## Chapter 6 Electromagnetic Induction Exercise 1 Multiple Choice Questions And Answers

## Chapter 6 Electromagnetic Induction Flux And Faraday’s Laws Of Electromagnetic Induction

**Question 1. The horizontal component of Earth’s magnetic field is 3 × 10 ^{-5 }Wb/m^{2}. The magnetic flux linked with a coil of area 1 m^{2} and having 5 turns, whose plane is normal to the magnetic field, will be**

- 3 x 10
^{-5}Wb - 5 x 10
^{-5}Wb - 15 x 10
^{-5}Wb - 1 x 10
^{-5}Wb

**Answer:** 3. 15 x 10^{-5 }Wb

**Question 2. Tesla is a unit of**

- Magnetic flux
- Magnetic flux density
- Electric flux
- Self-inductance

**Answer:** 2. Magnetic flux density

**Question 3. The formula of the induced emf due to the rate of change of magnetic flux passing through a coil will be**

- \(e=-\frac{d}{d t}(\vec{B} \cdot \vec{A})\)
- \(e=\frac{\overrightarrow{d B}}{d t}\)
- \(e=-\vec{A} \cdot\left(\frac{\overrightarrow{d B}}{d t}\right)\)
- \(\mathrm{e}=-\overrightarrow{\mathrm{B}} \cdot \frac{\overrightarrow{\mathrm{dA}}}{\mathrm{dt}}\)

**Answer:** 1. \(e=-\frac{d}{d t}(\vec{B} \cdot \vec{A})\)

**Question 4. A cube of side a is placed in a magnetic field of intensity B. The magnetic flux emerging out(outgoing flux only) of the cube will be**

- Ba
^{2} - –Ba
^{2} - 2Ba
^{2} - Zero

**Answer:** 1. Ba^{8}

**Question 5. The figure represents an area A = 0.5m ^{2} situated in a uniform magnetic field B = 2.0 weber/m^{2} and making an angle of 60º with respect to the magnetic field. The value of the magnetic flux through the area would be equal to**

- 2.0 weber
- √3 weber
- 3/2 weber
- 0.5 weber

**Answer:** 4. 0.5 Weber

**Question 6. If Φ = 0.02 cos 100 πt weber/turns and the number of turns is 50 in the coil, the maximum induced emf is**

- 314 volt
- 100 volt
- 31.4 volt
- 6.28 volt

**Answer:** 1. 314 volt

**Question 7. The magnetic flux linked with the coil varies with time as Φ = 3t² + 4t + 9. The magnitude of induced emf at t = 2 seconds is**

- 4V
- 3V
- 16 V
- 9 V

**Answer:** 3. 16 V

**Question 8. A conducting square loop of side land resistance R moves in its plane with a uniform velocity v perpendicular to one of its sides. A uniform and constant magnetic field B exists perpendicular to the plane of the loop in Figure. The current induced in the loop is**

- \(\text { Blv/R clockwise }\)
- \(\text { Blv/R anticlockwise }\)
- \(\text { 2Blv/R anticlockwise }\)
- Zero

**Answer:** 4. Zero

**Question 9. A long conductor AB lies along the axis of a circular loop of radius R. If the current in the conductor AB varies at the rate of I ampere/second, then the induced emf in the loop is**

- \(\frac{\mu_0 \mathrm{IR}}{2}\)
- \(\frac{\mu_0 I R}{4}\)
- \(\frac{\mu_0 \pi \mathrm{IR}}{2}\)
- Zero

**Answer:** 4. Zero

**Question 10. The magnetic flux through a circuit of resistance R changes by an amount ΔΦ in a time At. Then the total quantity of electric charge Q that passes any point in the circuit during the time Δt is represented by**

- \(\mathrm{Q}=\frac{\Delta \phi}{\mathrm{R}}\)
- \(\mathrm{Q}=\frac{\Delta \phi}{\Delta \mathrm{t}}\)
- \(Q=R \cdot \frac{\Delta \phi}{\Delta t}\)
- \(Q=\frac{1}{R} \cdot \frac{\Delta \phi}{\Delta t}\)

**Answer:** 1. \(Q=\frac{1}{R} \cdot \frac{\Delta \phi}{\Delta t}\)

## Chapter 6 Electromagnetic Induction Lenz’s Law

**Question 1. Lenz’s law is based on the law of conservation of**

- Charge
- Momentum
- Mass
- Energy

**Answer:** 4. Energy

**Question 2. A bar magnet is dropped vertically downward through a metal ring held horizontally. The acceleration of the falling magnet will be**

- Equal to g
- Greater than g
- Less than g
- Dependent on the radius of the ring

**Answer:** 3. Less than g

**Question 3. Two identical coils A and B are arranged coaxially as shown in the figure and the sign convention adopted is that the direction of currents are taken as positive when they flow in the direction of arrows. Which of the following statements is correct**

- If A carries a steady positive current and A is moved towards B, then a positive current is induced in B.
- If A carries a steady positive current and B is moved towards A, then a negative current is induced in B
- If both coils carry a positive current, then the coils repel each other.
- If a positive current flowing in A is switched off, then a negative current is induced momentarily in B

**Answer:** 2. If A carries a steady positive current and B is moved towards A, then a negative current is induced in B

**Question 4. An electron passes near a ring and approaches to ring, then the direction of the induced current in the ring is:**

- Clockwise
- Anticlockwise
- Both (1) and (2)
- No current

**Answer:** 2. Both (1) and (2)

**Question 5. A magnet is taken towards a coil-**

- Rapidly
- Slowly

**Then the induced emf is**

- More in (1)
- Less in (1)
- Same in both (1) and (2)
- It more or less depends on the radius

**Answer:** 1. More in (1)

**Question 6. The north pole of a magnet is brought near a metallic ring as shown. The direction of the induced current in the ring will be**

- Anticlockwise from the magnet side
- Clockwise from the magnet side
- First anticlockwise and then clockwise from the magnet side
- First clockwise and then anticlockwise from the magnet side

**Answer**: 1. Anti-clockwise from magnet side

**Question 7. When a magnet is moved with its north pole towards a coil placed in a closed circuit, then the nearest face of the coil-**

- Shows south polarity
- Shows north polarity
- Shows no polarity
- Shows sometimes north and sometimes south polarity

**Answer:** 2. Shows north polarity

**Question 8. Consider the situation shown. If the switch is closed and after some time it is opened again, the closed loop will show**

- An anticlockwise current-pulse
- A clockwise current-pulse
- An anticlockwise current-pulse and then a clockwise current-pulse
- A clockwise current-pulse and then an anticlockwise current-pulse

**Answer:** 4. A clockwise current-pulse and then an anticlockwise current-pulse

**Question 9. Solve the previous question if the closed loop is completely enclosed in the circuit containing the switch.**

- An anticlockwise current-pulse
- A clockwise current-pulse
- An anticlockwise current-pulse and then a clockwise current-pulse
- A clockwise current-pulse and then an anticlockwise current-pulse

**Answer:** 3. An anticlockwise current-pulse and then a clockwise current-pulse

**Question 10. A small, conducting circular loop is placed inside a long solenoid carrying a current. The plane of the loop contains the axis of the solenoid. If the current in the solenoid is varied, the current induced in the loop is**

- Clockwise
- Anticlockwise
- Zero
- Clockwise or anticlockwise depending on whether the resistance is increased or decreased.

**Answer:** 3. Zero

**Question 11. Shows a horizontal solenoid connected to a battery and a switch. A copper ring is placed on a frictionless track, the axis of the ring being along the axis of the solenoid. As the switch is closed, the ring will**

- Remain stationary
- Move towards the solenoid
- Move away from the solenoid
- Move towards the solenoid or away from it depending on which terminal (positive or negative) of the battery is connected to the left end of the solenoid.

**Answer:** 3. Move away from the solenoid

**Question 12. Two circular coils A and B are facing each other as shown in the figure. The current I through A can be altered**

- There will be repulsion between a and b if I is increased
- There will be an attraction between a and b if I am increased
- There will be neither attraction nor repulsion when I changed
- Attraction or repulsion between a and b depends on the direction of the current. It does not depend on whether the current is increased or decreased.

