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Year 12 Physics motors and generators

3.2.1 magnetic flux and induction

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motors and generators • Year 12 Physics

Prime Education

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Prime Education

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syllabus Students learn to:

Students:

2. The relative motion

between a conductor

and magnetic field is

used to generate an

electrical voltage

outline Michael Faraday’s

discovery of the generation of

an electric current by a moving

magnet

perform an investigation to model

the generation of an electric

current by moving a magnet in a

coil or a coil near a magnet

define magnetic field strength B

as magnetic flux density

describe the concept of

magnetic flux in terms of

magnetic flux density and

surface area

plan, choose equipment or

resources for, and perform a first-

hand investigation to predict and

verify the effect on a generated

electric current when:

- the distance between the coil

and magnet is varied

- the strength of the magnet is

varied

- the relative motion between

the coil and the magnet is

varied

describe generated potential

difference as the rate of change

of magnetic flux through a

circuit

account for Lenz’s Law in

terms of conservation of energy

and relate it to the production of

back emf in motors

gather, analyse and present

information to explain how

induction is used in cooktops in

electric ranges

explain that, in electric motors,

back emf opposes the supply

emf gather secondary information

to identify how eddy currents

have been utilised in

electromagnetic braking explain the production of

eddy currents in terms of

Lenz’s Law



Prime Education

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3.2.1.1 Faraday and Induction

Faraday’s experiments :

On 4th September 1821, Michael Faraday discovered that a vertically mounted wire carrying an

electric current would rotate continuously round a magnet sticking out of a bowl of mercury. He

named this phenomenon electro-magnetic rotations. He just discovered the motor effect. He would

use this to detect electric current (galvanometer) in his further investigations.

In 1831 Michael Faraday did a series of experiments and discovered electromagnetic induction.

This is the generation of an emf (electromagnetic force as well known as voltage) and/or an electric

current through the use of a variable magnetic field. Faraday had discovered the principle of the

electric generator — a discovery that has had far reaching effects on society.

In his first experiment he used two coils of wire wrapped around opposite sides of a soft iron ring.

He noticed that when he switched on the current in the first loop nothing happened, but when he

switched the current on and off continuously, a current was induced in the second circuit. He

concluded that it was the changing current in the first coil that caused the induced current in the

second coil (Figure 3.2.1 (1)).

Figure 3.2.1 (1) Faraday’s apparatus for electromagnetic induction

He reasoned that the induced current was due to the second coil responding to a change in the

magnetic field caused by switching the first coil on or off. To test his hypothesis he moved a

permanent magnet near a coil of wire and showed a current was induced in the coil. Increasing or

decreasing the magnetic field in the coil induced a current in the coil. He could move the magnet or

the coil, the effect was the same. See Figure 3.2.1 (2).

Figure 3.2.1 (2) Faraday’s simple experiment with coils and magnets



Prime Education

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Faraday’s theory

Faraday explained electromagnetic induction as follows:

When there is relative movement between a conductor and a magnetic field (either physical

movement or change in magnitude of the magnetic field) a potential difference is generated. If the

conductor is part of an electric circuit, a current is induced in the circuit. The magnitude of the

induced potential difference is directly proportional to the rate at which the conductor ‘cuts through’

the magnetic field.

Figure 3.2.1 (3) Magnet being moved towards a conducting coil

Faraday’s Conclusions

Faraday realised that a changing magnetic field induces a voltage in nearby conductors.

This voltage can cause current to flow.

The strength of the voltage depends on the magnetic field’s rate of change.

Question 1

Which of the following methods will produce a constant alternating current?

(A) Moving a wire that is part of a closed circuit through a magnetic field at different speeds.

(B) Moving a solenoid that is connected to a circuit up and down.

(C) Moving a solenoid in an open circuit in and out of a larger solenoid.

(D) Moving a magnet in an out of a solenoid which is part of a closed circuit.

Question 2

What job was performed by the metal ring in Faraday’s experiment?

(A) It allowed Faraday to coil the wires into solenoids.

(B) It contained the magnetic field created by one of the solenoids.

(C) It conducted electrical current from one solenoid to the other.

(D) It prevented the source of current from interfering with the galvanometer.



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Question 3

Recall the two statements with which Faraday summarised his observations on electromagnetic

induction.

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Question 4

When there is relative movement between a magnetic field and a wire, a current is induced in a wire.

Explain the idea of relative movement.

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Question 5

When Faraday tested the effect of moving magnets towards solenoids, he used permanent magnets.

What would be the effect of replacing the permanent magnets with electromagnets?

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Prime Education

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3.2.1.2 Magnetic flux and flux density

Magnetic Flux

Magnetic flux ϕ (measured in Weber (Wb)) is the amount of magnetic field passing through or

cutting a given area A, measured in meter squared (m2).

If the area A is plane perpendicular to a uniform magnetic field of strength B, measured in Tesla (T)

B A

If the angle between the area A and the magnetic field lines is θ

sinB A

Magnetic Flux Density

This is the magnetic flux per unit area and, as we can see from the equation above, is a measure of

the magnetic field intensity through a surface perpendicular to the magnetic field lines.

BA

Generating a potential difference by changing magnetic flux through a coil.

When we generated an emf in a coil by pushing a bar magnet into the coil, we changed the magnetic

field strength in the coil. The magnetic flux through the coil also changed. Faraday noted that in all

situations where there was a change in flux through a coil, there was also an induced emf

(electromotive force or voltage or potential difference) ε between the two end of the wire. When the

magnetic flux ceased changing and remained constant, the emf ε disappeared.

There are several ways of changing the flux through a circuit:

1. Change the magnetic field strength.

2. Change the area of the coil (e.g. by stretching the coil).

3. Change the orientation of the coil and magnetic field (e.g. by rotating the coil in the field).

So the emf ε generated depends on the rate of change of magnetic flux through the coil.

t

The negative sign indicate the direction of the induced emf.



