WBCHSE Class 12 Physics Electromagnetic Induction Multiple Choice Questions

Electromagnetic Induction And Alternating Current

Electromagnetic Induction Multiple Choice Questions And Answers

Question 1. A cylinder bar magnet is rotated about its axis. A wire is connected from the axis and is made to touch the cylindrical surface through contact. Then

1. A direct current flows in the ammeter A
2. No current flows through A
3. An alternating sinusoidal current flows through the ammeter A with period, \(T=\frac{2 \pi}{\omega}\)
4. A time-varying non-sinusoidal current flows through ammeter A.

Answer: 2. No current flows through A

Since there is no change in magnetic flux linked with the circuit, no current will flow through the ammeter A.

Question 2. There are two coils A and B. When A is brought towards B, a current flows through B which stops when A stops moving. The current In B is counterclockwise. B is stationary when A moves. We can infer that

1. A constant current flows through A in the clockwise direction
2. A varying current is passing through A
3. There is no current through A
4. A constant counterclockwise current is passing through A

Answer: 4. A constant counterclockwise current is passing through A

Question 3. A loop, made ofstraight edges has six comers at A(0, 0, 0), B(L, 0, 0), C(L, L, 0), D(0,L,0), E(0,L,L) and F(0, 0, L). A magnetic field \(\) is present in the region. The flux passing through the loop ABCDEFA (in that order) is:

1. \(B_0 L^2 \mathrm{~Wb}\)
2. \(2 B_0 L^2 \mathrm{~Wb}\)
3. \(\sqrt{2} B_0 L^2 \mathrm{~Wb}\)
4. \(4 B_0 L^2 W \mathrm{~b}\)

Answer: 2. \(2 B_0 L^2 \mathrm{~Wb}\)

= \(\vec{A}=L^2 \hat{k}+L^2 \hat{i}=L^2(\hat{i}+\hat{k})\)

∴ \(\phi=\vec{B} \cdot \vec{A}=B_0(\hat{i}+\hat{k}) \cdot L^2(\hat{i}+\hat{k})=2 B_0 L^2 \mathrm{~Wb}\)

WBBSE Class 12 Electromagnetic Induction MCQs

Question 4. The number of turns of a solenoid of length l and area of cross-section A is N. The self-inductance L increases as

1. l and A increase
2. l decreases and A increases
3. l increases and A decreases
4. Both Z and A decrease

Answer: 2. l decreases and A increases

∴ \(L=\frac{\mu_0 N^2 A}{l}\)

Question 5. The two coils A and B are the same as in Q. 2. The coil A is made to rotate about a vertical axis. No current flows in B if A is at rest. The current in coil A, when the current B (at t = 0) is counterclockwise and coil A is as shown at this instant t = 0, is

1. Constant current clockwise
2. Varying current clockwise
3. Varying current counterclockwise
4. Constant current counterclockwise

Answer: 1. Constant current clockwise

Common MCQs on Lenz’s Law

Question 6. A metal plate is getting heated. It can be because

1. A direct current is passing through it
2. It is placed in a time-varying magnetic field
3. It is placed in a magnetic field which varies with space but not with time
4. A current (either direct or alternating) is passing through it

Answer:

1. A direct current is passing through it
2. It is placed in a time-varying magnetic field
3. It is placed in a magnetic field which varies with space but not with time

Question 7. An emf is produced in a coil, which is not connected to an external voltage source. This can be due to

1. The coil is in a time-varying magnetic field
2. The coil moving in a time-varying magnetic field
3. The coil moving in a constant magnetic field
4. The coil is stationary in an external spatially varying magnetic field, which does not change with time

Answer:

When a coil is not connected to an external source of voltage, then emf in the coil is produced due to changing magnetic flux with time,

∴ \(e=-\frac{d \phi}{d t}\)

Question 8. A circular coil expands radially in a region of magnetic field but no electromotive force is produced in the coil. It can be because

1. The magnetic field is constant
2. The magnetic field is in the same plane as the circular coil and it may or may not vary
3. The magnetic field may have a perpendicular (to the plane of the coil) component with suitably decreasing magnitude
4. There is a constant magnetic field perpendicular (to the plane of the coil) direction

Answer:

2. The magnetic field is in the same plane as the circular coil and it may or may not vary

3. The magnetic field may have a perpendicular (to the plane of the coil) component with suitably decreasing magnitude

When the magnetic field is in the plane of the coil, no magnetic flux is linked with the coil. Since there is no change in magnetic flux linked with the coil, induced emf is zero.