**Answer:** 1. There will be repulsion between a and b if I am increased

**Question 13. Two identical conductors P and Q are placed on two frictionless fixed conducting rails R and S in a uniform magnetic field directed into the plane. If P is moved in the direction shown in the figure with a constant speed, then rod Q**

- Will be attracted towards P
- Will be repelled away from P
- will remain stationary
- Maybe repelled or attracted toward P

**Answer:** 1. Will be attracted toward P

**Question 14. In the figure shown, the magnet is pushed towards the fixed ring along the axis of the ring and it passes through the ring.**

- When the magnet goes towards the ring face B becomes the south pole and face A becomes the north pole
- When the magnet goes away from the ring face B becomes the north pole and face A becomes the south pole
- When the magnet goes away from the ring face A becomes the north pole and face B becomes the south pole
- The face A will always be a north pole.

**Answer:** 3. When the magnet goes away from the ring face A becomes the north pole and face B becomes the south pole

## Chapter 6 Electromagnetic Induction Induced Emf In A Moving Rod In Uniform Magnetic Field

**Question 1. A wire of length 2m is moving with a velocity of 1 m/s normal to a magnetic field of 0.5 Wb/m². The emf induced in it will be – \((\ell \perp \vec{v})\)**

- 0.5 V
- 0.1V
- 2 V
- 1 V

**Answer:** 4. 1 V

**Question 2. An airplane having a distance of 50 m between the edges of its wings is flying horizontally with a speed of 720 km/hour. If the vertical component of the earth’s magnetic field is 2 x 10 ^{-4 }Wb/m^{2}, then the induced emf will be**

- 2mV
- 2V
- 200V
- 0.2mV

**Answer:** 2. 2V

**Question 3. A straight conductor of length 0.4 m is moved in a magnetic field of 0.9 weber/m² with a velocity of 7 m/s. The maximum EMF induced in the conductor will be**

- 2.52 V
- 25 V
- 2.8 V
- 63 V

**Answer**: 1. 2.52 V

**Question 4. An athlete runs at a velocity of 30 km/hr. towards the east with a 3-meter rod. The horizontal component of the earth is 4 × 10 ^{-5} weber/m². If he runs, keep the rod**

**Horizontal and****Vertical, the p.d. at the ends of the rod in both cases, will be**

- Zero in the vertical case and 1 × 10
^{-3}V in the horizontal case. - 1 × 10
^{-3}V in the vertical case and zero in the horizontal case. - Zero in both cases.
- 1 × 10
^{-3}V in both the cases.

**Answer:** 2. 1 × 10^{-3} V in the vertical case and zero in the horizontal case.

**Question 5. A conducting wire is moving in a magnetic field B towards the right. The direction of the induced current is shown in the figure. The direction of the magnetic field will be**

- In the plane of paper pointing towards the right.
- In the plane of paper pointing towards the left.
- Perpendicular and downwards to the plane of the paper.
- Perpendicular to the plane of the paper and upwards.

**Answer:** 3. Perpendicular and downwards to the plane of paper.

**Question 6. A conducting rod is moved with a constant velocity \(\overrightarrow{\mathrm{v}}\) in a magnetic field. A potential difference appears across the two ends**

- if \(\bar{u} \| \vec{\ell}\)
- if \(\vec{v} \| \vec{B}\)
- if \(\vec{\ell} \| \vec{B}\)
- None of these

**Answer:** 4. if \(\vec{\ell} \| \vec{B}\)

**Question 7. A uniform magnetic field exists in the region given by \(\vec{B}=3 \hat{i}+4 \hat{j}+5 \hat{k}\). A rod of length 5 m is placed along the y−axis and is moved along the x−axis with a constant speed of 1 m/sec. Then induced e.m.f. in the rod will be:**

- Zero
- 25 v
- 20 v
- 15 v

**Answer:** 2. 25 v

**Question 8. A rod AB moves with a uniform velocity v in a uniform magnetic field as shown.**

- The rod becomes electrically charged
- The End A becomes positively charged
- End B becomes positively charged
- The rod becomes hot because of Joule heating

**Answer:** 2. The end A becomes positively charged

**Question 9. The distance between the ends of the wings of an airplane is 5m. The airplane is moving with a velocity of 200 km/sec in a magnetic field of 10T. The emf induced across the ends of wings will be:**

- 10
^{7}volt - 10 volt
- 10
^{6}volt - None of these

**Answer:** 1. 10^{7} volt

**Question 10. A straight conductor of length 4m moves at a speed of 10m/s. When the conductor makes an angle of 30° with the direction of the magnetic field of induction of 0.1 wb. per m ^{2} then induced emf is:**

- 8V
- 4V
- 1V
- 2V

**Answer:** 4. 2V

**Question 11. As a result of a change in the magnetic flux linked to the closed loop shown in the figure, an emf V volt is induced in the loop. The work done (joules) in taking a charge Q coulomb once along the loop is:**

- QV
- Zero
- 2QV
- 5QV

**Answer:** 1. QV

## Chapter 6 Electromagnetic Induction Circuit Problems And Mechanics

**Question 1. AB and CD are fixed conducting smooth rails placed in a vertical plane and joined by a constant current source at its upper end. PQ is a conducting rod that is free to slide on the rails. A horizontal uniform magnetic field exists in space as shown. If the rod PQ is released from rest then,**

- The rod PQ may move downward with constant acceleration
- The rod PQ may move upward with constant acceleration
- The rod will move downward with decreasing acceleration and finally acquire a constant velocity
- Either A or B.

**Answer:** 4. Either A or B.

**Question 2. A metallic rod completes its circuit as shown in the figure. The circuit is normal to a magnetic field of B = 0.15 tesla. If the resistance is 3Q the force required to move the rod with a constant velocity of 2 m/sec is**

- 3.75 x 10
^{-3}N - 3.75 x 10
^{-2}N - 3.75 x 10
^{2}N - 3.75 x 10
^{-4}N

**Answer:** 1. 3.75 x 10^{-3} N

**Question 3. Consider the situation shown in the figure. The wire AB is slid on the fixed rails with a constant velocity. If the wire AB is replaced by a semicircular wire, the magnitude of the induced current will**

- Increase
- Remain the same
- Decrease
- Increase or decrease depending on whether the semicircle bulges towards the resistance or away from it.

**Answer:** 2. Remain the same

**Question 4. Shows a square loop of side 0.5 m and resistance 10Ω. The magnetic field on the left side of the line PQ has a magnitude B = 1.0T. The work done in pulling the loop out of the field uniformly in 2.0 s is**

- 3.125 x 10
^{-3}J - 6.25 x 10
^{-4}J - 1.25 x 10
^{-2 }J - 5.0 x 10
^{-4}J

**Answer:** 1. 3.125 x 10^{-3} J

**Question 5. One conducting U tube can slide inside another as shown in the figure, maintaining electrical contacts between the tubes. The magnetic field B is perpendicular to the plane of the figure. If each tube is towards the other at a constant speed v, then the emf induced in the circuit in terms of B, l, and v, where l is the width of each tube, will be:**

- Blv
- -Blv
- Zero
- 2 Blv

**Answer:** 4. 2 Blv

## Chapter 6 Electromagnetic Induction Induced Emf In A-Rod, Ring, Disc Rotating In A Uniform Magnetic Field

**Question 1. A metal rod of length L is placed normally to a magnetic field and rotated in a circular path with frequency f. The potential difference between it ends will be**

- πL²Bf
- BL/f
- πL²B/f
- fBL

**Answer:** 1. πL²Bf

**Question 2. A rectangular coil ABCD is rotated anti-clockwise with a uniform angular velocity about the axis shown in the figure. The axis of rotation of the coil as well as the magnetic field B are horizontal. The induced emf in the coil would be maximum when**

- The plane of the coil is horizontal
- The plane of the coil makes an angle of 45° with the direction of the magnetic field
- The plane of the coil is at right angles to the magnetic field
- The plane of the coil makes an angle of 30° with the horizontal

