Question Set A

CBSE 12th Physics Electromagnetic Induction Important Questions And Answers Study Material - QB365

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Questions:

Multiple Choice Question

52 x 1 = 52

A coil of area 100 is kept at an angle of 30° with a magnetic field of 10 T. The magnetic field is reduced to zero in 10s. The induced emf in the coil is

(a)

5√3 V

(b)

50√3 V

(c)

5.0 V

(d)

50.0 V

There is a pair of concentric and coplanar conducting loops of radii R₁ and R₂ such that R₂ = 0.01 R₁. To which of the following is the mutual inductance M for this pair directly proportional?

(a)

1/R₁²

(b)

R₁²

(c)

1/R₁

(d)

R₁

The current in the primary coil of a pair of coils changes from 7 A to 3 A in 0.04 s. The mutual inductance between the two coils is 0.5H. The induced emf in the secondary coil is

(a)

50 V

(b)

75 V

(c)

100 V

(d)

220 V

The self-inductance of a solenoid of 600 turns is 108 mH. The self-inductance of a coil having 500 turns with the same length, the same radius and the same medium will be

(a)

95 mH

(b)

90 mH

(c)

85 mH

(d)

75 mH

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 vi. 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

(a)

any of the four loops

(b)

the circular and elliptical loops

(c)

the rectangular, circular and elliptical loops

(d)

only the elliptical loops

The direction of induced current in the loop abc is

(a)

along abc if I decreases

(b)

along acb if I increases

(c)

along abc if I is constant

(d)

along abc if I increases

A coil of resistance 400Ω is placed in a magnetic field. If the magnetic flux Φ linked with the coil varies with times t (see) as Φ = 50t² + 4, the current in the coil at t = 2 sec is

(a)

0.5 A

(b)

0.1 A

(c)

2 A

(d)

1 A

In a coil of resistance 10π, the induced current developed by changing magnitude of change in flux through the coil is weber is

(a)

(b)

(c)

(d)

While keeping area of cross-section of a solenoid same, the number of turns and length of solenoid are both doubled. The self-inductance of the coil will be

(a)

halved.

(b)

doubled.

(c)

1/4 times the original value

(d)

unaffected.

10.

The self-inductance of a coil having 500 turns is 50 mH. The magnetic flux through the cross-sectional area of the coil, while current through it is 8 mA, is found to be

(a)

4 x 10^-4 Wb

(b)

0.04 Wb

(c)

4 μ Wb

(d)

40 m Wb

11.

The self-inductance L of a solenoid of length I and area of cross-section A, with a fixed number of turns N increases as

(a)

I and A increase

(b)

I decreases and A increases

(c)

I increases and A decreases

(d)

both I and A decrease.

12.

In a coil of self-induction 5 H, the rate of change of current is 2 As^-1. Then emf induced in the coil is

(a)

10V

(b)

-10V

(c)

(d)

-5V

13.

The current flows from A to B is as shown in the figure. The direction of the induced current in the loop is

(a)

clockwise.

(b)

anticlockwise.

(c)

straight line.

(d)

no induced e.m.f. produced.

14.

Lenz's law of electromagnetic induction is as per law of conservation of

(a)

energy.

(b)

momentum angular.

(c)

charge.

(d)

electromotive force.

15.

A coil of 100 turns carries a current of 5 mA and creates a magnetic flux of 10^-5 weber. The inductance is

(a)

0.2 mH

(b)

2.0 mH

(c)

0.02 mH

(d)

0.002 H

16.

A coil having 500 sq. loops of side 10 cm is placed normal to magnetic flux which increases at a rate of 1 T/s. The induced emf is

(a)

0.1 V

(b)

0.5 V

(c)

(d)

17.

When current in a coil changes from 5 A to 2 A in 0.1 s, average voltage of 50 V is produced. The selfinductance of the coil is

(a)

1.67 H

(b)

6 H

(c)

3 H

(d)

0.67 H

18.

Same as question 4 except the coil A is made to rotate about a vertical axis (Figure). No current flows in B if A is at rest. The current in coil A, when the current in B (at t = 0) is counterclockwise and the coil A is as shown at this instant, t = 0, is

(a)

constant current clockwise.

(b)

varying current clockwise

(c)

varying current counterclockwise

(d)

constant current counterclockwise

19.

A loop, made of straight edges has six corners 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 \(B={ B }_{ 0 }\left( \hat { i } +\hat { k } \right) T\) is present in the region. The flux passing through the loop ABCDEFA (in that order) is.

