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ELECTROMAGNETIC INDUCTION

VERY SHORT ANSWER QUESTIONS

Q.1 – A lamp connected in parallel with a coil of large inductance glows brilliantly before going off. Why ?

Q.2 – What is the need of non-inductive coils ?

Q.3 – A wire-loop confined in a plane is rotated in its own plane with some angular velocity. A uniform

magnetic field exists in the region. Find the emf induced in the loop.

Q.4 – A conducting loop of face-area A and resistance R is placed perpendicular to a magnetic field B. The loop

is withdrawn completely from the field. Find the charge which flows through any cross-section of the

wire in the process. Note that it is independent of the shape of the loop as well as the way it is

withdrawn.

Q.5 – Write the dimensions of (a) ∫ (b) and (c)

. The symbols have their usual meanings.

Q.6 – A wire kept in east-west direction is allowed to fall freely. Will an emf be induced in the wire ?

Q.7 – Write down the most general formula for the self-inductance of a coil.

Q.8 – An artificial satellite with a metal surface is orbiting the earth in the equatorial plane. No current is

induced due to earth’s magnetism. Why ?

Q.9 – Can a wire act as an inductor ?

Q.10 – Why a thick metal plate oscillating about a horizontal axis stops when a strong magnetic field is applied

on the plate ?

Q.11 – A metal block and a brick of the same size are allowed to fall freely from the same height above the

ground. Which of the two would reach the ground earlier and why ?

Q.12 – Two identical loops, one of copper and another of iron, are rotated with the same angular velocity in a

uniform magnetic field. In which case the induced emf is more and why ?

Q.13 – A closed loop is held stationary in the magnetic field between the north and south poles of two

permanent magnets held fixed. Can we hope to generate current in the loop by using very strong

magnets ?

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Q.14 – A small piece of metal wire is dragged across the gap between the pole pieces of a magnet in 0.5 second.

The magnetic flux between the pole pieces is known to be 8 × 10-4 Wb. Estimate the emf induced in the

wire.

Q.15 – Predict the polarity of the capacitor in the situation described in Fig – 11.57.

Q.16 – A rectangular loop and a circular loop are moving out of a uniform magnetic field region to a field-free

region with a constant velocity. In which loop do you expect the induced emf to be constant during the

passage out of the field region ? The field is normal to the loops.

Q.17 – The magnetic flux through a coil changes from 12 m Wb to 6 m Wb in 0.01 s. What is the induced emf ?

Q.18 – Why the coil of a beat galvanometer is wound on a metal frame ?

Q.19 – What is the dimensional formula for the mutual inductance of two coils ?

Q.20 – Does Lenz’s law violate the law of conservation of energy ?

Q.21 – Name the physical quantity which is measured in weber (ampere)-1 .

Q.22 – What is the effect of metallic core on self-inductance ?

Q.23 – Write three factors on which the self-inductance of a coil depends.

Q.24 – Why the oscillations of a copper disc in a magnetic field are damped ?

Q.25 – Prove that the charge induced is independent of time.

Q.26 – Write three factors on which the mutual inductance between a pair of coils depends.

Q.27 – What is the SI unit of mutual inductance ?

Q.28 – The electric current in wire in the direction from B to A is decreasing. What is the direction of induced

current in the metallic loop kept above the wire as shown in Fig – 11.58 ?

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Q.29 – A conducting loop is held above a current-carrying wire PQ as shown in Fig – 11.59. What will be the

direction of the induced current in the loop if the current in the wire PQ is constantly increased ?

Q.30 – A metallic wire 1 m in length is moving normally across a magnetic field of 0.1 T with a speed of 5 m s-1.

What is the emf between the ends of the wire ?

Q.31 – How does the self-inductance of a coil change when an iron rod is introduced in the coil ?

Q.32 – How does the self-inductance of a coil change when the number of turns in the coil is decreased ?

Q.33 – A ring is fixed to the wall of a room. When south pole of a magnet is brought near the ring, what shall be

the direction of induced current in the ring ?

Q.34 – Will an induced current be always produced whenever there is change of magnetic flux linked with a coil

?

Or

Does change in magnetic flux induce emf or current ?

Q.35 – (a) When a magnet falls through a vertical coil, will its acceleration be different from the ‘acceleration due

to gravity’ ?