**Answer:** 1. The plane of the coil is horizontal

**Question 3. A coil is placed in a uniform magnetic field such that its plane is parallel to the magnetic field. In time interval Δt its plane becomes perpendicular to the magnetic field, then induced charge q in coil depends on the time interval Δt as**

- \(q \alpha \Delta t\)
- \(q \alpha \frac{1}{\Delta t}\)
- \(q \alpha(\Delta t)^0\)
- \(q \alpha(\Delta t)^2\)

**Answer:** 3. \(q \alpha(\Delta t)^0\)

**Question 4. A metallic conductor of 1 m length is rotated vertically its one end at an angular velocity of 5 rad/sec. If the horizontal component of the earth’s field is 0.2 x 10 ^{-4 }T, the voltage generated between the ends of the conductor will be**

- 5 mV
- 5 x 10
^{-4}V - 50 mV
- 50 μ V

**Answer:** 4. 50 μ V

**Question 5. A rectangular coil has 60 turns and its length and width are 20 cm and 10 cm respectively. The coil rotates at a speed of 1800 rotations per minute in a uniform magnetic field of 0.5 tesla. Then the maximum induced emf will be**

- 98 V
- 110 V
- 113 V
- 118 V

**Answer:** 3. 113 V

**Question 6. The resistance of a coil is 5 ohm and a current of 0.2 A is induced in it due to a varying magnetic field. The rate of change of magnetic flux in it will be –**

- 0.5 Wb/s
- 0.05 Wb/s
- 1 Wb/s
- 20 Wb/s

**Answer:** 3. 1 Wb/s

**Question 7. A rod of length l rotates with a uniform angular velocity ra about its perpendicular bisector. A uniform magnetic field B exists parallel to the axis of rotation. The potential difference between the two ends of the rod is**

- Zero
- \(\frac{1}{2} \omega \mathrm{B} \ell^2\)
- \(B \omega \ell^2\)
- \(2 \mathrm{~B} \omega \ell^2\)

**Answer:** 1. Zero

**Question 8. A semicircular wire of radius R is rotated with constant angular velocity ω about an axis passing through one end and perpendicular to the plane of the wire. There is a uniform magnetic field of strength B. The induced e.m.f. between the ends is:**

- B ωR²/2
- 2 B ωR²
- Is variable
- None of these

**Answer:** 2. 2 B ωR²

**Question 9. A coil having n turns and resistance R Ω is connected with a galvanometer of resistance 4RΩ. This combination is moved in time t seconds from a magnetic field W _{1} Weber/m² to W_{2} Weber/m². The induced current in the circuit is:**

- \(\frac{\left(W_2-W_1\right) A}{5 R n t}\)
- \(-\frac{n\left(W_2-W_1\right) A}{5 R t}\)
- \(-\frac{\left(W_2-W_1\right) A}{\text { Rnt }}\)
- \(-\frac{n\left(W_2-W_1\right) A}{R t}\)

**Answer:** 2. \(-\frac{n\left(W_2-W_1\right) A}{5 R t}\)

**Question 10. A metal conductor of length 1 m rotates vertically about one of its ends at an angular velocity of 5 radians per second. If the horizontal component of earth’s magnetic field is 0.2 x 10 ^{-4} T, then the emf developed between the two ends of the conductor is:**

- 5 μV
- 50 μV
- 5 mV
- 50 mV

**Answer:** 2. 50 μV

## Chapter 6 Electromagnetic Induction Fixed Loop In A Time-Varying Magnetic Field And Induced Electric Field

**Question 1. A coil of 100 turns having an average area of 100 cm² for each turn is held in a uniform field of 50 gauss, the direction of the field being at right angles to the plane of the coil. If the field is removed in 0.01 sec, then the average e.m.f induced in the coil is**

- 0.5 V
- 10 V
- 20 V
- 50 V

**Answer:** 1. 0.5 V

**Question 2. A coil is placed in the transverse magnetic field of 0.02 T. This coil starts shrinking at a rate of 1 mm/sec. When its radius is 4 cm, then what is the value of induced emf-**

- 2 μV
- 2.5 μV
- 5 μV
- 8 μV

**Answer:** 3. 5 μV

**Question 3. A uniform magnetic field of induction B is confined to a cylindrical region of radius R. The magnetic field is increasing at a constant rate of \(\frac{d B}{dt}\) (tesla/second). An electron of charge q, placed at the point P on the periphery of the field experiences an acceleration**

- \(\frac{1}{2} \frac{e R}{m} \frac{d B}{d t}\) toward left
- \(\frac{1}{2} \frac{\mathrm{eR}}{\mathrm{m}} \frac{\mathrm{dB}}{\mathrm{dt}}\) toward right
- \(\frac{e R}{m} \frac{d B}{d t}\) toward left
- Zero

**Answer:** 1. \(\frac{1}{2} \frac{e R}{m} \frac{d B}{d t}\) toward left

**Question 4. A uniform but time-varying magnetic field B (t) exists in a circular region of radius a and is directed into the plane of the paper, as shown figure. The magnitude of the induced electric field at point P at a distance r from the center of the circular region.**

- Is zero
- Decreases as 1/r
- Increases as r
- Decreases as 1/r²

**Answer:** 2. Decreases as 1/r

**Question 5. A conducting circular loop is placed in a uniform magnetic field of 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2mms ^{-1}. The induced emf in the loop when the radius is 2 cm is**

- 3.2 πμV
- 4.8 πμV
- 0.8 πμV
- 1.6 πμV

**Answer:** 1. 3.2 πμV

**Question 6. In a uniform magnetic field of induction B, a wire in the form of a semicircle of radius r rotates about the diameter of the circle with angular frequency ω. If the total resistance of the circuit is R, the mean power generated per period of rotation is:**

- \(\frac{B \pi^2 \omega}{2 R}\)
- \(\frac{\left(\mathrm{B} \pi \mathrm{r}^2 \omega\right)^2}{8 \mathrm{R}}\)
- \(\frac{(B \pi r \omega)^2}{2 R}\)
- \(\frac{\left(\mathrm{B} \pi \omega^2\right)^2}{8 \mathrm{R}}\)

**Answer:** 2. \(\frac{\left(\mathrm{B} \pi \mathrm{r}^2 \omega\right)^2}{8 \mathrm{R}}\)

## Chapter 6 Electromagnetic Induction Self Induction, Self Inductance Self Induced Emf, And Magnetic Energy Density

**Question 1. If the length and area of the cross-section of an inductor remain the same but the number of turns is doubled, its self-inductance will become**

- Half
- Four times
- Double
- One-fourth

**Answer:** 2. Four times

**Question 2. Dimensions of the coefficient of self-induction are**

- MLT
^{-2}A^{-2} - ML
^{-2}T^{-2}A^{-2} - ML
^{2}T^{-2}A^{-2} - M
^{2}LT^{-2}A^{-2}

**Answer:** 3. ML^{2}T^{-2}A^{-2}

**Question 3. The self-inductance of a solenoid depends on**

- The number of turns N of the coil
- The area of cross-section A and length l of the coil.
- The permeability of the core of the coil
- All the above

**Answer:** 3. The permeability of the core of the coil

**Question 4. When the current flowing in a coil changes from 3A to 2A in one millisecond, 5-volt emf is induced in it. The self-inductance of the coil will be**

- Zero
- 5kH
- 5H
- 5 mH

**Answer:** 4. 5 mH

**Question 5. The equivalent inductance of two inductances is 2.4 Henry when connected in parallel and 10 Henry when connected in series. The difference between the two inductance is**

- 2 henry
- 3 henry
- 4 henry
- 5 henry

**Answer:** 1. 2 henry

**Question 6. In the figure magnetic energy stored in the coil is (in a steady state)**

- 0
- ∞
- 25 joules
- None of these

**Answer:** 3. 25 joules

**Question 7. The value of self-inductance of a coil is 5 henry. The value of the current changes from 1 ampere to 2 amperes in 5 seconds. The value of induced emf in it is**

