CBSE Class 12 Physics Electromagnetic Induction Worksheet Set B

 

 

1 Two identical loops, one of copper and other of constantan ,are removed from a magnetic field within the same time interval. In which loop will the induced current be greater? Justify.

 

2 A conducting coil is moved relative to a magnetic field .Will there be induced emf and induced current always? Justify

 

3 Two identical bar magnets are dropped from the same height simultaneously, one falls through a copper tube and the other falls through air, will they reach ground at the same time? Justify.

 

4 The south pole of a magnet is brought near a conducting loop. What is the direction of induced current as observed by a person on the other side of the loop?

 

5 How does the self inductance of an air core coil change, when i) the number of turns in the coil is decreased? ii) an iron rod is introduced in the coil?

 

6 A bismuth rod is introduced in a solenoid carrying current, how do i) its self inductance ii) emf induced in the solenoid change?

 

7 A copper coil L wound on a soft iron core and a lamp B is connected to a battery E through a tap key K. When the key is closed, the lamp glows dimly .But when the key is suddenly opened , the lamp flashes for an instant to much greater brightness . Explain.

 

8 In any ac circuit is the applied instantaneous voltage equal to the algebraic sum of the instantaneous voltages across the series elements of the circuit?

 

9 A conducting loop of area A and resistance R is placed perpendicular to the magnetic field B. The loop is withdrawn completely from the field. Derive an expression for induced charge that flows through any cross section of the wire

 

10 The south pole of a magnet is brought near a conducting loop. What is the direction of induced current as observed by a person on the other side of the loop?

 

11 The figure shows a rectangular conducting frame MNOP of resistance R placed partly in a perpendicular magnetic field B and moved with velocity v as shown in the figure.

 

Obtain the expressions for the

 

(i) Force acting on the arm ON and its direction, and

(ii) Power required to move the frame to get a steady emf induced between the arms MN and PO.

 

12 A coil of number of turns N, area A, is rotated at a constant angular speed w, in a uniform magnetic field B, and connected to a resistor R. Deduce expressions for: (i) Maximum emf induced in the coil

(ii) Power dissipation in the coil.

 

13 What is the direction of induced currents in metal rings 1 and 2 when current I in the wire is increasing steadily?

14 (i) Define mutual inductance and write its SI unit.

(ii) A square loop pf side ‘a’ carrying current I2 is kept at distance ‘x’ from an infinitely long straight wire carrying a current I1 as shown in the figure. Obtain the expression for the resultant force acting on the loop.

 

15 (a) Describe a simple experiment (or activity) to show that the polarity of emf induced in a coil is always such that it tends to produce a current which opposes the change of magnetic flux that produces it.

 

(b) The current flowing through an inductor of self-inductance L is continuously increasing. Plot a graph showing the variation of

(i) Magnetic flux versus the current

(ii) Induced emf versus dI/dt

(iii)Magnetic potential energy stored versus the current.

 

16 State Faraday’s law of electromagnetic induction.

Figure shows a rectangular conductor PORS in which the conductor PQ is free to move in a uniform magnetic field B perpendicular to the plane of the paper. The field extends from x=0 to x=b and is zero for x>b. Assume that only the arm PQ possesses resistance r, when the arm PQ is pulled outward from x=0 with constant speed v, as in the expressions for the flux and the induced emf. Sketch the variations of these quantities with distance 0≤x≤2b.

 

17 (a) State Lenz’s law. Give one example to illustrate this law. The Lenz’s is a consequence of the principle of conservation of energy. ‘Justify this statement.

(b) Deduce an expression for the inductance of two long coaxial solenoids but having different radii and different number of turns.

 

 

1 A jet plane is travelling west at 450 ms- 1. If the horizontal component of earth’s magnetic field at that place is 4 X 10- 4 tesla and the angle of dip is 30°, find the emf induced between the ends of wings having a span of 30 m.

 

2 A train is running due north on metre gauge at a speed of 36km/h. What will be the emf generated between the rails, if the vertical component of the earth’s magnetic field at that place is 4 x 10-5 T?

 

3 A coil having an area of cross section 0.05 m2 and number of turns 100 is placed at right angles to a magnetic field of strength 0.08 T. How much emf will be induced in it, if the field is reduced to 0.04 T in 0.01s?

 

4 Magnetic flux in closed circuit varies with time t according to the equation φ = (6t2+5t+ 1) Wb. If the resistance of the circuit is 10Ω, what is the magnitude of induced current at t= 5s ?

 

5 A circular coil of radius 10 cm, 500 turns and resistance 2Ω is placed with its plane perpendicular to the horizontal component of the earth’s magnetic field. It is rotated about its vertical diameter through 180° in 0.25 s. Estimate the magnitudes of the emf and current induced in the coil. Horizontal component of the earth’s magnetic field at the place is 3.0 × 10–5 T.

 

6 A wheel with 10 metallic spokes each 0.5 m long is rotated with a speed of 120 rev/min in a plane normal to the horizontal component of earth’s magnetic field HE at a place. If HE = 0.4 G at the place, what is the induced emf between the axle and the rim of the wheel? Note that 1 G = 10–4 T.

 

7 A horizontal straight wire 10 m long extending from east to west is falling with a speed of 5.0 m s–1, at right angles to the horizontal component of the earth’s magnetic field, 0.30 × 10–4 Wb m–2.

(a) What is the instantaneous value of the emf induced in the wire?

(b) What is the direction of the emf?