(b) Why does the acceleration of a magnet falling through a long solenoid decrease ?

Q.36 – How does the mutual inductance of a pair of coils change when the number of turns in each coil is

decreased ?

Q.37 – A vertical metallic pole falls down through the plane of magnetic meridian. Will any emf be induced

between its ends ?

Q.38 – A train is moving with uniform velocity from north to south. Will any induced emf appear across the

ends of the axle ?

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Q.39 – Self-inductance of an air core inductor increases from 0.01 mH to 10 mH on introducing an iron core into

it. What is the relative permeability of the core used ?

Q.40 – A solenoid with an iron core and a bulb are connected to a dc source. How does the brightness of the bulb

change, when the iron core is removed from the solenoid ?

Q.41 – Define electromagnetic induction.

Q.42 – State Fleming’s right hand rule.

Q.43 – Why resistance coils are usually double wound ?

Q.44 – What is the basic cause of induced emf ?

Q.45 – Two identical loops, one of copper and another of constantan, are removed from a magnetic field within

the same time interval. In which loop will the induced current be greater ?

Q.46 – What are the SI units of (i) magnetic flux and (ii) magnetic field strength ?

Q.47 – Name the physical quantity whose SI unit is weber. Is it a scalar or a vector quantity ?

Q.48 – Does Faraday’s induced emf depend on resistance of the material of the coil ?

Q.49 – How can a space traveller detect the presence of magnetic field on an unknown planet with the help of a

sensitive galvanometer and a coil of wire ?

Q.50 – Fig – 11.60 shows a coil wound on a cylindrical support and connected to a battery. This current-carrying

coil is moved towards a test coil which is connected to a galvanometer. What would you do to obtain a

large deflection of the galvanometer ?

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Q.51 – In the previous question, how would you demonstrate the presence of an induced current in the absence

of a galvanometer ?

Q.52 – An iron bar falling vertically through the hollow region of a thick cylindrical shell made of copper

experiences a retarding force. What can you conclude about the iron bar ?

Q.53 – A coil is wound on an iron core and looped back on itself so that the core has two sets of closely wound

wires in series carrying currents in the opposite senses. What do you expect about its self-inductance ?

Will it be large or small ?

Q.54 – Two similar circular co-axial loops carry equal currents in the same direction. If the loops be brought

nearer, what will happen to the current in them ?

Q.55 – Give the direction in which the induced current flows in the wire loop, when the magnet moves towards

it as shown in Fig – 11.61.

Q.56 – When a fan is switched off, a spark is produced in the switch. Why ?

Q.57 – 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 ?

Q.58 – A coil B is connected to low voltage Bulb L and placed near another coil A as shown in Fig – 11.63.

Explain the following observations. (i) Bulb lights (ii) Bulb get dimmer if the coil B is moved upwords.

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Q.59 – Two straight and parallel wires A and B are being brought towards each other. If current in A be i, what

will be the direction of induced current in B ? If A and B are taken away from each other, then ?

Q.60 – Two inductors L1 and L2 sufficient distance apart are connected (i) in series (ii) in parallel. What is their

equivalent inductance ?

Q.61 – Define the term magnetic flux. Compute its dimensions.

Q.62 – The closed loop PQRS is moving into a uniform magnetic field acting at right angles to the plane of the

paper as shown in Fig – 11.64 – State the direction in which the induced current flows in the loop.

Q.63 – Find the induced current in the circular loop KLMN of radius r, if the straight wire PQ carries a steady

current of I ampere ?

Q.64 – Define the unit of self-inductance. Or Define one henry.

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Q.65 – A uniform magnetic field exists normal to the plane of the paper over a small region of space. A

rectangular loop of wire is slowly moved with a uniform velocity across the field as shown in Fig – 11.66

Draw the graph showing the variation of (i) magnetic flux linked with the loop and (ii) the induced emf

in the loop with time.

Q.66 – Fig – 11.68 – shows two identical rectangular loops (1) and (2), placed on a table along with a straight long

current-carrying conductor between them.

(i) What will be the direction of the induced currents in the loops when they are pulled away from the

conductor with same velocity v ?

(ii) Will the emf induced in the two loops be equal ? justify your answer.

