Induction

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Induced Emf

Electromagnetic induction occurs when an e.m.f. is induced due to relative movement between a conductor and a magnetic field.
This can happen when a conductor moves relative to a magnetic field, or when a magnetic field varies relative to a conductor.
When a conductor cuts through magnetic field lines, free electrons experience a magnetic force, work is done to separate charges, and an e.m.f. is induced.
The induced e.m.f. is defined as the work done per unit charge in separating charges to the ends of a conductor.
If the conductor is part of a closed circuit, an induced current will flow.
For a straight conductor of length L moving perpendicular to a uniform magnetic field B at speed v, the induced e.m.f. is ε = BLv.
For a coil with N turns moving through a magnetic field, the induced e.m.f. is ε = BLvN.
The magnitude of the induced e.m.f. increases if the conductor length in the field increases, the magnetic field strength increases, or the conductor cuts field lines faster.

Demonstrating Induction

Experiment 1: Moving a bar magnet through a coil connected to a voltmeter induces an e.m.f. only while the magnet is moving.
When the magnet is stationary, the voltmeter reads zero because the rate of change of flux is zero.
When the magnet moves into the coil, a reading is observed; when it is removed, the reading is in the opposite direction.
Increasing the speed of the magnet increases the magnitude of the induced e.m.f. because the rate of change of flux increases.
Experiment 2: Moving a wire between two magnets induces an e.m.f. only while the wire is moving.
The magnitude of the induced e.m.f. increases with the length of wire, the speed of movement, and the strength of the magnets.

Electromagnetic induction

Magnetic Flux

Magnetic flux is the product of the magnetic flux density and the cross-sectional area perpendicular to the field.
It is calculated using Φ = BA when the field is perpendicular to the area.
The unit of magnetic flux is the weber (Wb).
Magnetic flux is maximum when the field lines are perpendicular to the plane of the area (θ = 0°).
Magnetic flux is zero when the field lines are parallel to the plane of the area (θ = 90°).
When the field is not perpendicular, the component of B perpendicular to the area is used: Φ = BA cos θ, where θ is the angle between the field lines and the normal to the area.

Magnetic Flux Linkage

Magnetic flux linkage is the product of magnetic flux and the number of turns of a coil.
It is calculated using NΦ = BAN.
The unit of magnetic flux linkage is the weber turn (Wb turns).
An e.m.f. is induced when the magnetic flux linkage changes with respect to time.
This occurs when there is a change in magnetic flux density B, cross-sectional area A, or angle θ.
For a rotating coil, flux linkage is given by NΦ = BAN cos θ.

Faraday's Law of Induction

Faraday's law states that the magnitude of an induced e.m.f. is directly proportional to the rate of change of magnetic flux linkage.
It is expressed as ε = N (ΔΦ / Δt).
When a coil is vertical relative to the field lines, flux linkage is maximum and no e.m.f. is induced.
When a coil is horizontal relative to the field lines, flux linkage is zero and the e.m.f. is maximum.
The induced e.m.f. varies sinusoidally and is 90° out of phase with the flux linkage.

Lenz's Law

Lenz's law states that the induced e.m.f. is such that it will oppose the change causing it.
It is a consequence of the principle of conservation of energy.
Combined with Faraday's law, it is given by ε = −N (ΔΦ / Δt).
The negative sign indicates that the induced e.m.f. opposes the change in magnetic flux.
When a magnet approaches a coil, the coil induces a pole to repel the magnet; when the magnet leaves, the coil induces a pole to attract it.
Work must be done to overcome the opposing force, which is consistent with energy conservation.

Self Induction and Mutual Induction

Self-induction is the effect in which a change in current in a circuit induces an e.m.f. that opposes the change in current in the same circuit.
The induced e.m.f. in self-induction is called a back e.m.f. and is proportional to the negative rate of change of current.
Mutual induction is the effect in which a change in current in one circuit induces an e.m.f. in a neighbouring circuit.
An important application of mutual induction is the transformer.
A transformer changes high alternating voltage at low current to low alternating voltage at high current, and vice versa.
A transformer consists of a primary coil, a secondary coil, and a soft iron core.
A step-up transformer has more turns in the secondary coil than the primary; a step-down transformer has more turns in the primary coil.