Prime Education

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Example 1

A coil of wire with area 0.4 m2 is placed in a magnetic field of strength 0.2 T as shown in the figure

below.

(a) Find the magnetic flux through the coil in the three positions shown.

Data: 0.4A m2 and 0.2B T

In position A, the plane of the coil is parallel to the magnetic field and hence the flux is zero.

In position B, the area of the coil perpendicular to the magnetic field is o0.4sin 45 and hence the

flux is osin 2 0.4cos45 0.56BA webers.

In position C, the coil is perpendicular to the magnetic field and the magnetic flux linking the coil is

given by 2 0.4 0.8BA webers.

(b) Will a current be induced in this coil as it is turned from position A to position C?

Yes, because the magnetic flux is changing a current will be induced in the coil.

Question 6

What is the correct unit to measure rate of change of flux?

(A) Webers

(B) Weber seconds

(C) Volts

(D) Tesla

Question 7

What is the correct unit to measure flux per square metre?

(A) Webers

(B) Weber metres squared

(C) Volts

(D) Tesla



Prime Education

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Question 8

Define magnetic field strength in terms of magnetic flux.

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Question 9

Both of these regions contain a magnetic field. Compare the regions in terms of magnetic flux and

magnetic field strength.

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Prime Education

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Question 10

Determine the magnetic flux passing through an area of 21 cm at right angles to a 84.0 10 T

magnetic field.

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Question 11

A 2 cm 1 cm rectangular loop of wire, perpendicular to a 0.002 T magnetic field, takes 0.1 s to

rotate so that it is parallel to the field. What emf is induced in the wire?

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Prime Education

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3.2.1.3 Generating a potential difference by cutting magnetic field lines with a wire.

If a straight wire is moving across a uniform magnetic field an emf ε is induced between the two

ends of the wire and

t

With the flux through the surface A cut by the wire while it is moving in the magnetic field

during t .

If the wire is connected to a circuit an induced current I would flow. The direction of the induced

current is found by using the right hand generator rule.

The thumb shows the direction of the velocity of the wire. The fingers show the direction of the

magnetic field and the palm show the direction of the current.

Example 2

A disc of metal, called a Faraday disc, rotates at a constant rate, in a uniform magnetic field, B,

parallel to the axis of rotation of the disc. The plane of the disc is perpendicular to the axis of

rotation, as shown in the figure below. Assume that the radius of the axle can be disregarded. The

machine in the figure below is known as Faraday's homopolar generator. G is a sensitive current-

measuring device called a galvanometer.



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Example 2 (continued)

(a) Describe and explain how Faraday’s homopolar generator works.

From Faraday’s law:

Consider the disc to be composed of a rotating spoke of wire. Each spoke of wire is cutting flux

over the area A of the disc in the time t taken for the disc to rotate once.

The induced emf in the rotating spoke of wire is, from Faraday's law, directly proportional to the

rate at which a conductor cuts magnetic field lines. Therefore a voltage is induced across the spoke

of the disc as it spins at right angles to the magnetic field.

(b) What factors determine the size of the emf produced by this generator?

The magnetic field strength B, the area of the disc, the rate of spin of the disc.

(c) Which way does the induced current flow between X and Y?

From X to Y in the galvanometer (Right Hand Generator Rule).

(d) If the disc spins in the opposite direction, what effect does this have on the induced current?

From Y to X.

First-hand investigation: Electromagnetic induction

Demonstrate electromagnetic induction by either:

(a) moving a bar magnet in a coil; or

(b) moving a coil over a stationary bar magnet.

Figure 3.2.1 (4)



Prime Education

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Procedure

Set up apparatus as shown in Figure 3.2.1 (4).

1. Move magnet into coil at constant speed to change the strength of magnetic field cutting the

coil.

2. Move coil onto magnet at constant speed to change the strength of magnetic field being cut

by the coil.

3. Place the magnet in the coil and move it along the axis of the coil at different speeds to

change the relative speed and rate of cutting of lines of force.

4. Use two magnets held with like poles together to increase the strength, B, of the magnetic

field and repeat 1 and 2.

5. Use a coil with more turns to increase the number, n, of lines of force being cut, and repeat 1

and 2.

Note that the induced emf:

exists only when there is relative motion between magnet and coil

changes direction when the direction of motion of the magnet or the coil is reversed

increases with the speed of relative motion between magnet and coil

increases with the number of turns on the coil; that is, with the area of flux cut

increases with the strength of the magnets

decreases as the distance from the magnet to the conductor is increased.

In these demonstrations mechanical energy is converted to electrical energy by electromagnetic

induction.

Question 12

An aeroplane flies towards the Earth’s North Pole, where there is a considerable vertical magnetic

field pointing towards the ground.

Which statement about the aeroplane is correct?

(A) There will be a build-up of electrons on the left wing.

(B) There will be a build-up of electrons on the right wing.

(C) There will be a build-up of electrons on the nose.

(D) There will be a build-up of electrons on the tail.



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Question 13

A metal ring sits perpendicular to a magnetic field pointing away from you. You pull the ring to the

right, and out of the field. What current (if any) flows in the ring? Why?

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Question 14

A conductor is pulled across a 10 cm × 10 cm loop of wire at a speed of 0.2 m s–1

as shown. If the

field strength is 0.003 T, calculate the emf induced and the direction of current.

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Question 15

This device is Faraday’s homopolar generator. The disc in the middle is made of a conductive metal.

Describe what happens when the disc spins as shown.

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Question 16

A loop of wire with area A and n turns is placed in a magnetic field of strength B. The loop spins so

that it makes f full turns per second. Find the maximum emf through the loop.

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