Q.67 – In Fig – 11.69, a bar magnet moving towards the right or left induces an emf in the coils (1) and (2). Find

the directions of the induced currents through the resistors AB and CD when the magnet is moving (a)

towards the right, and (b) towards the left.

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Q.68 – Give the direction in which the induced current flows in the coil mounted on an insulating stand when a

bar magnet is quickly moved along the axis of coil from one side to the other as shown in Fig – 11.70.

Q.69 – Fig – 11.71 shows a bar magnet M falling under gravity through an air-cored coil C. Plot a graph showing

the variation of induced emf (E) with time (t). What does the area enclosed by the E-t curve depict ?

Q.70 – Define magnetic flux. Name its SI unit.

Q.71 – Self-induction is called the inertia of electricity. Explain why ?

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Q.72 – How is the mutual inductance of a pair of coils affected when :

(i) separation between the coils is increased ?

(ii) the number of turns of each coil is increased

(iii) A thin iron sheet is placed between the two coils, other factors remaining the same ?

Explain your answer in each case.

Q.73 – A rectangular coil of area A, having number of turns N is rotated at f revolutions per second in a uniform

magnetic field B, the field being perpendicular to the coil. Prove that the maximum emf induced in the

coil is 2 f N B A.

SHORT ANSWER QUESTIONS

Q.74 – The north pole of a magnet is brought down along the axis of a horizontal circular coil (Fig – 11.73). As a

result, the flux through the coil changes from 0.35 weber to 0.85 weber in an interval of half a second.

Find the average emf induced during this period. Is the induced current clockwise or anticlockwise as

you look into the coil from the side of the magnet ?

Q.75 – Fig – 11.74 shows three different orientations of a circular coil rotating in the magnetic field between the

poles of a horse shoe magnet. (a) Determine the direction of induced current in the coil if the rotation is

anticlockwise as viewed by the reader. (b) In which orientation during rotation (with uniform angular

speed) is the induced emf greatest ?

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Q.76 – Fig – 11.75 shows planar loops of different shapes moving out of or into a region of a magnetic field

which is directed normal to the plane of the loop away from the reader. Determine the direction of

induced current in each loop using Lenz’s law.

Q.77 – Discuss energy consideration in LR circuit.

Q.78 – The flux of magnetic field through a closed conducting loop changes with time according to the equation,

ØB = at2 + bt + c. (a) Write the SI unit of a, b and c. (b) If the magnitudes of a, b and c are 0.20, 0.40 and

0.60 respectively, find the induced emf at t = 2 s.

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Q.79 – A horizontal telephone wire 103 m long is lying along east in earth’s magnetic field. It falls freely to the

ground from a height of 10 m. Calculate the emf induced in the wire when the wire strikes the ground

assuming that the horizontal component of earth’s magnetic field has flux density 0.32 × 10-4 T.

Q.80 – A conducting circular loop of area 1 mm2 is placed coplanarly with a long, straight wire at a distance of 20

cm from it. The straight wire carries an electric current which changes from 10 A to zero in 0.1 s. Find the

average emf induced in the loop in 0.1 s.

Q.81 – A closed coil having 100 turns is rotated in a uniform magnetic field B = 4.0 × 10-4 T about a diameter

which is perpendicular to the field. The angular velocity of rotation is 300 revolutions per minute. The

area of the coil is 25 cm2 and its resistance is 4.0 Ω Find (a) the average emf developed in half a turn from

a position where the coil is perpendicular to the magnetic field, (b) the average emf in a full turn, and (c)

the net charge induced in part (a).

Q.82 – A circular coil of radius 2.00 cm has 50 turns. A uniform magnetic field B = 0.200 T exists in the space in a

direction parallel to the axis of the loop. The coil is now rotated about a diameter through an angle of

60.00. The operation takes 0.100 s. (a) Find the average emf induced in the coil. (b) If the coil is a closed

one (with the two ends joined together) and has a resistance of 4.00 Ω, calculate the net charge crossing a

cross-section of the wire of the coil.

Q.83 – Find the emf in a coil of 50 turns, each of area 80 cm2, When making 1800 revolutions per minute in a

uniform field of flux density 6 × 10-3 T.

Q.84 – A bar magnet M is dropped so that it falls vertically through the coil C. The graph obtained for voltage

produced across the coil versus time is shown in Fig – 11.77 (b).