AC Generators

An AC generator converts mechanical energy into electrical energy in the form of alternating current.
It consists of a coil rotating in a uniform magnetic field, connected to a centre-reading meter via slip rings and brushes.
The induced e.m.f. and current alternate direction as the coil rotates.
The maximum e.m.f. occurs when the coil cuts through the most field lines (plane parallel to field).
The flux linkage is given by NΦ = BAN cos ωt, where ω is the angular speed.
The induced e.m.f. is given by ε = ε₀ sin ωt or ε = BANω sin ωt.
Increasing the frequency of rotation increases both the frequency and the amplitude of the alternating voltage.
Doubling the angular speed doubles the maximum induced e.m.f. and doubles the frequency.

The relationship between the rotation of a coil in a magnetic field and the induced e.m.f. in an AC generator

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1.A coil is connected to a galvanometer. A magnet is held at rest inside the coil. What is the reading on the galvanometer?
Easy
- AZero, because there is no change in magnetic flux linkage
- BA constant non-zero value, because the magnet is inside the coil
- CA value that increases steadily with time
- DA value that alternates direction
2.An e.m.f. is induced in a conductor whenever it is placed in a magnetic field.
Easy
True or false?
3.Which of the following will increase the magnitude of the e.m.f. induced in a coil? (select all that apply)
Medium
- AMoving the magnet faster through the coil
- BAdding more turns to the coil
- CIncreasing the strength of the bar magnet
- DHolding the magnet still inside the coil
- EUsing a coil with a larger resistance
4.What is the definition of magnetic flux?
Medium
- AThe product of the magnetic flux density and the cross-sectional area perpendicular to the magnetic field
- BThe product of the magnetic flux density and the number of turns of a coil
- CThe rate of change of magnetic flux linkage
- DThe force per unit charge on a moving charge in a magnetic field
5.A rectangular coil rotates in a uniform magnetic field. At what orientation is the magnetic flux linkage through the coil a maximum?
Medium
- AWhen the plane of the coil is perpendicular to the field lines
- BWhen the plane of the coil is parallel to the field lines
- CWhen the plane of the coil is at 45° to the field lines
- DThe flux linkage is constant at all orientations
6.When the plane of a coil is parallel to the magnetic field lines, the induced e.m.f. in the coil is at a maximum.
Easy
True or false?
7.A straight conductor of length 0.30 m moves perpendicular to a uniform magnetic field of flux density 2.0 T at a speed of 2.5 m s⁻¹. What is the magnitude of the induced e.m.f.?
Medium
- A1.5 V
- B0.15 V
- C6.0 V
- D0.60 V
8.Match each term with its correct definition.
Medium
- Magnetic flux
- Magnetic flux linkage
- Faraday's law
- Lenz's law
- The product of magnetic flux density and cross-sectional area perpendicular to the field
- The product of magnetic flux and the number of turns of a coil
- The magnitude of an induced e.m.f. is directly proportional to the rate of change of magnetic flux linkage
- The induced e.m.f. is such that it will oppose the change causing it