(a)

\({ B }_{ 0 }{ L }^{ 2 }Wb\)

(b)

\(2{ B }_{ 0 }{ L }^{ 2 }Wb\)

(c)

\(\sqrt { 2 } { B }_{ 0 }{ L }^{ 2 }Wb\)

(d)

\(4{ B }_{ 0 }{ L }^{ 2 }Wb.\)

20.

The self-induced emf in a coil of 0.4 H self-inductance when current in it is changing at the rate of 50 As^-1, is

(a)

8 x 10^-4 V

(b)

8 x 10^-3 V

(c)

20V

(d)

500V

21.

If the number of turns in a coil becomes doubled, then it self-inductance will become

(a)

double

(b)

halved

(c)

four times

(d)

unchanged

22.

Eddy currents are generated in

(a)

insulator

(b)

conductor

(c)

Both (a) and (b)

(d)

Neither (a) nor (b)

23.

An electron moves along the line PQ which lies in the same plane as a circular loop of conducting wire as shown in figure. What will be the direction of the induced current in the loop?

(a)

Anti-clockwise

(b)

Clockwise

(c)

Alternating

(d)

Non-current will be induced

24.

A rectangular loop and a circular loop are moving out of a uniform magnetic field region in the given figure to a field-free region with a constant velocity v. In which loop do you expect the induced emf to be constant during the passage out of the field region?

(a)

Rectangular loop

(b)

Circular loop

(c)

Both (a) and (b)

(d)

Neither (a) nor (b)

25.

A 50 turns circular coil has a radius of 3 cm, it is kept in a magnetic field acting normal to the area of the coil. The magnetic field B increased from 0.10 T to 0.35 T in 2 ms^_-1, The average induced emf in the coil is

(a)

1.77V

(b)

17.7V

(c)

177V

(d)

0.177V

26.

The direction of induced current is decided by

(a)

Lenz's law

(b)

Fleming's left hand rule

(c)

Biot-Savart's law

(d)

Ampere's law

27.

The magnitude of the induced emf in a circuit is equal to the time rate of change of magnetic flux through the circuit, is statment of

(a)

Fleming's right hand rule

(b)

Fleming's left hand rule

(c)

Felming's third law

(d)

Faraday's law of electromagnetic induction

28.

What will happen with the galvanometer when the tapping key K is pressed?

(a)

A momentary deflection

(b)

A long time deflection

(c)

No deflection

(d)

None of the above

29.

A square of side L metres lies in the xy-plane in a region, where the magnetic field is given by B \(=B_{0}(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}) \mathrm{T}\), where B_o is constant. The magnitude of flux passing through the square is

(a)

\(2 B_{0} L^{2} \mathrm{~Wb}\)

(b)

\(3 B_{0} L^{2} \mathrm{~Wb}\)

(c)

\(4 B_{0} L^{2} \mathrm{~Wb}\)

(d)

\(\sqrt{29} B_{0} L^{2} \mathrm{~Wb}\)

30.

The effective area of the coil exposed to the magnetic field lines changes with time, the flux at any time is

(a)

\(\phi_{B}=B A \cot \omega t\)

(b)

\(\phi_{B}=B A \cos \omega t\)

(c)

\(\phi_{B}=B A \tan \omega t\)

(d)

\( \phi_{B}=B A \sec \omega t\)

31.

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

(a)

the rates at which currents are changing in the two coils

(b)

relative position and orientation of the two coils

(c)

the materials of the wires of the coils

(d)

the currents in the two coils

32.

If a medium of relative permeability \(\mu\)_r had been present instead of air, the mutual inductance would be

(a)

\(M=\mu_{r} \mu_{0} n_{1} n_{2} \pi r_{1} l\)

(b)

\(M=\mu_{0} n_{1} n_{2} \pi r_{1}^{2} l\)

(c)

\(M=\mu_{r} n_{1} n_{2} \pi r_{1}^{2} l\)

(d)

\(M=\mu_{r} \mu_{0} n_{1} n_{2} \pi r_{1}^{2} l\)

33.

The self inductance L of a solenoid of length I and area of cross-section A, with a fixed number of turns N increases as

(a)

l and A increase

(b)

I decreases and A increases

(c)

l increases and A decreases

(d)

both l and A decrease

34.