 

Question. A square metal loop of side 10 cm and resistance 1 Ω is moved with a constant velocity partly inside a uniform magnetic field of 2 Wbm^–2, directed into the paper, as shown in the figure. The loop is connected to a network of five resistors each of value 3Ω. If a steady current of 1 mA flows in the loop, then the speed of the loop is 

(a) 0.5 cms^–1
(b) 1 cms^–1
(c) 2 cms^–1
(d) 4 cms^–1

Answer: C

Question. A cylindrical bar magnet is rotated about its axis. A wire is connected from the axis and is made to touch the cylindrical surface through a contact. Then,
(a) a direct current flows in the ammeter A
(b) no current flows through the ammeter A
(c) an alternating sinusoidal current flows through the ammeter A with a time period T = 2π/ω 
(d) a time varying non-sinusoidal current flows through the ammeter A.

Answer: B

Question. 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
(a) 0.5 A
(b) 0.1 A
(c) 2 A
(d) 1 A

Answer: A

Question. A coil of self-inductance L is connected in series with a bulb B and an AC source. Brightness of the bulb decreases when
(a) number of turns in the coil is reduced
(b) a capacitance of reactance X_C = X_L is included in the same circuit
(c) an iron rod is inserted in the coil
(d) frequency of the AC source is decreased

Answer: C

Question. A magnetic field of 2 × 10^–2 T acts at right angles to a coil of area 100 cm², with 50 turns. The average e.m.f. induced in the coil is 0.1 V, when it is removed from the field in t sec. The value of t is
(a) 10 s
(b) 0.1 s
(c) 0.01 s
(d) 1 s

Answer: B

Question. A rectangular coil of 20 turns and area of cross-section 25 sq. cm has a resistance of 100Ω. If a magnetic field which is perpendicular to the plane of coil changes at a rate of 1000 tesla per second, the current in the coil is
(a) 1 A
(b) 50 A
(c) 0.5 A
(d) 5 A

Answer: C

Question. The current in a coil of L = 40 mH is to be increased uniformly from 1A to 11A in 4 milli sec. The induced e.m.f. will be
(a) 100 V
(b) 0.4 V
(c) 440 V
(d) 40 V

Answer: A

Question. In fig., final value of current in 10W resistor, when plug of key K is inserted is 

(a) 3/10 A
(b) 3/20 A
(c) 3/11 A
(d) zero

Answer: D

Question. A square of side L metres lies in the xy-plane in a region, where the magnetic field is given by B = B0 (2î + 3ĵ + 4k̂) T, where B0 is constant. The magnitude of flux passing through the square is
(a) 2B₀L²Wb
(b) 3B₀L²Wb
(c) 4B₀L²Wb
(d) √29B₀L² Wb

Answer: C

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

(a) 8
(b) 2
(c) 6
(d) 4

Answer: B

Question. The magnetic flux through a circuit of resistance R changes by an amount Df in a time Dt. Then the total quantity of electric charge Q that passes any point in the circuit during the time Δt is represented by
(a) Q = R. ΔΦ/Δt
(b) Q = 1/R . ΔΦ/Δt
(c) Q = ΔΦ/R
(d) Q = ΔΦ/Δt

Answer: C

Question. An electron moves on a straight line path XY as shown. The abcd is a coil adjacent to the path of electron. What will be the direction of current if any, induced in the coil? 

(a) adcb
(b) The current will reverse its direction as the electron goes past the coil
(c) No current induced
(d) abcd

Answer: B

Question. A square loop of side a is rotating about its diagonal with angular velocity w in a perpendicular magnetic field B̅. It has 10 turns. The emf induced is
(a) B a² sin Ωt
(b) B a² cos Ωt
(c) 5 √2 B a²
(d) 10 B a² sin Ωt

Answer: D

Question. 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 = B0 (î + ĵ) T is present in the region. The flux passing through the loop ABCDEFA (in that order) is
(a) B₀L² Wb
(b) 2B₀L²Wb
(c) √2B₀L² Wb
(d) 4B₀L²Wb

Answer: B

Question. Same as problem 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 counter-clockwise and the coil A is as shown at this instant, t = 0, is
(a) constant current clockwise
(b) varying current clockwise
(c) varying current counter clockwise
(d) constant current counter clockwise 

Answer: A

Question. 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
(a) remains stationary
(b) is attracted by loop A
(c) is repelled by loop A
(d) rotates about is CM with CM fixed

Answer: C

Question. Choke coil works on the principle of
(a) transient current
(b) self induction
(c) mutual induction
(d) wattless current

Answer: B

Question. The self inductance L of a solenoid of length l and area of cross-section A, with a fixed number of turns N increases as
(a) l and A increase
(b) l decreases and A increases
(c) l increases and A decreases
(d) both l and A decrease

Answer: B

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

Answer: A

DIRECTIONS for : Each question contains STATEMENT-1 and STATEMENT-2. Choose the correct answer from the following.
(a) Statement -1 is false, Statement-2 is true
(b) Statement -2 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1
(c) Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1
(d) Statement -2 is true, Statement-2 is false

Question. Statement 1 : When number of turns in a coil is doubled, coefficient of self-inductance of the coil becomes 4 times.
Statement 2 : This is because L ∞ N².

Answer: B

Question. Statement 1 : An induced current has a direction such that the magnetic field due to the current opposes the change in the magnetic flux that induces the current.
Statement 2 : Above statement is in accordance with conservation of energy.

Answer: B

Question. Statement 1 : An induced emf appears in any coil in which the current is changing.
Statement 2 : Self induction phenomenon obeys Faraday's law of induction.

Answer: B

Question. Statement 1 : Lenz's law violates the principle of conservation of energy.
Statement 2 : Induced emf always opposes the change in magnetic flux responsible for its production.

Answer: A