varying magnetic fields.   


ANSWER: When the magnetic field outside the copper box suddenly changes, eddy currents develop on the surface of the copper box because it is a low-resistivity metal. According to Lenz's law, the directions of the eddy currents are such that they oppose the change of magnetic field. Thus the varying magnetic field can not affect the objects inside the box.  

    




    8.  Metallic (nonferromagnetic) and nonmetallic particles in solid waste may be separated as follows. The waste is allowed to slide down an incline over permanent magnets. The metallic particles slow down as compared to the nonmetallic ones and hence are separated. Discuss the role of eddy currents in the process. 


ANSWER: When the particles slide over permanent magnets, due to the movement, the magnetic flux near the particles changes. This flux change induces eddy currents in the metallic particles. According to Lenz's law, these induced eddy currents oppose the movement that is the cause of the induced currents. So the metallic particles slow down and the nonmetallic particles are unaffected.    

     




    9.  A pivoted aluminum bar falls much more slowly through a small region containing a magnetic field than a similar bar of insulating material. Explain.  


ANSWER: In a magnetic field, when the pivoted aluminum bar falls, the magnetic flux over it changes due to the change of angle between the bar and the magnetic field. See the diagram below. 
Diagram for Q-9

   Due to the change of flux, eddy currents are induced on the surface of the aluminum bar that opposes the movement (Cause of the induced eddy currents). Thus the aluminum bar falls much more slowly than a similar bar of insulating material that is free from eddy currents.

       




    10.  A metallic bob A oscillates through the space between the poles of an electromagnet (figure 38-Q1). The oscillations are more quickly damped when the circuit is on, as compared to the case when the circuit is off. Explain. 
The figure for Q-10


ANSWER: When the circuit is off, the electromagnet is demagnetized. There is no magnetic field between the ends of the magnet and the metallic bob dampens due to the general causes of friction at the point of hanging and air resistance. As soon as the circuit is kept on, the ends of the electromagnet get poles of opposite nature and the space between them is filled with the magnetic field. When the bob passes through this space, the magnetic flux over it changes. This change of magnetic flux produces eddy currents on the surface of the metallic bob. These induced eddy currents oppose the movement of the bob that causes them to be induced. So the oscillations are more quickly damped than the case when the circuit is off. 

     




    11.  Two circular loops are placed with their centers separated by a fixed distance. How would you orient the loops to have (a) the largest mutual inductance, (b) the smallest mutual inductance?  


ANSWER: When the magnetic flux produced by one loop goes through the boundary of the second loop, an induced current appears in the second loop whenever there is a change of flux. 

  (a) when both the loops are placed coaxially and parallel to each other, maximum magnetic flux passes through them. Hence the mutual inductance is the largest. 

    (b) When the loops are placed with their planes and axes perpendicular to each other, minimum common flux passes through them. Hence in this case the mutual inductance is the smallest.  

       




    12.  Calculate the self-inductance per unit length of a solenoid at its center and that near its ends. Which of the two is greater?  


ANSWER: Self-inductance of a solenoid is 

L =µₒn²πr²l, where l is the length of the solenoid.

   Thus the self-inductance per unit length of the coil is, 

L/l =µₒn²πr² 

   Since this expression has been derived taking the magnetic field inside a solenoid as the same everywhere and the R.H.S. of the above expression depends only on n (number of terms per unit length) and the radius of the solenoid, r. So the self-inductance of the coil is the same near the ends and at the center of the coil.     

      




    13.  Consider the energy density in a solenoid at its center and that near its ends. Which of the two is greater?  


ANSWER: The energy density inside a solenoid is, 

u =B²/(2µₒ). 

In deriving this expression, it is assumed that the magnetic field throughout the volume of the solenoid is uniform and zero outside. Hence the energy density is the same at its center and near its ends.      

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Links to the Chapters





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

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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

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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".

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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)

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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


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CHAPTER- 3 - Kinematics - Rest and Motion

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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"

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Click here for "OBJECTIVE-II"

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