The self-inductance of a coil is 2 mH. The rate of flow of current in it is 10³ A/S. The induced electromotive force in the coil is

(a)

(b)

(c)

(d)

35.

A horizontal straight wire 20 m long extending from east to west is falling with a speed of 5.0 ms^-1at right angles to the horizontal component of the earth's magnetic field 0.30 x 10^-4 Wbm^-2. The instantaneous value of the emf induced in the wire will be

(a)

6.0 mV

(b)

3 mV

(c)

4.5 mV

(d)

1.5 mV

36.

There are two coils and B as shown in figure. A current starts flowing in B as shown, when A is moved towards B and stops when A stops moving. The current in A is counter clockwise. B is kept stationary when A moves. We can infer that

(a)

there is a constant current in the clockwise direction inA

(b)

there is a varying current in A

(c)

there is no current in A

(d)

there is a constant current in the counter clockwise direction in A

37.

The instantaneous magnetic flux linked with a coil is given by φ = (5t³ - 100t + 300) Wb. The emf induced in the coil at time t = 2 s is

(a)

-40V

(b)

40V

(c)

140V

(d)

300V

38.

Current in the coil is larger

(a)

when the magnet is pushed towards the coil faster

(b)

when the magnet is pulled away the coil faster

(c)

Both (a) and (b)

(d)

Neither (a) nor (b)

39.

A physicist works in a laboratory where the magnetic field is 2T. She wears a necklace enclosing area 0.01m² in such a way that the plane of the necklace is normal to the field and is having a resistance R = 0.01\(\Omega \). Because of power failure, the field decays to 1 T in time 10^-3s. Then what is the total heat produced in her necklace?

(a)

10 J

(b)

20 J

(c)

30 J

(d)

40 J

40.

A coil having n turns and resistance R is connected with a galvanometer of resistance 4R. This combination is moved in time t seconds from a magnetic flux \({ \phi }_{ 1 }\) Weber to \({ \phi }_{ 2 }\) Weber. The induced current in the circuit is :

(a)

\(\frac { { \phi }_{ 2 }-{ \phi }_{ 1 } }{ 5Rnt } \)

(b)

\(\frac { -n\left( { \phi }_{ 2 }-{ \phi }_{ 1 } \right) }{ 5Rt } \)

(c)

\(\frac { -\left( { \phi }_{ 2 }-{ \phi }_{ 1 } \right) }{ Rnt } \)

(d)

\(\frac { -n\left( { \phi }_{ 2 }-{ \phi }_{ 1 } \right) }{ Rt } \)

41.

A conducting circuit loop is placed in a uniform magnetic field of induction B tesla with its plane normal to the field. Now, the radius of the loop starts sharinking at the rate dr/dt. The induced emf at the instant when the radius is R is:

(a)

\(\pi rB\left( \frac { dr }{ dt } \right) \)

(b)

\(2\pi rB\left( \frac { dr }{ dt } \right) \)

(c)

\(\pi r^{ 2 }\left( \frac { dr }{ dt } \right) \)

(d)

\(\left( \frac { \pi r^{ 2 } }{ 2 } \right) ^{ 2 }\left( \frac { dr }{ dt } \right) \)

42.

In a uniform magnetic field of induction B, a wire in the form of semicirclr of radius r rotates about the diameter of the circle with angulat frequency. The axis of rotation is perpendicular to the field. If the total resistance of the circuit is R, then the mean power generated per period of rotation is

(a)

\(\frac { B\pi { r }^{ 2 }\omega }{ 2R } \)

(b)

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

(c)

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

(d)

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

43.

A circular coil expands radially in a region of magnetic field and no electromotive force is produced in the coil. This can be because

(a)

the magentic field is constant

(b)

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

(c)

the magnetic field has a perpendicular componet whose magnitude is decreasing suitably

(d)

there is a constant magnetic field in the perpendicular direction.

44.

An e.m.f. is produced in a coil, which is not connected to an external voltage source. This can be due to

(a)

the coil being in a time varying magnetic field

(b)

the coil moving in a time varying magnetic field

(c)

the coil moving in a constant magnetic field

(d)

the coil is stationary in external spatially varying magnetic field, which does not change with time

45.

A wire of length 2m moves with a speed of 5m/s perpendicular to a magnetic field of induction 0.1 Wb/m². The e.m.f. induced in the wire is

(a)

1 V

(b)

10 V

(c)

5 V

(d)

2 V

46.

