Electromagnetic Induction
OBJECTIVE-II
1. A bar magnet is moved along the axis of a copper ring placed far away from the magnet. Looking from the side of the magnet, an anticlockwise current is found to be induced in the ring. Which of the following may be true?
(a) The south pole faces the ring and the magnet moves towards it.
(b) The north pole faces the ring and the magnet moves towards it.
(c) The south pole faces the ring and the magnet moves away from it.
(d) The north pole faces the ring and the magnet moves away from it.
ANSWER: (b), (c).
EXPLANATION: The induced current opposes the cause of its occurrence. Since the induced current is anticlockwise when viewed from the magnet, the north pole of the equivalent magnetic dipole of the ring is towards the magnet. It means that the direction of the magnetic flux by the ring is towards the magnet. By this flux, the ring opposes the flux by the magnet.
(1) one condition is that the north pole of the magnet is facing the ring and approaching it and the ring is opposing the increase of flux towards it. Option (b) is correct.
(2) the second condition is that the south pole of the magnet is towards the ring and is going away from the ring resulting in the decrease of flux near the ring. The induced current in the ring produces flux towards the magnet to maintain the original flux. Option (c) is correct.
The other two conditions will induce a clockwise current in the ring.
2. A conducting rod is moved with a constant velocity v in a magnetic field. A potential difference appears across the two ends
(a) if v || l
(b) if v || B
(c) if l || B
(d) none of these.
ANSWER: (d)
EXPLANATION: The potential difference in a rod moving in a magnetic field is due to the magnetic force on the free electrons in the rod, and they concentrate towards one end. If the velocity is along the length any magnetic force on electrons will not be able to concentrate them towards an end. Option (a) is not correct.
If the velocity is along the magnetic field, no magnetic force will be on the electrons. Option (b) is not correct.
If the length is parallel to the magnetic field, even a perpendicular to field movement can not produce potential difference because the force on the electrons will be transverse to the length and electrons can not concentrate at one end. So option (c) is also not correct.
Hence none of these options are correct. Option (d) is correct.
3. A conducting loop is placed in a uniform magnetic field with its plane perpendicular to the field. An emf is induced in the loop if
(a) it is translated
(b) it is rotated about its axis
(c) it is rotated about about a diameter
(d) it is deformed.
ANSWER: (c), (d).
EXPLANATION: emf is induced in a loop when the flux density perpendicular to its plane changes. The flux density does not change if the loop is translated or rotated about its axis. No emf is induced in these two cases. Options (a) and (b) are not correct.
When the loop is rotated or deformed the flux density through it changes, hence emf will be induced. Options (c) and (d) are correct.
4. A metal sheet is placed in front of a strong magnetic pole. A force is needed to
(a) hold the sheet there if the metal is magnetic.
(b) hold the sheet there if the metal is nonmagnetic
(c) move the sheet away from the pole with uniform velocity if the metal is magnetic
(d) move the sheet away from the pole with uniform velocity if the metal is nonmagnetic.
Neglect any effect of paramagnetism, diamagnetism, and gravity.
ANSWER: (a), (c), (d).
EXPLANATION: If the sheet is magnetic, it will be attracted towards the magnetic pole and a force will be needed to hold it. Option (a) is correct.
For a nonmagnetic metal sheet, there will be no attraction, thus no force needed. Option (b) is not correct.
When a magnetic or nonmagnetic metal sheet is moved away from the pole, magnetic flux near the sheet changes. Thus induced eddy currents develop in the sheet that opposes the movement. Hence a force will be needed to keep it moving with constant velocity. Options (c) and (d) are correct.
5. A constant current i is maintained in a solenoid. Which of the following quantities will increase if an iron rod is inserted in the solenoid along its axis?
(a) the magnetic field at the center
(b) magnetic flux linked with the solenoid
(c) self-inductance of the solenoid
(d) rate of Joule heating.
ANSWER: (a), (b), (c).