Plus de questions

9.A straight conductor of length 30 cm moves normally across a uniform magnetic field of flux density 2.0 T. Calculate the speed the conductor needs to induce an e.m.f. of magnitude 1.5 V.
Hard
- A2.5 m s⁻¹
- B0.25 m s⁻¹
- C0.90 m s⁻¹
- D9.0 m s⁻¹
10.A single loop of wire moves normally across a uniform magnetic field. The induced e.m.f. is 0 V. Why?
Hard
- AThe magnetic flux through the loop is constant, so there is no change in flux linkage
- BThe loop is not cutting any magnetic field lines
- CThe resistance of the loop is too high
- DThe magnetic field is too strong
11.When a bar magnet is pushed into a coil, the coil will try to pull the magnet in.
Medium
True or false?
12.Which of the following changes will induce an e.m.f. in a coil? (select all that apply)
Medium
- AA changing magnetic flux density B through the coil
- BA changing cross-sectional area A of the coil
- CA change in the angle θ between the coil and the field
- DKeeping the coil stationary in a uniform magnetic field
- EIncreasing the resistance of the coil
13.State the quantity represented by the gradient of a graph of magnetic flux linkage NΦ against time t.
Medium
- AInduced e.m.f.
- BMagnetic flux density
- CMagnetic flux
- DPower
14.A rectangular coil with a magnetic flux of 0.15 mWb spins in a uniform magnetic field of flux density 0.50 mT. Calculate the cross-sectional area of the coil.
Medium
- A0.30 m²
- B0.30 cm²
- C3.0 m²
- D0.075 m²
15.The rotational speed of a coil in an AC generator is doubled. Which row correctly identifies the new output e.m.f. and the new frequency?
Hard
- Ae.m.f. = 2ε, frequency = 2f
- Be.m.f. = 2ε, frequency = f
- Ce.m.f. = ε, frequency = 2f
- De.m.f. = ε/2, frequency = f/2
16.Magnetic flux is zero when the magnetic field lines are parallel to the plane of the area.
Medium
True or false?
17.Which of the following is the correct definition of self-induction?
Medium
- AThe effect in which a change in the current tends to produce an induced e.m.f. which opposes the change in current in the same circuit
- BThe effect in which a change in current in one circuit induces an e.m.f. in a neighbouring circuit
- CThe process of inducing an e.m.f. by moving a magnet through a coil
- DThe process of converting mechanical energy into electrical energy
18.Which of the following is an important application of mutual induction?
Medium
- ATransformers
- BA simple AC generator
- CA moving-coil galvanometer
- DA straight conductor moving in a magnetic field
19.A step-up transformer has more turns in the secondary coil than in the primary coil.
Easy
True or false?
20.A transformer has a soft iron core. Why is soft iron used?
Medium
- AIt can easily be magnetised and demagnetised, enhancing the magnetic field from the primary to the secondary coil
- BIt is a good electrical insulator
- CIt increases the resistance of the coils
- DIt reduces the frequency of the alternating current
21.A conducting ring is dropped so that it falls towards the north pole of a fixed bar magnet. Which of the following statements about the induced effects in the ring are correct? (select all that apply)
Medium
- AAn e.m.f. is induced in the ring as it falls
- BThe induced current in the ring produces a north pole on the face nearest the magnet
- CThe ring experiences an upward magnetic force opposing its fall
- DThe induced current flows only while the ring is at rest relative to the magnet
- EThe magnetic flux linkage through the ring is constant as it falls
22.Which of the following changes will increase the maximum e.m.f. induced in a coil rotating in a uniform magnetic field? (select all that apply)
Medium
- AIncreasing the number of turns on the coil
- BIncreasing the angular speed of rotation
- CIncreasing the magnetic flux density
- DDecreasing the cross-sectional area of the coil
- EOrienting the coil so its plane is parallel to the field at all times
23.Match each quantity with its correct SI unit.
Medium
- Magnetic flux
- Magnetic flux linkage
- Magnetic flux density
- Induced e.m.f.
- Weber (Wb)
- Weber turns (Wb turns)
- Tesla (T)
- Volt (V)
24.Place the following steps in the correct order to describe how an e.m.f. is induced when a bar magnet is pushed into a coil connected to a voltmeter.
Medium
- The magnet is moved towards the coil
- The magnetic field lines cut through the coil
- The magnetic flux linkage through the coil changes
- An e.m.f. is induced in the coil
- The voltmeter shows a reading
25.Which of the following is the correct definition of mutual induction?
Easy