The magnetic flux linked with a coil is \(\phi \) = (3t-2t+1) milliweber. The e.m.f. induced in the coil at t = 1sec is

(a)

(b)

4\(\times\)10^-3V

(c)

(d)

4\(\times\)10³V

47.

Out of the following, choose the correct relation

(a)

1henry = \(\frac{1\ volt}{1\ ampere}\)

(b)

1henry = \(\frac{1\ amp}{1\ volt}\)

(c)

1 henry = \(\frac{1volt}{1\ amp/sec}\)

(d)

1 henry = \(\frac{1volt}{1\ amp\ .\ sec}\)

48.

Amount of charge induced in a circuit of resistance R is given by

(a)

\(dQ=(d\phi )\times R\)

(b)

\(dQ=\frac { d\phi }{ R } \)

(c)

\(dQ={ R }^{ 2 }d\phi \)

(d)

\(dQ=\frac { d\phi }{ R^{ 2 } } \)

49.

Choose the wrong statement:

(a)

When ever the amount of magnetic flux linked with a circuit changes, an e.m.f. is induced in the circuit.

(b)

The induced e.m.f. lasts so long as the change in magnetic flux continues

(c)

Large the amount of magnetic flux linked with a circuit, greater is the e.m.f. induced in it.

(d)

The direction of induced e.m.f. is given by Lenz's Llaw.

50.

The cause of induced e.m.f. is

(a)

magnetic flux

(b)

magnetic field

(c)

area

(d)

change in magnetic flux

51.

SI unit of magnetic flux is

(a)

henry

(b)

weber

(c)

coulomb

(d)

volt

52.

In the relation \(\phi \) = BA cos \(\theta \), \(\theta \) is angle........

(a)

which normal to surface area makes with the direction of magnetic field

(b)

which magnetic field makes with the surface

(c)

which is never constant

(d)

none of the above

Assertion and reason

9 x 1 = 9

53.

Assertion : Whenever magnetic flux linked with the coil changes with respect to time, then an emf is induced in it.
Reason : According to lenz law, the direction of induced current in any coil in such a way that it always oposses the cause by which it is produced.
Codes:
(a) If both Assertion & Reason are true & the Reason is a correct explanation of the Assertion.
(b) If both Assertion and Reason are true but Reason is not a correct explanation of the Assertion.
(c) If Assertion is true but the Reason is false.
(d) If Assertion & Reason both are false.

54.

Assertion : An inductor can not have zero resistance.
Reason : This is because inductor has to be made up of some material, which must have some resistance.
Codes:
(a) If both Assertion & Reason are true & the Reason is a correct explanation of the Assertion.
(b) If both Assertion and Reason are true but Reason is not a correct explanation of the Assertion.
(c) If Assertion is true but the Reason is false.
(d) If Assertion & Reason both are false.

55.

Assertion (A) : Lenz's law violates the principle of conservation of energy.
Reason (R) : Induced emf always opposes the change in magnetic flux responsible for its production.
(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
(c) Assertion is true but Reason is false.
(d) Assertion is false but Reason is true.

56.

Assertion (A) : The resistance of a coil for direct current is 5 ohms. An alternating current is sent through it. The resistance will remain same
Reason (R) : The resistance of a coil does not depend upon nature of current.
Codes:
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is NOT the correct explanation of A
(c) A is true but R is false
(d) A is false and R is also false

57.

Assertion (A) : When number of turns in a coil doubled, coefficient of self inductance of the coil becomes four times.
Reason (R) : Coefficient of self inductance is proportional to the square of number of turns.
Codes:
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is NOT the correct explanation of A
(c) A is true but R is false
(d) A is false and R is also false

58.

Assertion (A) : Self-inductance is called the inertia of electricity.
Reason (R) : Self-inductance is the phenomenon, according to which an opposing induced e.m.f is produced in a coil as a result of change in current or magnetic flux linked with the coil
Codes:
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is NOT the correct explanation of A
(c) A is true but R is false
(d) A is false and R is also false

59.

Assertion (A) : Changing magnetic flux can produce induced e.m.f ..
Reason (R) : Faraday established induced e.m.f experimentally
Codes:
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is NOT the correct explanation of A
(c) A is true but R is false
(d) A is false and R is also false

60.

Assertion (A) : An induced current is developed when the number of magnetic lines of force associated with conductor is changed.
Reason (R) : An induced current developJn a conductor moved in a direction parallel to the magnetic field.
Codes:
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is NOT the correct explanation of A
(c) A is true but R is false
(d) A is false and R is also false

61.