EXPLANATION: Before the rod is inserted in the solenoid, the magnetic field at the center is µₒni. As the rod is inserted the magnetic field becomes, µni, where µ is the permeability of the iron. Option (a ) correct.
The magnetic flux also changes from "(µₒni)πr²" to "(µni)πr²" after the iron rod is inserted. Option (b) is correct.
Self-inductance of the coil also changes from "µₒn²πr²l" to "µn²πr²l". Hence option (c) is also correct.
The rate of Joule heating depends on the resistance of the coil which does not change. Hence option (d) is not correct.
6. Two solenoids have identical geometrical construction but one is made of thick wire and the other of thin wire.
Which of the following quantities are different for the two solenoids?
(a) self-inductance
(b) rate of Joule heating if the same current goes through them
(c) magnetic field energy if the same current goes through them
(d) the time constant if one solenoid is connected to one battery and the other is connected to another battery.
ANSWER: (b), (d).
EXPLANATION: The self-inductance of a solenoid depends only on the geometrical factors that are the same in both solenoids. Hence self-inductance is not different for them. Option (a) is not correct.
The thin wired solenoid will have higher resistance, so Joule heating will be more in it for the same current. Option (b) is correct.
Magnetic field energy in a solenoid =½Li. So it will be the same in both solenoids, not different. Option (c) is not correct.
The time constant =L/R. L is the same for both but not R. Hence time constant is different for them. Option (d) is correct.
7. An LR circuit with a battery is connected at t =0. Which of the following quantities is not zero just after the connection?
(a) current in the circuit
(b) magnetic field energy in the inductor
(c) power delivered by the battery
(d) emf induced in the inductor.
ANSWER: (d)
EXPLANATION: As the connection is made, the current begins to grow. So a small current is present just after the connection. Magnetic field energy depends on the current. Hence it is also not zero. Power delivered by the battery =i²R, so it is not zero too. Thus options (a), (b), and (c) are not correct.
Emf is induced when there is a change in the current. When the battery is just connected, the current just begins, not changes. Hence no emf. Option (d) is correct.
8. A rod AB moves with a uniform velocity v in a uniform magnetic field as shown in figure (38-Q7).
(a) The rod becomes electrically charged.
(b) The end A becomes positively charged.
(c) The end B becomes positively charged.
(d) The rod becomes hot because of Joule heating. 
The figure for Q-8
ANSWER: (b)
EXPLANATION: Since total electrons remain in the rod, there is no question of the rod being electrically charged. Option (a) is not correct.
From the right-hand rule, the magnetic force on a positive charge moving with the given velocity will be towards end A. Since there are free electrons in the rod, not positive charges, the magnetic force will be towards end B on the electrons. The electrons in the rod will concentrate towards end B and end A will be deficient in electrons. So end A will be positively charged. Option (b) is correct. Option (c) is not correct
With the end A positively charged and end B negatively, an emf is developed between the ends A and B. But there is no current flowing, it is like a disconnected battery. So no Joule heating because i =0. Option (d) is not correct.
9. L, C, and R represent the physical quantities inductance, capacitance, and resistance respectively. Which of the following combinations have dimensions of frequency?
(a) 1/RC
(b) R/L
(c) 1/√(LC)
(d) C/L.
ANSWER: (a), (b), (c).
EXPLANATION: Dimensions of L, C and R are as follows.
L = M L² T⁻² I⁻²
C = M⁻¹ L⁻² T⁴ I²
R = M L² T⁻³ I⁻²
So,
[RC] = [T]
and dimensions of 1/RC = [T⁻¹], which is the dimensions of frequency. Option (a) is correct.
[R/L] = [T⁻¹], which is also the dimensions of frequency. Option (b) is correct.
[LC] = [T²], hence,
[1/√(LC)] = [T⁻¹]. It is also the dimensions of frequency. So option (c) is also correct.
[C/L] = [M⁻² L⁻⁴ T⁶ I⁴], and it is not the dimensions of frequency. Option (d) is not correct.