- AThe effect in which a change in current in one circuit produces an induced e.m.f. in a neighbouring circuit
- BThe effect in which a change in current in a circuit produces an induced e.m.f. that opposes the change in the same circuit
- CThe process by which a magnetic field is produced by a current-carrying conductor
- DThe process by which a changing magnetic field induces an e.m.f. in a conductor moving through it
26.A step-down transformer is used to change a 240 V alternating input to a 12 V output. Which statement about the transformer is correct?
Easy
- AThe primary coil has more turns than the secondary coil
- BThe secondary coil has more turns than the primary coil
- CThe primary and secondary coils have the same number of turns
- DThe output current is smaller than the input current
27.An e.m.f. is induced in a coil only when the magnetic flux linkage through the coil changes.
Easy
True or false?
28.In a transformer, the output alternating voltage has a different frequency from the input alternating voltage.
Easy
True or false?
29.A copper rod of length 0.8 m moves at a constant speed of 5.7 m s⁻¹ perpendicular to a uniform magnetic field. The induced e.m.f. is 9 mV. What is the magnitude of the magnetic field strength?
Hard
- A2.0 × 10⁻³ T
- B2.0 T
- C5.1 × 10⁻² T
- D4.1 × 10⁻² T
30.A coil of wire moves normally through a uniform magnetic field. The graph of magnetic flux linkage NΦ against time t shows a straight line with positive gradient, then a horizontal line at a non-zero value, then a straight line with negative gradient. What is the induced e.m.f. in the coil during the horizontal section?
Medium
- AZero
- BConstant and positive
- CConstant and negative
- DIncreasing linearly
31.A coil of 5000 turns and area 0.15 m² is placed in a uniform magnetic field of 2.5 T with the field perpendicular to the coil face. What is the magnetic flux linkage through the coil?
Hard
- A1.9 × 10³ Wb turns
- B3.8 × 10⁻⁴ Wb turns
- C1.9 × 10⁻³ Wb turns
- D7.5 × 10² Wb turns
32.A rectangular coil with a magnetic flux of 0.15 mWb spins in a uniform magnetic field of flux density 0.50 mT. What is the cross-sectional area of the coil?
Medium
- A0.30 m²
- B3.3 × 10⁻⁶ m²
- C3.0 × 10⁻⁴ m²
- D0.30 cm²
33.A bar magnet oscillates vertically on a spring above a fixed coil. The graph of induced e.m.f. against time shows two peaks of different magnitudes. Why do the peaks have different magnitudes?
Hard
- AThe magnet's speed is different at the two positions, so the rate of change of flux linkage differs.
- BThe coil's resistance changes with time.
- CThe magnetic field strength of the magnet changes as it moves.
- DThe number of turns in the coil changes as the magnet moves.
34.A vertical copper rod oscillates horizontally with simple harmonic motion in a uniform magnetic field. The rod has length 25 cm and magnetic field strength 68 μT. At the equilibrium position, the rod moves with speed 5.1 m s⁻¹. What is the maximum e.m.f. induced between the ends of the rod?
Hard
- A8.7 × 10⁻⁵ V
- B8.7 × 10⁻² V
- C1.7 × 10⁻³ V
- D1.7 × 10⁻⁶ V
35.A conducting ring is dropped so that it falls towards the north pole of a fixed bar magnet. Which of the following statements are correct? (select all that apply)
Medium
- AAn e.m.f. is induced in the ring.
- BA current is induced in the ring.
- CThe ring experiences a repulsive force from the magnet.
- DThe induced current in the ring creates a south pole facing the magnet.
- EThe ring falls with acceleration greater than g.
36.Which of the following changes will increase the maximum induced e.m.f. in a coil rotating in a uniform magnetic field? (select all that apply)
Hard
- AIncreasing the number of turns in the coil.
- BIncreasing the magnetic flux density.
- CIncreasing the frequency of rotation.
- DIncreasing the cross-sectional area of the coil.
- EDecreasing the frequency of rotation.
37.The induced e.m.f. in a straight conductor moving through a magnetic field is directly proportional to the speed of the conductor.
Easy
True or false?
38.When a magnet is held stationary inside a coil, an e.m.f. is induced in the coil.
Medium
True or false?
39.A student investigates electromagnetic induction by moving a bar magnet quickly into a coil connected to a sensitive galvanometer. The student then removes the magnet more quickly than it entered. Which statement correctly describes the expected galvanometer observations?
Medium
- AThe needle deflects in the opposite direction with a larger magnitude
- BThe needle deflects in the same direction with a larger magnitude
- CThe needle deflects in the opposite direction with a smaller magnitude