When the magnetic field perpendicular to the plane of the coil decreases suitably and the magnetic flux linked with the coil remains constant, e = 0.

Question 9. The mutual inductance M₁₂ of coil 1 concerning coil 2

1. Increases when they are brought nearer
2. Depends on the current passing through the coils
3. Increases when one of them is rotated about an axis
4. Is the same as M₂₁ coil 2 concerning coil 1

Answer:

1. Increases when they are brought nearer

4. Is the same as M₂₁ coil 2 concerning coil 1

When the coils are brought nearer, the flux linked with them increases, thus M₂₁ is increased.

Again, \(M_{12}=k \sqrt{L_1 L_2}=M_{21}\)

Practice MCQs on Magnetic Flux

Question 10. If the emf induced in an electrical circuit is e and the current induced by i then,

1. Both e and i depend on the resistance of the circuit
2. None of e and i depends on the resistance of the circuit.
3. e depends on the resistance of the circuit but noti
4. i depends on the resistance of the circuit but not e

Answer: 4. i depends on the resistance of the circuit but not e

Question 11. The magnetic flux across a coil, of 50 turns and a diameter of 0.1 m, changes from 3 x 10^-4 to 10^-4 Wb in 0.02 s. The EMF induced in the coil is

1. 3.9 mV
2. 10 mV
3. 15 mV
4. 196 mV

Answer: 2. 10 mV

Question 12. A coil with a small area of 10^-5 m² is lying on the xy-plane around point P. If the magnetic field at P is \(\)Wb.m^-2, the magnetic flux passing through the coil would be

1. 10^-5 Wb
2. 2 x 10^-5 Wb
3. 3 x 10^-5 Wb
4. 3 x 10^-5 Wb

Answer: 1. 10^-5 Wb

Question 13. The magnetic flux linked with a coil varies with time Φ = at² + bt + c, where a, b and c are constants. The emf induced in the coil will be zero at a time of

1. \(\frac{b}{a}\)
2. \(-\frac{b}{a}\)
3. \(\frac{b}{2a}\)
4. \(-\frac{b}{2a}\)

Answer: 4. \(-\frac{b}{2a}\)

Question 14. The induced current in a coil due to electromagnetic induction does not depend upon

1. Rate of change of flux
2. Shape of the coil
3. Resistance of coil
4. None of these

Answer: 4. None of these

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Question 15. A metal ring is held horizontally with the ground and a bar magnet is dropped through the ring with its length along the axis of the ring. The acceleration of the falling magnet is

1. Equal to g
2. Less than g
3. More than g
4. Zero

Answer: 2. Less than g

Important Definitions in Electromagnetic Induction

Question 16. An electric potential difference will be induced between the die ends of the die conductor (AB) shown in the figure when the die conductor moves along

1. OP
2. OQ
3. OL
4. OM

Answer: 4. OM

Question 17. In a circular loop of radius r and resistance R is shown. A variable magnetic field of induction B = e^-t exists inside the loop. If the key (K) is closed at t = 0, the electrical power developed in the circuit at diet instant is equal to

1. \(\frac{\pi r^2}{R}\)
2. \(\frac{10 r^3}{R}\)
3. \(\frac{\pi^2 r^4 R}{5}\)
4. \(\frac{10 r^4}{R}\)

Answer: 4. \(\frac{10 r^4}{R}\)

Hint: Induced emf,

⇒ \(e=-A \frac{d B}{d t}=-\pi r^2 \frac{d}{d t}\left(e^{-t}\right)=\pi r^2 e^{-t}\)

or, \(\left.e\right|_{t=0}=\pi r^2\)

Hence the power developed in the circuit at the instant of closing the key,

∴ \(P=\frac{\left(\left.e\right|_{t=0}\right)^2}{R}=\frac{\pi^2 r^4}{R} \approx \frac{10 r^4}{R}\).

Question 18. Two identical circular loops of metal wire are lying on a table without touching each other. Loop A carries a current which increases with time. In response, the loop B

1. Remains stationary
2. Is attracted by the loop A
3. Is repelled in the loop A
4. Rotates about its centre of mass with the centre of mass fixed.