- 10 Volt
- 0.10 Volt
- 1.0 Volt
- 100 Volt

**Answer:** 3. 1.0 Volt

**Question 8. The self-inductance of a solenoid of length L, area of cross-section A, and having N turns is**

- \(\frac{\mu_0 N^2 A}{L}\)
- \(\frac{\mu_0 N A}{L}\)
- \(\mu_0 \mathrm{~N}^2 L A\)
- \(\mu_0 \mathrm{NAL}\)

**Answer:** 1. \(\frac{\mu_0 N^2 A}{L}\)

**Question 9. A long solenoid has 200 turns per cm. and carries a current of 2.5 amps. The magnetic field at its centre is- [μ _{0} = 4π x 10^{-7} Weber/m^{2}]**

- 3.14 x 10
^{-2}Weber/m^{2} - 6.28 x 10
^{-2}Weber/m^{2} - 9.42 x 10
^{-2}Weber/m^{2} - 12.56 x 10
^{-2}Weber/m^{2}

**Answer:** 2. 6.28 x 10^{-2} Weber/m^{2}

**Question 10. Energy is stored in the choke coil in the form of**

- Heat
- Electric energy
- Magnetic energy
- Electro-magnetic energy

**Answer:** 3. Magnetic energy

**Question 11. For an inductor coil L = 0.04 H then work done by the source to establish a current of 5A in it is**

- 0.5 J
- 1.00 J
- 100 J
- 20 J

**Answer:** 2. 1.00 J

**Question 12. Current passing through a coil is changing at the rate of 1.5 ampere per second. If it induces an emf of 45 volts, then the self-inductance of the coil will be**

- 30 H
- 67.5 H
- 60 H
- 33.3 H

**Answer:** 1. 30 H

**Question 13. An inductor coil stores energy U when a current i is passed through it and dissipates heat energy at the rate of P. The time constant of the circuit, when this coil is connected across a battery of zero internal resistance, is:**

- \(\frac{4 U}{P}\)
- \(\frac{U}{P}\)
- \(\frac{2 U}{P}\)
- \(\frac{2 P}{U}\)

**Answer:** 3. \(\frac{2 U}{P}\)

**Question 14. L, C, and R represent the physical quantities inductance, capacitance, and resistance. Which of the following combinations have dimensions of time?**

- \(\frac{1}{\mathrm{RC}}\)
- \(\frac{R}{L}\)
- \(\frac{1}{\sqrt{L C}}\)
- \(\sqrt{L C}\)

**Answer:** 4.\(\sqrt{L C}\)

**Question 15. Two inductors L _{1} and L_{1} are connected in parallel and a time varting current i flows as shown. The ratio of current i_{1}/i_{2} at any time t is**

- \(L_1 / L_2\)
- \(L_2 / L_1\)
- \(\frac{L_1^2}{\left(L_1+L_2\right)^2}\)
- \(\frac{L_2^2}{\left(L_1+L_2\right)^2}\)

**Answer:** 2. \(L_2 / L_1\)

**Question 16. An LR circuit with a battery is connected at t =0. Which of the following quantities is not zero just after the connection?**

- Current in the circuit
- Magnetic field energy in the inductor
- Power delivered by the battery
- emf induced in the inductor

**Answer:** 4. emf induced in the inductor

**Question 17. When the current in the portion of the circuit shown in the figure is 2A and increasing at the rate of 1A/s, the measured potential difference V _{ab} = 8V. However when the current is 2A and decreasing at the rate of 1A/s, the measured potential difference V_{ab}= 4V. The values of R and L are:**

- 3 ohm and 2 henries respectively
- 2 ohm and 3 henries respectively
- 10 ohm and 6 henries respectively
- 6 ohm and 1 Henry respectively

**Answer:** 1. 3 ohm and 2 Henry respectively

**Question 18. When the current changes from +2A to -2A in 0.05s, an emf of 8V is induced in a coil. The coefficient of self-induction of the coil is**

- 0.2 H
- 0.4H
- 0.8H
- 0.1H

**Answer:** 4. 0.1H

**Question 19. A coil of resistance R and inductance L is connected to a battery of emf E volt. The final current in the coil is**

- E/R
- E/L
- \(\sqrt{E /\left(R^2+L^2\right)}\)
- \(\sqrt{\frac{E L}{\left(R^2+L^2\right)}}\)

**Answer:** 1. E/R

**Question 20. Two circular coils can be arranged in any of the three situations shown in the figure. Their mutual inductance will be:**

- Maximum in situation (1)
- Maximum in situation (2)
- Maximum in situation (3)
- The same in all situations

**Answer:** 1. Maximum in situation (1)

**Question 21. Which of the following is proportional to energy density in magnetic field B:**

- \(\frac{1}{B}[latex]
- [latex]\frac{1}{\mathrm{~B}^2}\)
- \(\mathrm{B}\)
- \(B^2\)

**Answer:** 4. \(B^2\)

**Question 22. In the given circuit find the ratio of i _{1} to i_{2}. Where i_{1} is the initial (at t = 0) current, and i_{2} is steady state (at t = ∞) current through the battery:**

- 1.0
- 0.8
- 1.2
- 1.5

**Answer:** 2. 0.8

**Question 23. The inductance between A and D is:**

- 3.66 H
- 9 H
- 0.66 H
- 1 H

**Answer**: 4. 1 H

**Question 24. In an oscillating LC circuit the maximum charge on the capacitor is Q. The charge on the capacitor when the energy is stored equally between the electric and magnetic field is:**

- Q/2
- Q/√3
- Q/√2
- Q

**Answer:** 3. Q/√2

**Question 25. An inductor (L = 100 mH), a resistor (R = 100 Ω), and a battery (E = 100 V) are initially connected in series as shown in the figure. After a long time, the battery is disconnected after short-circuiting the points A and B. The current in the circuit, 1 ms after the short circuit is:**

- 1A
- 1/e A
- e A
- 0.1 A

**Answer:** 2. 1/e A

## Chapter 6 Electromagnetic Induction Mutual Induction And Mutual Inductance

**Question 1. The unit of mutual inductance is**

- Volt
- Weber
- Tesla
- Henry

**Answer:** 4. Henry

**Question 2. The self-inductances of two identical coils are 0.1 H. They are wound over each other. The mutual inductance will be**

- 0.1 H
- 0.2 H
- 0.01 H
- 0.05 H

**Answer:** 1. 0.1 H

**Question 3. Two conducting loops of radius R _{1} and R_{2} are concentric and are placed in the same plane. If R_{1}>> R_{2} the mutual inductance M between them will be directly proportional to**

- \(\frac{R_1}{R_2}\)
- \(\frac{R_2}{R_1}\)
- \(\frac{R_1^2}{R_2}\)
- \(\frac{R_2^2}{R_1}\)

**Answer:** 4. \(\frac{R_2^2}{R_1}\)

**Question 4. The mutual inductance between primary and secondary circuits is 0.5H. The resistance of the primary and the secondary circuits are 20Ω and 5Ω respectively. To generate a current of 0.4 A in the secondary, the current in the primary must be changed at the rate of**

- 4.0 amp./sec.
- 16.0 amp./sec.
- 1.6 amp./sec.
- 8.0 amp./sec.