- DThe needle remains at zero throughout
40.A coil is connected to a galvanometer centred at zero. A magnet is moved vertically into the coil so that the galvanometer deflects to the right. The magnet is then held at rest inside the coil. What is the expected reading on the galvanometer?
Medium
- AZero
- BA steady non-zero reading to the right
- CA steady non-zero reading to the left
- DA reading that oscillates between left and right
41.Complete the sentence about magnetic flux linkage.
Easy
Magnetic flux linkage is the product of the magnetic flux and the ____ of the coil, and it is measured in ____.
42.A coil of 5000 turns has an area of 0.15 m². It is placed in a uniform magnetic field of flux density 2.5 T, with the field perpendicular to the coil face. Calculate the magnitude of the magnetic flux linkage through the coil, in Wb turns.
Medium
43.A straight conductor of length 0.8 m moves at a speed of 5.7 m s⁻¹ perpendicular to a uniform magnetic field. The induced e.m.f. is 9 mV. Determine the magnitude of the magnetic field strength, in T.
Hard
44.Complete the sentence about the induced e.m.f. in a moving conductor.
Medium
The induced e.m.f. in a straight conductor moving through a magnetic field is given by ε = ____, where B is the magnetic flux density, L is the ____ of the conductor in the field, and v is the ____ of the conductor.
45.State the name of the law that predicts the direction of an induced e.m.f.
Easy
46.A coil of 500 turns has a cross-sectional area of 0.020 m². It is placed in a uniform magnetic field of flux density 0.50 T with the field perpendicular to the coil face. Calculate the magnetic flux linkage through the coil.
Medium
47.Complete the sentence about Lenz's law.
Medium
Lenz's law states that the induced e.m.f. is such that it will ____ the change causing it.
48.What is the unit of magnetic flux linkage?
Medium
49.A coil of 500 turns has an area of 0.020 m² and is in a uniform magnetic field of 0.50 T perpendicular to the coil. Calculate the magnetic flux linkage in Wb turns.
Medium
50.A straight conductor of length 0.50 m moves at 4.0 m s⁻¹ perpendicular to a magnetic field of flux density 0.30 T. Calculate the induced e.m.f. in volts.
Hard
51.Complete the sentence about the area under a graph of induced e.m.f. against time.
Medium
The area under a graph of induced e.m.f. against time represents the change in ____.
52.Calculate the change in magnetic flux linkage through the coil during the rotation.
Hard
53.State Faraday's law of electromagnetic induction.
Medium
54.State Lenz's law and explain why it is a consequence of the principle of conservation of energy.
Medium
55.Outline the operation of a simple alternating current (AC) generator.
Medium
56.Explain, by reference to at least one law of induction, why the induced e.m.f. graph becomes negative when a magnet oscillating on a spring passes its lowest point and moves back upwards.
Hard
57.Explain how Lenz's law relates to a copper rod moving on conducting rails through a uniform magnetic field.
Hard
58.A coil of 5000 turns has an area of 0.15 m². It is placed in a uniform magnetic field of flux density 2.5 T, with the field perpendicular to the coil face. Calculate the magnitude of the magnetic flux linkage through the coil, in Wb turns.
Medium
- A1875 Wb turns
- B2063 Wb turns
- C2251 Wb turns
- D1687 Wb turns
59.A straight conductor of length 0.8 m moves at a speed of 5.7 m s⁻¹ perpendicular to a uniform magnetic field. The induced e.m.f. is 9 mV. Determine the magnitude of the magnetic field strength, in T.
Hard
- A0.00197 T
- B-0.998 T
- C2.002 T
- D1.002 T
60.A coil of 500 turns has a cross-sectional area of 0.020 m². It is placed in a uniform magnetic field of flux density 0.50 T with the field perpendicular to the coil face. Calculate the magnetic flux linkage through the coil.
Medium
- A4 Wb turns
- B7 Wb turns
- C6 Wb turns
- D5 Wb turns
61.A coil of 500 turns has an area of 0.020 m² and is in a uniform magnetic field of 0.50 T perpendicular to the coil. Calculate the magnetic flux linkage in Wb turns.
Medium
- A4 Wb turns
- B5 Wb turns
- C6 Wb turns
- D7 Wb turns
62.A straight conductor of length 0.50 m moves at 4.0 m s⁻¹ perpendicular to a magnetic field of flux density 0.30 T. Calculate the induced e.m.f. in volts.
Hard
- A0.6 V
- B2.6 V
- C-0.4 V
- D1.6 V
63.Calculate the change in magnetic flux linkage through the coil during the rotation.
Hard
- A0.2 Wb turns
- B2.2 Wb turns
- C1.2 Wb turns
- D3.2 Wb turns

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