Assertion (A) : An induced emf is generated when magnet is withdrawn from the solenoid.
Reason (R) : The relative motion between magnet and solenoid induces emf
Codes:
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is NOT the correct explanation of A
(c) A is true but R is false
(d) A is false and R is also false

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Answers Key:

Multiple Choice Question

52 x 1 = 52

(a)
5√3 V

(d)
R₁

(a)
50 V

(d)
75 mH

(b)
the circular and elliptical loops

(a)
0.5 A

(b)
2

(b)
doubled.

10.

(a)
4 x 10^-4 Wb

11.

(b)
I decreases and A increases

12.

(b)
-10V

13.

(a)
clockwise.

14.

(a)
energy.

15.

16.

(d)
5V

17.

(a)
1.67 H

18.

(a)
constant current clockwise.

19.

(b)
\(2{ B }_{ 0 }{ L }^{ 2 }Wb\)

20.

21.

22.

(b)
conductor

23.

(a)
Anti-clockwise

24.

(a)
Rectangular loop

25.

(b)
17.7V

26.

(a)
Lenz's law

27.

(d)
Faraday's law of electromagnetic induction

28.

(a)
A momentary deflection

29.

30.

(b)
\(\phi_{B}=B A \cos \omega t\)

31.

(b)
relative position and orientation of the two coils

32.

(d)
\(M=\mu_{r} \mu_{0} n_{1} n_{2} \pi r_{1}^{2} l\)

33.

(b)
I decreases and A increases

34.

(b)
2V

35.

(b)
3 mV

36.

(d)
there is a constant current in the counter clockwise direction in A

37.

(b)
40V

38.

39.

(a)
10 J

40.

(b)
\(\frac { -n\left( { \phi }_{ 2 }-{ \phi }_{ 1 } \right) }{ 5Rt } \)

41.

(b)
\(2\pi rB\left( \frac { dr }{ dt } \right) \)

42.

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

43.

(b)
the magnetic field is in the same plane as the circular coil and it may or may not vary

44.

(b)
the coil moving in a time varying magnetic field

45.

(a)
1 V

46.

(b)
4\(\times\)10^-3V

47.

48.

(b)
\(dQ=\frac { d\phi }{ R } \)

49.

50.

(d)
change in magnetic flux

51.

(b)
weber

52.

(a)
which normal to surface area makes with the direction of magnetic field

Assertion and reason

9 x 1 = 9

53.

(b) If both Assertion and Reason are true but Reason is not a correct explanation of the Assertion.

54.

(a) If both Assertion & Reason are true & the Reason is a correct explanation of the Assertion.

55.

(d) Assertion is false but Reason is true.
Lenz's law is based on conservation of energy and induced emf always opposes the cause of it, change in magnetic flux.

56.

(d): Both assertion and reason are false. When an alternating current is sent through the coil then effective resistance of the coil will be \(\sqrt{R^{2}+(\omega L)^{2}}\) while it was only R for direct current i.e., effective resistance of coil will increases for A.C.

57.

(a): The coefficient of self inductance of the coil is given by \(L=\frac{\mu_{0} N^{2} A}{l}\)
where N is number of turns, 1 is length of the coil and
A is area of coil, so \(L \propto N^{2}\)

58.

(a): Self-inductance of a coil is its property by virtue of which the coil opposes any change in the current flowing through it. It is because, the induced emf produced opposes the change in current. For this reason, self induction is called inertia of electricity

59.

(b): E.m .f. induces, when there is change in magnetic flux. The magnitude of induced e.m.f depends upon the rate at which the magnetic flux changes. When magnetic flux is steady or constant no e.m.f is induced. Faraday did experiment in which, there is relative motion between the coil and magnet, the flux linked with the coil changes and e.m.f induces.

60.

(a): An induced current develop in a conductor cannot moved in a direction parallel to magnetic field. This is because when the conductor moved in a direction parallel to magnetic field, amount of flux linked with the conductor does not change. Thus the induced current develops only when conductor cuts the lines of magnetic force. The direction of flow of induced current can also be found by applying Fleming's right hand rule, when the direction of motion of conductor inside the magnetic field and the direction of magnetic field action on it are known.

61.

(a): According to Faraday's law of electromagnetic induction, induced emf will be generated in the solenoid because of the relative motion between magnet and solenoid.