**Answer**: 1. 4.0 amp./sec.

**Question 5. Two coils A and B having turned 300 and 600 respectively are placed near each other, on a passing current of 3.0 A in A, the flux linked with A is 1.2 x 10 ^{-4 }Weber and with B it is 9.0 x 10^{-5} Weber. The mutual inductance of the system is**

- 2 x 10
^{-5}Henry - 3 x 10
^{-5}Henry - 4 x 10
^{-5}Henry - 6 x 10
^{-5}Henry

**Answer:** 2. 3 x 10^{-5} henry

**Question 6. A steel wire of length l has magnetic moment M. It is bent into a semi-circle. Now its magnetic moment is**

- \(\frac{2 M}{\pi}\)
- \(\frac{3 M}{2 \pi}\)
- \(\frac{M}{\pi}\)
- \(\frac{M}{2 \pi}\)

**Answer:** 1. \(\frac{2 M}{\pi}\)

**Question 7. Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon:**

- The rates at which currents are changing in the two coils
- The relative position and orientation of the two coils
- The materials of the wires of the coils
- The currents in the two coils

**Answer:** 2. Relative position and orientation of the two coils

**Question 8. Two inductance coils of inductance L _{1} and L_{2} are kept at sufficiently large distances apart. On connecting them in parallel their equivalent inductance will be**

- \(\frac{L_1+L_2}{L_1 L_2}\)
- \(\frac{L_1 L_2}{L_1+L_2}\)
- \(L_1+L_2\)
- \(\sqrt{L_1 L_2}\)

**Answer:** 2. \(\frac{L_1 L_2}{L_1+L_2}\)

**Question 9. Two circular coils can be arranged in any of the three situations shown in the figure. Their mutual inductance will be:**

- Maximum in situation (1)
- Maximum in situation (2)
- Maximum in situation (3)
- The same in all situations

**Answer**: 1. Maximum in situation (1)

**Question 10. Two coils of self-inductances 2 mH and 8 mH are located so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is:**

- 10 mH
- 6 mH
- 4 mH
- 16 mH

**Answer:** 3. 4 mH

**Question 11. A long solenoid has 500 turns. When a current of 2 A is passed through it, the resulting magnetic flux linked with each turn of the solenoid is 4 x 10 ^{-3}_{ }Wb. The self-inductance of the solenoid is**

- 2.5 H
- 2.0 H
- 1.0 H
- 4.0 H

**Answer:** 3. 1.0 H

**Question 12. Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area A =10cm² and length = 20 cm. If one of the solenoids has 300 turns and the other 400 turns, their mutual inductance is (μ _{0} = 4π x 10^{-7} T m A^{-1}):**

- 4.8π x 10
^{-4}H - 4.8π x 10
^{-5}H - 2.4π x 10
^{-4}H - 2.4π x 10
^{-5}H

**Answer:** 2. 4.8π x 10^{-5} H

## Chapter 6 Electromagnetic Induction Exercise 2 Multiple Choice Questions And Answers

**Question 1. A circular loop of radius R, carrying current I, lies in the x-y plane with its center at the origin. The total magnetic flux through the x-y plane is**

- Directly proportional to I
- Directly proportional to R
- Directly proportional to R²
- Zero

**Answer:** 4. Zero

**Question 2. A square coil ACDE with its plane vertical is released from rest in a horizontal uniform magnetic field of length 2L. The acceleration of the coil is**

- Less than g for all the time till the loop crosses the magnetic field completely
- Less than g when it enters the field and greater than g when it comes out of the field
- g all the time
- Less than g when it enters and comes out of the field but equal to g when it is within the field

**Answer:** 4. Less than g when it enters and comes out of the field but equal to g when it is within the field

**Question 3. A conducting ring lies fixed on a horizontal plane. If a charged nonmagnetic particle is released from a point (on the axis) at some height from the plane, then:**

- An induced current will flow in a clockwise or anticlockwise direction in the loop depending upon the nature of the charge
- The acceleration of the particle will decrease as it comes down
- The rate of production of heat in the ring will increase as the particle comes down
- No heat will be produced in the ring.

**Answer:** 4. No heat will be produced in the ring.

**Question 4. A bar magnet is released from rest coaxially along the axis of a very long, vertical copper tube. After some time the magnet**

- Will stop in the tube
- Will move with almost constant speed
- Will move with an acceleration g
- Will oscillate

**Answer:** 2. Will move with almost constant speed

**Question 5. In the given arrangement, the loop is moved with constant velocity v in a uniform magnetic field B in a restricted region of width a. The time for which the emf is induced in the circuit is:**

- \(\frac{2 b}{v}\)
- \(\frac{2 a}{v}\)
- \(\frac{(a+b)}{v}\)
- \(\frac{2(a-b)}{v}\)

**Answer:** 2. \(\frac{2 a}{v}\)

**Question 6. A metallic square loop ABCD is moving in its own plane with velocity v in a uniform magnetic field perpendicular to its plane as shown in the figure**

**An electric field is induced**

- In AD, but not in BC
- In BC, but not in AD
- Neither in AD nor in BC
- In both AD and BC

**Answer:** 4. In both AD and BC

**Question 7. A constant force F is being applied on a rod of length ‘l’ kept at rest on two parallel conducting rails connected at ends by resistance R in uniform magnetic field B as shown.**

- The power delivered by force will be constant with time
- The power delivered by force will increase first and then decrease
- The rate of power delivered by the external force will be increasing continuously
- The rate of power delivered by external force will be decreasing continuously.

**Answer:** 4. The rate of power delivered by external force will be decreasing continuously.

**Question 8. A metal rod of resistance 20 Q is fixed along a diameter of conducting ring of radius 0.1 m and lies in the x- y plane. There is a magnetic field \(\vec{B}=(50 \mathrm{~T}) \hat{\mathrm{k}}\). The ring rotates with an angular velocity ω = 20 rad/s about its axis. An external resistance of 10 Ω is connected across the center of the ring and rim. The current through external resistance is**

- \(\frac{1}{4} \mathrm{~A}\)
- \(\frac{1}{2} \mathrm{~A}\)
- \(\frac{1}{3} \mathrm{~A}\)
- zero

**Answer:** 3. \(\frac{1}{3} \mathrm{~A}\)

**Question 9. The radius of the circular conducting loop shown in the figure is R. Magnetic field is decreasing at a constant rate a. Resistance per unit length of the loop is ρ. Then current in wire AB is (AB is one of the diameters)**

- \(\frac{R \alpha}{2 \rho}\) from A to B
- \(\frac{R \alpha}{2 p}\) from B to A
- \(\frac{2 R \alpha}{\rho}\) from A to B
- Zero

**Answer:** 4. Zero

**Question 10. Two different coils have self-inductance L _{1} = 8 mH, L_{2} = 2 mH. The current in one coil is increased at a constant rate. The current in the second coil is also increased at the same rate. At a certain instant of time, the power given to the two coils is the same. At that time the current, the induced voltage, and the energy stored in the first coil are i_{1}, V_{1,} and W_{1} respectively. Corresponding values for the second coil at the same instant are i_{2}, V_{2,} and W_{2} respectively. Then which is incorrect:**

- \(i_1 i_2=\frac{1}{4}\)
- \(\frac{i_1}{i_2}=4\)
- \(\frac{W_2}{W_1}=4\)
- \(\frac{V_2}{V_1}=\frac{1}{4}\)

**Answer**: 2. \(\frac{i_1}{i_2}=4\)

**Question 11. In an LR circuit current at t = 0 is 20 A. After 2s it reduces to 18 A. The time constant of the circuit is (in second):**

- \(\ln \left(\frac{10}{9}\right)\)
- 2
- \(\frac{2}{\ln \left(\frac{10}{9}\right)}\)
- \(2 \ln \left(\frac{10}{9}\right)\)

**Answer:** 3. \(\frac{2}{\ln \left(\frac{10}{9}\right)}\)

**Question 12. In the circuit shown in the figure, switch S is closed at t = 0. Then:**

- After a long time interval, the potential difference across the capacitor and inductor will be equal.
- After a long time interval charge on the capacitor will be EC.
- After a long time interval current in the inductor will be E/R.
- After a long time interval current through the battery will be the same as the current through it initially.

**Answer:** 4. After a long time interval current through the battery will be the same as the current through it initially.