Answer: 3. Is repelled in the loop A

Question 19. A circular disc of ratlins 0.2 m is placed In a uniform magnetic field of induction \(\frac{1}{\pi} \mathrm{Wb} / \mathrm{m}^2\) in such a way that Its axis makes an angle 60° with the field. The magnetic flux linked with the disc is

1. 0.01 Wb
2. 0.02 Wb
3. 0.06Wb
4. 0.08 Wb

Answer: 2. 0.02 Wb

Question 20. A square wire loop of side 10 cm is placed at an angle of 45° with a magnetic field that changes uniformly from 0.1 T to zero in 0.7 s. If the resistance of the loop is 1 Ω, then die induced current in it is

1. 1 mA
2. 2.5 mA
3. 3.5 mA
4. 4 mA

Answer: 1. 1 mA

Examples of Electromagnetic Induction Applications

Question 21. A rod of length b moves with a constant velocity v in the magnetic field of an infinitely long straight conducting wire that carries a current i as shown in the figure. The induced emf in the rod is

1. \(\frac{\mu_0 i v}{2 \pi} \tan ^{-1}\left(\frac{a}{b}\right)\)
2. \(\frac{\mu_0 i v}{2 \pi} \ln \left(1+\frac{b}{a}\right)\)
3. \(\frac{\mu_0 i v \sqrt{a b}}{4 \pi(a+b)}\)
4. \(\frac{\mu_0 i v(a+b)}{4 \pi a b}\)

Answer: 2. \(\frac{\mu_0 i v}{2 \pi} \ln \left(1+\frac{b}{a}\right)\)

Hint: The induced emf between two ends of a segment dx, de = Bv.dx

[B = magnetic field due to current i in the wire at perpendicular distance \(x=\frac{\mu_0 i}{2 \pi x}\)]

∴ \(e=\int d e=\frac{\mu_0 i v}{2 \pi} \int_a^{a+b} \frac{d x}{x}\)

∴ \(\frac{\mu_0 i v}{2 \pi} \ln \left(1+\frac{b}{a}\right)\)

Question 22. A boat is moving due east in a region where the earth’s magnetic field is 5.0 x 10^-5 N A^-1.m^-1 due north and horizontal. The boat carries a vertical aerial 2 m long. If the speed of the boat is 1.50 m.s^-1, the magnitude of the induced emf in the wire of the aerial is

1. 0.75 mV
2. 0.50 mV
3. 0.15 mV
4. 1 mV

Answer: 3. 0.15 mV

Hint: The induced emf,

e = BHlv = 5 x 10^-5 x 2 x 1.50 = 0.15 mV

Question 23. SI unit Henry (H) of inductance can be written as

1. \(\mathrm{Wb} \cdot \mathrm{A}^{-2}\)
2. \(\mathrm{J} \cdot \mathrm{A}^{-1}\)
3. \(\mathrm{V} \cdot \mathrm{s} \cdot \mathrm{A}^{-2}\)
4. \(\Omega \cdot \mathbf{s}\)

Answer: 4. \(\Omega \cdot \mathbf{s}\)

Question 24. The self-inductance of a long straight solenoid isL Each of the length, the diameter and the number of turns of another solenoid is double that of the first. The self-inductance of the second solenoid is

1. 2L
2. 4L
3. 8L
4. 16L

Answer: 3. 8L

Question 25. The self-inductances of the two coils are 16 mH and 25 mH, and they have a mutual inductance of 10 mH. Their coupling constant is

1. 0.025
2. 0.05
3. 0.25
4. 0.5

Answer: 4. 0.5

Real-Life Scenarios in Electromagnetic Induction

Question 26. If current I passes through a pure inductor of self-inductance L, the energy stored is

1. \(L I^2\)
2. \(\frac{L I^2}{2}\)
3. \(\frac{L I^2}{4}\)
4. Zero

Answer: 2. \(\frac{L I^2}{2}\)

Question 27. Two solenoids of equal number of turns have their lengths and radii in the same ratio of 1:2. The ratio of their self-inductances will be

1. 1:2
2. 2:1
3. 1:1
4. 1:4

Answer: 1. 1:2

Hint: We know, the self-inductance of a solenoid,

∴ \(L=\frac{\mu_0 N^2 A}{l}=\frac{\mu_0 N^2\left(\pi r^2\right)}{l}\)

So, \(\frac{L_1}{L_2}=\left(\frac{N_1}{N_2}\right)^2\left(\frac{r_1}{r_2}\right)^2\left(\frac{l_2}{l_1}\right)=\frac{1}{4} \times \frac{2}{1}=\frac{1}{2}\)

Question 28. The current in a coil varies with time as shown. The variation of induced emf with time would be

Answer: 1.