10. The switches in figure (38-Qa) and (38-8b) are closed at t = 0 and reopened after a long time at t = tₒ. 
The figure for Q -10
(a) The charge on C just after t =0 is ξC.
(b) The charge on C long after t =0 is ξC.
(c) The current in L just before t = tₒ is ξ/R.
(d) The current in L long after t = tₒ is ξ/R.
ANSWER: (b), (c).
EXPLANATION: The charge on a capacitor becomes maximum after a long time and it is = ξC. Hence option (a) is not correct but option (b) is correct.
The current in the inductance reaches to the maximum before a long time. So just before, t = tₒ, the full current is developed in L and this current is equal to ξ/R. So option (c) is correct. Since at t = tₒ the switch is reopened, after this, the current decreases from ξ/R. So option (d) is not correct.
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Links to the Chapters
Links to the Chapters
CHAPTER- 38- Electromagnetic Induction
CHAPTER- 37- Magnetic Properties of MatterCHAPTER- 36- Permanent Magnets
CHAPTER- 35- Magnetic Field due to a Current
CHAPTER- 34- Magnetic Field
CHAPTER- 33- Thermal and Chemical Effects of Electric Current
CHAPTER- 38- Electromagnetic Induction
CHAPTER- 37- Magnetic Properties of Matter
CHAPTER- 36- Permanent Magnets
CHAPTER- 35- Magnetic Field due to a Current
CHAPTER- 34- Magnetic Field
CHAPTER- 33- Thermal and Chemical Effects of Electric Current
CHAPTER- 32- Electric Current in ConductorsCHAPTER- 31- CapacitorsCHAPTER- 30- Gauss's Law
CHAPTER- 29- Electric Field and Potential
CHAPTER- 28- Heat Transfer
OBJECTIVE -I
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- 21 - Speed of Light
CHAPTER- 20 - Dispersion and Spectra
CHAPTER- 19 - Optical Instruments
CHAPTER- 18 - Geometrical Optics
CHAPTER- 17 - Light Waves
CHAPTER- 16 - Sound Waves
CHAPTER- 15 - Wave Motion and Waves on a String
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- 32- Electric Current in Conductors
CHAPTER- 31- Capacitors
CHAPTER- 30- Gauss's Law
CHAPTER- 29- Electric Field and Potential
CHAPTER- 28- Heat Transfer
CHAPTER- 26-Laws of Thermodynamics
CHAPTER- 25-CALORIMETRY
Questions for Short Answer
OBJECTIVE-I
OBJECTIVE-II
CHAPTER- 24-Kinetic Theory of Gases
CHAPTER- 23 - Heat and Temperature
CHAPTER- 21 - Speed of Light
CHAPTER- 20 - Dispersion and Spectra
CHAPTER- 19 - Optical Instruments
CHAPTER- 18 - Geometrical Optics
CHAPTER- 17 - Light Waves
CHAPTER- 16 - Sound Waves
CHAPTER- 15 - Wave Motion and Waves on a String
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 → Question for Short Answers
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Click here for → Exercises (11-20)
CHAPTER- 7 - Circular Motion
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Click here for → EXERCISES (11-20)
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CHAPTER- 6 - Friction
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CHAPTER- 6 - Friction
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Click here for → Friction - OBJECTIVE-II
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Click here for → Exercises (11-20)
Click here for → EXERCISES (21-31)
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CHAPTER- 5 - Newton's Laws of Motion
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Click here for → QUESTIONS FOR SHORT ANSWER
Click here for→ Newton's laws of motion - Objective - I
Click here for → Newton's Laws of Motion - Objective -II
Click here for → Newton's Laws of Motion-Exercises(Q. No. 1 to 12)
Click here for→ Newton's laws of motion - Objective - I
Click here for → Newton's Laws of Motion - Objective -II
Click here for → Newton's Laws of Motion-Exercises(Q. No. 1 to 12)
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 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"
CHAPTER- 2 - "Physics and Mathematics"