**Question 13. The battery shown in the figure is ideal. The values are ε = 10 V, R = 5Ω, L = 2H . Initially, the current in the inductor is zero. The current through the battery at t = 2s is**

- 12 A
- 7 A
- 3 A
- None of these

**Answer:** 1. 12 A

**Question 14. Two coils are at fixed locations. When coil 1 has no current and the current in coil 2 increases at the rate of 15.0 A/s the e.m.f. in coil 1 is 25.0 mV, when coil 2 has no current and coil 1 has a current of 3.6 A, flux linkage in coil 2 is**

- 16 mWb
- 10 mWb
- 4.00 mWb
- 6.00 mWb

**Answer:** 4. 6.00 mWb

**Question 15. A long straight wire is placed along the axis of a circular ring of radius R. The mutual inductance of this system is**

- \(\frac{\mu_0 R}{2}\)
- \(\frac{\mu_0 \pi R}{2}\)
- \(\frac{\mu_0}{2}\)
- 0

**Answer:** 4. 0

**Question 16. Two identical circular loops of metal wire are lying on a table without touching each other. Loop-A carries a current that increases with time. In response, the loop-B**

- Remains stationary
- Is attracted by the loop-A
- Is repelled by the loop-A
- Rotates about its CM, with CM fixed

**Answer:** 3. Is repelled by the loop-A

**Question 17. When two co-axial coils having the same current in the same direction are brought to each other, then the value of current in both coils:**

- Increases
- Decreases
- First increases and then decreases
- Remain same

**Answer:** 2. Decreases

**Question 18. For the given arrangement (in the horizontal plane) the possible direction of the magnetic field:**

- Towards right
- Towards left
- Vertically upward
- Vertically downward

**Answer:** 4. Vertically downward

**Question 19. A magnetic field can be produced by**

- A moving charge
- A changing electric field
- A stationary charge
- Both (1) and (2)

**Answer:** 4. Both (1) and (2)

**Question 20. A coil of inductance 300 mH and resistance 2Ω is connected to a source of voltage 2V. The current reaches half of its steady state value in**

- 0.05 s
- 0.1 s
- 0.15s
- 0.3 s

**Answer:** 2. 0.1 s

**Question 21. If a bar magnet is dropping through the copper ring, then its velocity (gravity-free space):**

- Decreases
- Increases
- Remain unaffected
- None of these

**Answer:** 1. Decreases

**Question 22. Lenz’s law gives:**

- The magnitude of the induced emf
- The direction of the induced current
- Both the magnitude and direction of the induced current
- The magnitude of the induced current

**Answer:** 2. The direction of the induced current

**Question 23. The unit of mutual inductance of a coil can be expressed as:**

- weber. amp
- weber/amp.
- weber meter
- weber/meter

**Answer:** 2. Weber/amp.

**Question 24. A conducting ring is placed in a uniform magnetic field with its plane perpendicular to the field. An EMF is induced in the ring if**

- It is rotated about its axis
- It is translated
- It is rotated about a diameter
- None of these

**Answer:** 3. It is rotated about a diameter

**Question 25. An equilateral triangular loop ADC having some resistance is pulled with a constant velocity v out of a uniform magnetic field directed into the paper. At time t = 0, the side DC of the loop is at the edge of the magnetic field. The induced current (i) versus time (t) graph will be as**

**Answer**: 2

**Question 26. Shows a conducting disc rotating about its axis in a perpendicular magnetic field B. A resistor of resistance R is connected between the center and the rim. The radius of the disc is 5.0 cm, angular speed ω = 40 rad/s, B = 0.10 T, and R = 1 Ω. The current through the resistor is**

- 5 mA
- 50 A
- 5 A
- 10 mA

**Answer:** 1. 5 mA

**Question 27. A rectangular loop of sides ‘a‘ and ‘b‘ is placed in the xy plane. A very long wire is also placed in the xy plane such that the side of the length ‘a‘ of the loop is parallel to the wire. The distance between the wire and the nearest edge of the loop is ‘d‘. The mutual inductance of this system is proportional to:**

- a
- b
- 1/d
- Current in wire

**Answer:** 1. a

**Question 28. Two inductor coils of self-inductance 3H and 6H respectively are connected with a resistance of 10Ω and a battery of 10V as shown in the figure. The ratio of the total energy stored at a steady state in the inductors to that of heat developed in resistance in 10 seconds at the steady state is(neglecting mutual inductance between L _{1} and L_{2}):**

- \(\frac{1}{10}\)
- \(\frac{1}{100}\)
- \(\frac{1}{1000}\)
- 1

**Answer:** 2. \(\frac{1}{100}\)

**Question 29. A conducting wire frame is placed in a magnetic field which is directed into the paper. The magnetic field is increasing at a constant rate. The directions of induced currents in wires AB and CD are:**

- B to A and D to C
- A to B and C to D
- A to B and D to C
- B to A and C to D

**Answer:** 1. B to A and D to C

**Question 30. The frequency of oscillation of current in the inductor is:**

- \(\frac{1}{3 \sqrt{\mathrm{LC}}}\)
- \(\frac{1}{6 \pi \sqrt{L C}}\)
- \(\frac{1}{\sqrt{\mathrm{LC}}}\)
- \(\frac{1}{2 \pi \sqrt{L C}}\)

**Answer:** 2. \(\frac{1}{6 \pi \sqrt{L C}}\)

**Question 31. A short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of turns were to be four times and the wire radius halved keeping the radius of the loop unchanged, the electrical power dissipated would be:**

- Halved
- The same
- Doubled
- Quadrupled

**Answer:** 2. The same

## Chapter 6 Electromagnetic Induction Exercise 3 Multiple Choice Questions And Answers

**Question 1. A rectangular, a square, a circular, and an elliptical loop, all in the (x-y) plane, are moving out of a uniform magnetic field with a constant velocity \(\overrightarrow{\mathrm{v}}=v \hat{i}\). The magnetic field is directed along the negative z-axis direction. The induced emf, during the passage of these loops, out of the field region, will not remain constant for**

- The rectangular, circular, and elliptical loops
- The circular and the elliptical loops
- Only the elliptical loop
- Any of the four loops

**Answer:** 2. The circular and the elliptical loops

**Question 2. A condenser of capacity C is charged to a potential difference of V _{1}. The plates of the condenser are then connected to an ideal inductor of inductance L. The current through the inductor when the potential difference across the condenser reduces to V_{2} is**

- \(\left(\frac{C\left(V_1-V_2\right)^2}{L}\right)^{\frac{1}{2}}\)
- \(\frac{\mathrm{C}\left(\mathrm{V}_1^2-V_2^2\right)}{L}\)
- \(\frac{\mathrm{C}\left(\mathrm{V}_1^2+\mathrm{V}_2^2\right)}{\mathrm{L}}\)
- \(\left(\frac{\mathrm{C}\left(\mathrm{V}_1^2-\mathrm{V}_2^2\right)}{\mathrm{L}}\right)^{\frac{1}{2}}\)

**Answer:** 4. \(\left(\frac{\mathrm{C}\left(\mathrm{V}_1^2-\mathrm{V}_2^2\right)}{\mathrm{L}}\right)^{\frac{1}{2}}\)

**Question 3. The current i in a coil varies with time as shown in the figure. The variation of induced emf with time would be:**

**Answer:** 1

**Question 4. A coil of resistance 400Ω is placed in a magnetic field. If the magnetic flux Φ (wb) linked with the coil varies with time t (sec) as Φ = 50t² + 4. The current in the coil at t = 2 sec is:**

- 0.5A
- 0.1 A
- 2 A
- 1 A

**Answer:** 1. 0.5A

**Question 5. The current (I) in the inductance varies with time according to the plot shown in the figure.**

**Which one of the following is the correct variation of voltage with time in the coil?**

**Answer:** 4

**Question 6. In a coil of resistance 10 Ω, the induced current developed by changing magnetic flux through it, is shown in the figure as a function of time. The magnitude of change in flux through the coil in Weber is:**

- 8
- 2
- 6
- 4

**Answer:** 2. 2

**Question 7. A wire loop is rotated in a magnetic field. The**

- Twice per revolution
- Four times per revolution
- Six times per revolution
- Once per revolution

**Answer:** 1. Twice per revolution

**Question 8. A thin semicircular conducting ring (PQR) of radius ‘r’ is falling with its plane vertical in a horizontal magnetic field B, as shown in the figure. The potential difference developed across the ring when its speed is v is:**

- Zero
- Bvπr²/2 and P is at higher potential
- πrBv and R is at higher potential
- 2rBv and R have a higher potential

**Answer:** 4. 2rBv and R is at higher potential

**Question 9. A transformer having an efficiency of 90% is working on 200 V and 3 kW power supply. If the current in the secondary coil is 6 A the voltage across the secondary coil and the current in the primary coil respectively are:**