Hint: e = \(e=-L \frac{d i}{d t}\)

When, 0 ≤ t ≤ \(\frac{T}{4}, \frac{d i}{d t}\) = constant, so e is negative and constant.

When, \(\frac{T}{4} ≤ t ≤ \frac{T}{2}, \frac{d i}{d t}=0, \text { so } e=0\).

When, \(\frac{T}{2} ≤ t ≤ \frac{3 T}{4}, \frac{d i}{d t}\) = constant’ so e is Positive and constant.

When, \(\frac{3 T}{4} ≤ t ≤ T, \frac{d i}{d t}=0, \text { so } e=0\).

Question 29. In the case of electromagnetic induction in a conductor

1. Electromotive force is induced whenever the conductor starts moving in a magnetic field
2. Induced electromotive force is proportional to the magnetic flux linked with the conductor
3. The induced current may be zero even if the induced emf is not zero
4. Induced emf does not depend on the resistance of the conductor

Answer:

3. Induced current may be zero even if the induced emf is not zero

4. Induced emf does not depend on the resistance of the conductor

Question 30. The induced emf between the two ends of a straight conductor moving perpendicular to its axis in a uniform magnetic field is

1. Proportional to the length of the conductor
2. Proportional to the velocity of the conductor
3. Proportional to the magnetic field
4. Inversely proportional to the magnetic field

Answer:

1. Proportional to the length of the conductor

3. Proportional to the magnetic field

4. Inversely proportional to the magnetic field

Question 31. The length and radius of a solenoid of N turns are l and r respectively. The self-inductance of the solenoid is

1. Proportional to N
2. Proportional to N²
3. Inversely proportional to r
4. Inversely proportional to l

Answer:

2. Proportional to N2

4. Inversely proportional to l

Question 32. Which of the following relations is correct?

1. Henry = ohm x second
2. Farad = ohm/second
3. Weber = volt x second
4. Henry = weber/ampere

Answer:

1. Henry = ohm x second

3. Weber = volt x second

4. Henry = weber/ampere

Question 33. The mutual inductance of two adjacent coils depends on the

1. Rate of change of current in any one of them
2. Number of turns of the two solenoids
3. Length of the solenoids
4. Relative position of the solenoids

Answer:

2. Number of turns of the two solenoids

3. Length of the solenoids

4. Length of the solenoids

Conceptual Questions on Self and Mutual Inductance

Question 34. A conducting coil of resistance R and radius r has its centre at the origin of the coordinate system in a uniform magnetic field of induction B. When it is rotated about the y-axis through 90°, the change of flux in the coil is directly proportional to

1. B
2. R
3. r²
4. r

Answer:

1. B

3. r²

Question 35. A V-shaped conducting wire is moved with a speed of v in a magnetic field as shown in the figure. The magnetic field is perpendicular to the paper, directed inwards; then

1. \(v_a=v_c\)
2. \(v_a>v_c\)
3. \(v_a>v_b\)
4. \(v_c>v_b\)

Answer:

1. \(v_a=v_c\)

3. \(v_a>v_b\)

4. \(v_c>v_b\)

Question 36. The magnetic flux (Φ) linked with a coil varies with time (t) as Φ = atⁿ, where a and n are constants. The induced emf in the coil is e. Which of the following is correct?

1. if 0 < n < l,e = 0
2. if 0 < n < l,e ii 0 and |e| decreases with time
3. if n = 1, e is constant
4. if n > 1, |e| increases with time

Answer:

2. if 0 < n < l,e ii 0 and |e| decreases with time

3. if n = 1, e is constant

4. if n > 1, |e| increases with time

Question 37. Current (i) passing through a coil varies with time t as i = 2t². At 1 s total flux passing through the coil is 10 Wb. Then

1. The self-inductance of the coil is 10 H
2. The self-inductance of the coil is 5 H
3. Induced emf across the coil at 1 s is 20 V
4. Induced emf across the coil at 1 s is 10 V

Answer:

2. Self-inductance of the coil is 5 H

3. Induced emf across the coil at 1 s is 20 V