(i) Explain the shape of the graph.

(ii) Why is the negative peak longer than the positive peak ?

CONCEPTUAL PROBLEMS

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Q.85 – A glass rod of length moves with velocity v in uniform magnetic field B. What is the emf induced in the

rod ?

Q.86 – A wheel with a certain number of spokes is rotated in a plane normal to the earth’s magnetic field so that

an emf is induced between the axle and rim of the wheel. Keeping all other things same, the number of

spokes is changed. What will be the effect ?

Q.87 – Will an induced current be always produced whenever there is change of magnetic flux linked with a coil

?

Q.88 – Why the inductance per unit length for a solenoid near its centre is different from inductance per unit

length near its end ?

Q.89 – A soft iron core is introduced in an inductor. What is the effect on the self-inductance of the inductor ?

Q.90 – Two coils are being moved out of magnetic field one coil is moved rapidly and the other slowly. In which

case is more work done and why ?

Q.91 – Why birds fly off a high-tension wire when current is switched on ?

Q.92 – A cylindrical bar magnet is kept along the axis of a circular coil. Will there be a current induced in the coil

if the magnet is rotated about its axis ?

Q.93 – A closed conducting loop moves normal to the electric field between the plates of a large capacitor. Is a

current induced in the loop when it is (i) wholly inside the capacitor. (ii) partially outside the plates of

the capacitor ? The electric field is normal to plane of the loop.

Q.94 – An electron moves in a circle with uniform speed in a stationary magnetic field normal to the plane of the

circle. If the field magnitude is made to increase with time, will the electron speed up or speed down ?

Will it continue to revolve in the same circle ?

Q.95 – A conductor placed in a magnetic field is moved parallel to magnetic field. Will an induced emf be set up

in the conductor ?

Q.96 – Three identical coils A,B and C are placed with their planes parallel to one an other. Coils A and C carry

currents as shown in Fig – 11.78. Coils B and C are fixed. The coil A is moved towards B with uniform

motion. Is there any induced current in B ?

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Q.97 – A small resistor (say a lamp) is usually put in parallel to the current-carrying coil of an electromagnet.

What purpose does it serve ? [Fig – 11.79]

Q.98 – A copper ring is held horizontally and a bar magnet is dropped through the ring with its length along the

axis of the ring. Will the acceleration of the falling magnet be equal to greater than or less than that due to

gravity ?

Q.99 – An induced emf has no direction of its own. Comment.

Q.100 – Fig – 11.80 shows an inductor L and a resistor R connected in parallel to a battery through a switch. The

resistance of R is the same as that of the coil that makes L. Two identical electric bulbs B1 and B2 are put

in each arm of the circuit.

(i) Which of the bulbs light up earlier when S is closed ?

(ii) Will the bulbs be equally bright after some time Justify your answer.

Q.101 – What are eddy currents. How are these produced ? In what sense are eddy currents considered

undesirable in a transformer and how are these reduced in such a device ?

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LONG ANSWER QUESTIONS

Q.102 – (a) State Faraday’s laws of electromagnetic induction.

(b) State Lenz’s law. How will you verify it experimentally ?

Q.103 – What is meant by self-induction ? Define coefficient of self-induction. Also define its SI unit. Derive an

expression for the coefficient of self-induction for a long air-cored solenoid.

Q.104 – What is meant by mutual induction ? Define coefficient of mutual induction. Also define its SI unit.

Derive an expression for the coefficient of mutual induction between two long solenoids.

Q.105 – What is self-induction ? Define coefficient of self-induction and its unit. Derive an expression for

coefficient of self-induction of a long solenoid.

Q.106 – What is electromagnetic induction ? State its laws. Describe two methods for producing induced emf.

Define the law by which the direction of induced current can be determined.

Q.107 – What are eddy currents ? Give an experiment to explain their origin. Discuss briefly two important

applications of eddy currents.

Q.108 – A conducting rod of length is moved in a magnetic field of magnitude B with velocity such that the

arrangement is mutually perpendicular. Prove that the emf induced in the rod is = B/v.

Q.109 – Deduce an expression for the self-inductance of a long solenoid of N turns, having a core of relative

permeability μr.

Q.110 – What are eddy currents ? How are these minimised ? Mention two applications of eddy currents.