- 300 V, 15 A
- 450 V, 15 A
- 450 V, 13.5 A
- 600 V, 15A

**Answer:** 2. 450 V, 15 A

**Question 10. A conducting square frame of side ‘a’ and a long straight wire carrying current I are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity ‘V’. The emf induced in the frame will be proportional to:**

- \(\frac{1}{(2 x-a)^2}\)
- \(\frac{1}{(2 x+a)^2}\)
- \(\frac{1}{(2 x-a)(2 x+a)}\)
- \(\frac{1}{x^2}\)

**Answer:** 3. \(\frac{1}{(2 x-a)(2 x+a)}\)

**Question 11. A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in an equilibrium state. The energy required to rotate it by 60º is W. Now the torque required to keep the magnet in this new position is:**

- \(\frac{2 W}{\sqrt{3}}\)
- \(\frac{W}{\sqrt{3}}\)
- \(\sqrt{3} \mathrm{~W}\)
- \(\frac{\sqrt{3} W}{2}\)

**Answer:** 3. \(\sqrt{3} \mathrm{~W}\)

**Question 12. A uniform magnetic field is restricted within a region of radius r. The magnetic field changes with time at a rate \(\frac{\mathrm{d} \overrightarrow{\mathrm{B}}}{\mathrm{dt}}\). Loop 1 of radius R > r encloses the region r and loop 2 of radius R is outside the region of the magnetic field as shown in the figure below. Then the e.m.f. generated is:**

- –\(\frac{\mathrm{d} \overrightarrow{\mathrm{B}}}{\mathrm{dt}} \pi \mathrm{r}^2\) in loop 1 and zero in loop 2
- zero in loop 1 and zero in loop 2
- –\(\frac{\mathrm{d} \overrightarrow{\mathrm{B}}}{\mathrm{dt}} \pi \mathrm{r}^2\) in loop 1 and –\(\frac{\mathrm{d} \overrightarrow{\mathrm{B}}}{\mathrm{dt}} \pi \mathrm{r}^2\) in loop 2
- –\(\frac{\mathrm{d} \overrightarrow{\mathrm{B}}}{\mathrm{dt}} \pi \mathrm{R}^2\)in loop 1 and zero in loop 2

**Answer:** 1. –\(\frac{\mathrm{d} \overrightarrow{\mathrm{B}}}{\mathrm{dt}} \pi \mathrm{r}^2\) in loop 1 and zero in loop 2

**Question 13. The figure shows a circuit that contains three identical resistors with resistance R = 9.0 Ω each, two identical inductors with inductance L = 2.0 mH each and an ideal battery with emf ε = 18 V. The current ‘i’ through the battery just after the switch closed is.**

- 2 mA
- 0.2 A
- 2 A
- 4 ampere

**Answer:** 4. 4 ampere

**Question 14. A long solenoid of diameter 0.1 m has 2 × 10 ^{4} turns per meter. At the center of the solenoid, a coil of 100 turns and a radius of 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0A from 4A in 0.05 s. If the resistance of the coil is 10π²2Ω, the total charge flowing through the coil during this time is:**

- 32 πμC
- 16 μC
- 32 μC
- 16 πμC

**Answer**: 3. 32 πμC

**Question 15. The magnetic potential energy stored in a certain inductor is 25 mJ then the current in the inductor is 60 mA. This inductor is of inductance**

- 0.138 H
- 13.89 H
- 1.389 H
- 138.88 H

**Answer:** 2. 13.89 H

**Question 16. In which of the following devices, the eddy current effect is not used?**

- Electric heater
- Induction furnace
- Magnetic braking in train
- Electromagnet

**Answer:** 1. Electric heater

**Question 17. An 800-turn coil of effective area 0.05 m² is kept perpendicular to a magnetic field 5×10 ^{-5} T. When the plane of the coil is rotated by 90° around any of its coplanar axes in 0.1 s, the emf induced in the coil will be:**

- 0.02 V
- 2 V
- 0.2 V
- 2×10
^{-3 }V

**Answer:** 1. 0.02 V

**Question 18. A cycle wheel of radius 0.5 m is rotated with a constant angular velocity of 10 rad/s in a region of magnetic field of 0.1 T which is perpendicular to the plane of the wheel. The EMF generated between its center and the rim is,**

- 0.25 V
- 0.125 V
- 0.5 V
- Zero

**Answer:** 2. 0.125 V

**Question 19. The magnetic flux linked with a coil (in Wb) is given by the equation Φ = 5t¹ + 3t + 16. The magnitude of induced emf in the coil at the fourth second will be**

- 33 V
- 43 V
- 108 V
- 10 V

**Answer:** 2. 43 V

**Question 20. A light bulb and an inductor coil are connected to an ac source through a key as shown in the figure below. The key is closed and after some time an iron rod is inserted into the interior of the inductor. The glow of the light bulb**

- Decreases
- Remains unchanged
- Will fluctuate
- Increases

**Answer:** 1. Decreases

**Question 21. A wheel with 20 metallic spokes each 1 m long is rotated with a speed of 120 rpm in a plane perpendicular to a magnetic field of 0.4 G. The induced emf between the axle and rim of the wheel will be, (1 G = 10 ^{-4} T)**

- 2.51 x 10
^{-4}V - 2.51 x 10
^{-5 }V - 4.0 x 10
^{-5}V - 2.51 V

**Answer**: 1. 2.51 x 10^{-4} V

**Question 22. Two conducting circular loops of radii R _{1 }and R_{2} are placed in the same plane with their centers coinciding. If R_{1} >> R_{2}, the mutual inductance M between them will be directly proportional to**

- \(\frac{R_2}{R_1}\)
- \(\frac{R_1^2}{R_2}\)
- \(\frac{R_2^2}{R_1}\)
- \(\frac{R_1}{R_2}\)

**Answer:** 3. \(\frac{R_2^2}{R_1}\)

**Question 23. An inductor of inductance L = 400 mH and resistors of resistances R _{1} = 2Ω and R_{2} = 2Ω are connected to a battery of emf 12 V as shown in the figure. The internal resistance of the battery is negligible. The switch S is closed at t = 0. The potential drop across L as a function of time is:**

- \(\frac{12}{t} e^{-3 t} V\)
- \(6\left(1-e^{-t / 0.2}\right) V\)
- \(12 e^{-5 t} \mathrm{~V}\)
- \(6 e^{-5 t} V\)

**Answer:** 3. \(12 e^{-5 t} \mathrm{~V}\)

**Question 24. In the circuit shown below, the key K is closed at t = 0. The current through the battery is:**

- \(\frac{V R_1 R_2}{\sqrt{R_1^2+R_2^2}}\) at t=0 and \(\frac{V}{R_2}\) at \(t=\infty\)
- \(\frac{V}{R_2}\) at t=0 and \(\frac{V\left(R_1+R_2\right)}{R_1 R_2}\) at \(t=\infty\)
- \(\frac{V}{R_2}\) at t=0 and \(\frac{V R_1 R_2}{\sqrt{R_1^2+R_2^2}}\) at \(t=\infty\)
- \(\frac{V\left(R_1+R_2\right)}{R_1 R_2}\) at t=0 and \(\frac{V}{R_2}\) at \(t=\infty\)

**Answer:** 2. \(\frac{V}{R_2}\) at t=0 and \(\frac{V\left(R_1+R_2\right)}{R_1 R_2}\) at \(t=\infty\)

**Question 25. In a series LCR circuit R = 200 Q and the voltage and the frequency of the main supply are 220 V and 50 Hz respectively. On taking out the capacitance from the circuit the current lags behind the voltage by 30°. On taking out the inductor from the circuit the current leads the voltage by 30°. The power dissipated in the LCR circuit is**

- 305 W
- 210 W
- Zero W
- 242 W

**Answer:** 4. 242 W

**Question 26. A fully charged capacitor C with initial charge q _{0} is connected to a coil of self-inductance L at t = 0. The time at which the energy is stored equally between the electric and the magnetic fields is:**

- \(\pi \sqrt{L C}\)
- \(\frac{\pi}{4} \sqrt{\text { LC }}\)
- \(2 \pi \sqrt{L C}\)
- \(\sqrt{L C}\)

**Answer:** 2. \(\frac{\pi}{4} \sqrt{\text { LC }}\)

**Question 27. A boat is moving due east in a region where the earth’s magnetic field is 5.0 x 10 ^{-5} NA^{-1 }m^{-1} due north and horizontal. The boat carries a vertical aerial 2m long. If the speed of the boat is 1.50 ms^{-1}, the magnitude of the induced emf in the wire of the aerial is:**

- 1 mV
- 0.75 mV
- 0.50 mV
- 0.15 mV

**Answer**: 4. 0.15 mV

**Question 28. A horizontal straight wire 20 m long extending from east to west falling with a speed of 5.0 M\s, at right angles to the horizontal component of the earth’s magnetic field 0.30 x 10 ^{-4 }Wb \ m^{2}. The instantaneous Value of the e.m. f. induced in the wire will be :**

- 3 mV
- 4.5 mV
- 1.5 mV
- 6.0 mV

**Answer:** 1. 3 mV

**Question 29. A coil is suspended in a uniform magnetic field, with the plane of the coil parallel to the magnetic lines of force. When a current is passed through the coil it starts oscillating; it is very difficult to stop. But if an aluminum plate is placed near to the coil, it stops. This is due to:**

- Development of air current when the plate is placed.
- Induction of electrical charge on the plate
- Shielding of magnetic lines of force as aluminum is a paramagnetic material.
- Electromagnetic induction in the aluminum plate gives rise to electromagnetic damping.

**Answer:** 4. Electromagnetic induction in the aluminum plate gives rise to electromagnetic damping.

**Question 30. A metallic rod of length ‘l’ is tied to a string of length 2l and made to rotate with angular speed ω on a horizontal table with one end of the string fixed. If there is a vertical magnetic field ‘B’ in the region, the e.m.f. induced across the ends of the rod is:**

- \(\frac{2 \mathrm{~B} \omega \mathrm{l}^2}{2}\)
- \(\frac{\left.3 B \omega\right|^2}{2}\)
- \(\frac{4 B \omega l^2}{2}\)
- \(\frac{5 B \omega l^2}{2}\)

**Answer:** 4. \(\frac{5 B \omega l^2}{2}\)

**Question 31. A circular loop of radius 0.3 cm lies parallel to a much bigger circular loop of radius 20 cm. The center of the small loop is on the axis of the bigger loop. The distance between their centers is 15 cm. If a current of 2.0 A flows through the smaller loop, then the flux linked with the bigger loop is:**

- 9.1 x 10
^{-11}weber - 6 x 10
^{-11}weber - 3.3 x 10
^{-11}Weber - 6.6 x 10
^{-9}Weber

**Answer:** 1. 9.1 x 10^{-11} weber

**Question 32. In the circuit shown here, the point ‘C’ is kept connected to point ‘A’ till the current flowing through the circuit becomes constant. Afterward, suddenly point ‘C’ is disconnected from point ‘A’ and connected to point ‘B’ at time t = 0. The ratio of the voltage across resistance and the inductor at t = L/R will be equal to:**

- \(\frac{e}{1-e}\)
- 1
- -1
- \(\frac{1-e}{e}\)

**Answer:** 3. -1

**Question 33. An inductor (L = 0.03H) and a resistor (R = 0.15 kΩ) are connected in series to a battery of 15V EMF in a circuit shown below. The key K _{1} has been kept closed for a long time. Then at t = 0, K_{1} is opened and key K_{2} is closed simultaneously. At t = 1ms, the current in the circuit will be: (e^{5} ≅150)**

- 100 mA
- 67 mA
- 6.7 mA
- 0.67 mA

**Answer:** 4. 0.67 mA

**Question 34. In a coil resistance of 100Ω, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is:**

- 275 Wb
- 200 Wb
- 225 Wb
- 250 Wb

**Answer:** 4. 250 Wb

**Question 35. A conducting circular loop made of a thin wire has an area of 3.5 x 10 ^{-3} m^{2} and a resistance of 10Ω. It is perpendicular to a time-dependent magnetic field B(t) = (0.4T)sin(50πt). The field is uniform in Then the net charge flowing through the loop during t = 0 s and t = 10 ms is close to:**

- 7 mC
- 14 mC
- 21 mC
- 6 mC

**Answer:** 3. 21 mC

**Question 36. A solid metal cube of edge length 2 cm is moving in a positive y-direction at a constant speed of 6 m/s. There is a uniform magnetic field of 0.1 T in the positive z-direction. The potential difference between the two faces of the cube perpendicular to the x-axis is:**

- 6 mV
- 2 mV
- 12 mV
- 1 mV

**Answer:** 4. 1 mV

**Question 37. The self-induced emf of a coil is 25 volts. When the current in it is changed at a uniform rate from 10A to 25A in 1s, the change in the energy of the inductance is:**

- 540 J
- 740 J
- 637.5 J
- 437.5 J

**Answer:** 1. 540 J

**Question 38. A copper wire is wound on a wooden frame, whose shape is that of each side of the frame is increased by a factor of 3, keeping the number of turns of the coil per unit length of the frame the same, then the self-inductance of the coil:**

- Increases by a factor of 3
- Decreases by a factor of 9√3
- Increases by a factor of 27
- Decreases by a factor of 9

**Answer:** 1. Increases by a factor of 3

**Question 39. The region between y = 0 and y = d contains a magnetic field \(\vec{B}=B \hat{Z}.\) A particle of mass m and charge q enters the region from point (0, d) with a velocity \(\vec{v}=v \hat{i}\). If \(d=\frac{m v}{2 q B}\), the acceleration of the charged particle at the point of its emergence at the other side is:**

- \(\frac{q v B}{m}\left(\frac{1}{2} \hat{i}-\frac{\sqrt{3}}{2} \hat{j}\right)\)
- \(\frac{q v B}{m}\left(\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right)\)
- \(\frac{q v B}{m}\left(\frac{-\hat{j}+\hat{i}}{\sqrt{2}}\right)\)
- \(\frac{q v B}{m}\left(\frac{\sqrt{3}}{2} \hat{\mathrm{i}}+\frac{1}{2} \hat{\mathrm{j}}\right)\)

**Answer:** 4. \(\frac{q v B}{m}\left(\frac{\sqrt{3}}{2} \hat{\mathrm{i}}+\frac{1}{2} \hat{\mathrm{j}}\right)\)

**Question 40. In an experiment, electrons are accelerated, from rest, by applying a voltage of 500 V. Calculate the radius of the path if a magnetic field of 100 mT is then applied. [Charge of the electron = 1.6 x 10 ^{-19} C Mass of the electron = 9.1 x 10^{-31}**

**kg]**

- 7.5 x 10
^{-2}m - 7.5 m
- 7.5 x 10
^{-4}m - 7.5 x 10
^{-3}m

**Answer:** 3. 7.5 x 10^{-4} m

**Question 41. There are two long co-axial solenoids of the same length l. The inner and outer coils have radii r _{1} and r_{2} and number of turns per unit length n_{1} and n_{2}, respectively. The ratio of mutual inductance to the self¬inductance of the inner coil is:**

- \(\frac{n_2}{n_1} \cdot \frac{r_2^2}{r_1^2}\)
- \(\frac{n_2}{n_1}\)
- \(\frac{n_1}{n_2}\)
- \(\frac{n_2}{n_1} \cdot \frac{r_1}{r_2}\)

**Answer:** 2. \(\frac{n_2}{n_1}\)

**Question 42. A 10 m long horizontal wire extends from North East to South West. It is falling with a speed of 5.0 ms ^{-1}, at right angles to the horizontal component of the earth’s magnetic field, of 0.3 x 10^{-4 }Wb/m². The value of the induced emf in the wire is:**

- 1.1 x 10
^{-3}V - 2.5 x 10
^{-3}V - 0.3 x 10
^{-3}V - 1.5 x 10
^{-3}V

**Answer:** 1. 1.1 x 10^{-3} V