1: Michael Faraday discovers electromagnetic induction

motors and

generators

He noticed that this current was only induced while the magnet was moving.

He moved the magnet out of the coil, and this time he measured a current in

Following many

the opposite direction within the coil (Figure 5.1.1b).

other experiments, he put forward his general principle of electromagnetic

induction that a changing magnetic field can cause a current to be generated in

a wire. This change can be caused by either the relative motion of the field and

the coil or by a change in the strength of the magnetic field.

In light of Faraday’s conclusion, let’s offer a simple way to understand his

observations. In Figure 5.1.1 we can consider the change in the magnetic field

through the coil to be represented by the number of magnetic field lines passing

within the coil. In Figure 5.1.1a, notice that the magnetic field around the bar

magnet is not uniform. You see that as you get closer to the poles of the magnet

the magnetic field lines get closer together, indicating that the field is stronger.

Therefore, as the magnet gets closer to the coil more field lines pass within the

coil, indicating that the magnetic field within the coil gets stronger. So, as the

magnet gets closer to the coil the strength of the field within the coil is changing

and this induces the current. This gives us a general explanation for

electromagnetic induction. Now let’s take things a bit further.



Faraday’s law: explaining electromagnetic induction

Electromagnetic induction can be summarised by Faraday’s law.

The induced emf in a coil is proportional to the product of the number

of turns and the rate at which the magnetic field changes within the turns.

Faraday’s law is quantified by an equation, and it is very useful to analyse the

equation to understand the relationships involved. This equation is:

ε = n(∆ΦB/∆t)

Let us spend a little time now looking at what each of the variables in this

equation means and then we can understand the relationships.



Magnetic flux ΦB

Magnetic flux is a measure of the ‘amount’ of magnetic field passing

through a given area. There are two variables that determine the value of

magnetic flux: the strength of the magnetic field B and the area the field is

passing through A. Magnetic flux ΦB is measured in weber (Wb) and can be

expressed by the equation:

ΦB = BA⊥

Magnetic field strength B, a quantity we are already familiar with,

is also called magnetic flux density. This quantity is measured in tesla (T), or

equivalently in webers per square metre (Wb m–2). This is a measure of the field

strength per square metre.

A ⊥ is an area that is perpendicular to the magnetic field lines. If a magnetic

field passes through a circular wire loop of area A (Figure 5.1.2a) and the loop is

at an angle to the field (see Figure 5.1.2b), then the field passes through an

‘effective’ area A⊥ that is perpendicular to the field and is smaller than area A (see

Figure 5.1.2c). Note that flux could also be calculated using the perpendicular

component of the magnetic field strength, B⊥, and the total area A.



a

N



A

b

N



A



Figure 5.1.1 The changing magnetic field of

a moving magnet can induce a

current in a coil of wire.



Our sun’s

magnetic

influence



L



arge outbursts from the Sun cause

changes in the strength of the

magnetic field at the Earth’s surface.

This changing magnetic field induces

currents in long metal pipelines and the

wires of power grids, especially at high

latitudes. Currents of 1000 amps have

been measured in pipelines in Alaska,

causing accelerated corrosion. Large

currents in power grids have overloaded

circuits and left millions of people in

the dark for hours.



PRACTICAL

EXPERIENCES

Activity 5.1



Activity Manual, Page

33



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.



101



5



Induction:

the influence of

changing magnetism

This line is the perpendicular

height of area A.

B

A



a



A⊥



P



b



c



Figure 5.1.2 (a) A circular coil of area A. (b) A side view of the coil at an angle to the magnetic

field. (c) The ‘effective’ area of the coil perpendicular to the magnetic field viewed

from point P (b)



The product of the magnetic flux density B and the area A ⊥ gives a

measure of the total ‘amount’ of magnetic field passing through that area. This

is the magnetic flux ΦB.

The delta (∆) symbols in Faraday’s law mean a change in some quantity. So

the two terms with delta symbols attached are differences between an initial

value and a final value. The term ∆ΦB stands for the change in the magnetic

flux and is given by:

∆ΦB = ∆ΦB final – ∆ΦB initial

The ∆t term represents a period of time. This is the period of time over

which the change in flux ∆ΦB is measured.

We can see that the ∆ΦB/∆t term in Faraday’s law is actually the rate

of change of magnetic flux, just as acceleration is the rate of change of velocity

(aav = ∆v/∆t). The term ∆ΦB/∆t tells us how fast the flux is changing.



emf ε

The symbol ε stands for emf, measured in volts. It is the difference in electrical

potential between the two ends of a coil (X and Y in Figure 5.1.3).

This emf creates an electric field within the wire of the coil and a current is

established, provided the circuit is complete (X and Y are not connected in

Figure 5.1.3). A current will flow as long as there is a change in the magnetic

field within the coil.

Qualitative analysis of Faraday’s law

Let’s now look at the relationship between emf and the other terms in the

equation. Recall that the equation for Faraday’s law is:

ε = n(∆ΦB/∆t)



B

N



S



X Y



Figure 5.1.3 A moveable magnet passes

through a stationary coil with

terminals X and Y.

102



The emf is proportional to the rate of change of the magnetic flux (∆ΦB/∆t).

If there is a large change in flux in a small amount of time, then ∆ΦB/∆t is

large; therefore, the emf produced will be large. This emf is responsible for the

induced current in a closed loop of wire. If the emf is large, then so is the

induced current. Another way of saying this is that if we wanted to induce a

large current, we would change the magnetic field within the coil as much as

possible in the shortest time possible. To do this in the example we have seen,

we could move the magnet more quickly, use a stronger magnet or make the

perpendicular area as large as possible for the coil.

The emf is also proportional to n, the number of turns in the coil. Again, if

we wanted to create a large current we would want to have as many turns in the

coil as possible.



motors and

generators

By inspecting all the variables in Faraday’s law we can conclude that

an induced potential difference, and therefore an induced current in a coil,

is proportional to the rate of change of magnetic flux (∆ΦB/∆t) and the

number of turns (n) within the coil. Further, we can conclude that induced

currents are produced by changing the magnetic field strength B, the relative

motion between B and the area A, or changing the perpendicular area A ⊥ of

the coil.

Our next challenge is to find the direction of an induced current, and for

that we need Lenz’s law. We will cover this in section 5.2.



Try this!

skipping currents



T



ake a length of wire about

30–40 metres long and

connect the ends to a sensitive

ammeter. Lay the wire out in

a large open space and swing it

like a skipping rope. Can you

induce a current by changing the

size of the loop and using the

Earth’s magnetic field? Can you

explain why this should work?



Induction without relative motion

Now that we have a basic understanding of electromagnetic induction, we will

look at another example.

In one of his early experiments Faraday wound two coils of wire around an

iron ring (Figure 5.1.4). He noticed that a current was induced in coil B for a

short time after the current in coil A was switched on or off. To explain this

induced current, recall that a current travelling through a wire produces a

magnetic field around the wire. We can then follow similar reasoning to that

in the different situation described earlier. The list of events below explains

why Faraday observed induced currents for a short time after he connected or

disconnected coil A. The steps below are indicated in Figure 5.1.5, which

shows the currents in both coils and the magnetic field produced in coil A.

1 Coil A is connected by closing the switch and a current begins to flow.

2 The current in coil A produces a magnetic field around the iron ring

(see Figure 4.1.9). This field gets stronger as the current increases to

its maximum value. The changing magnetic flux from coil A causes

a changing magnetic flux in coil B, which induces an emf and

therefore a current in coil B. The rate of change of magnetic flux

power

in coil B is positive, rapid at first but then slows down (Figure

supply

5.1.5), so the induced current is positive, high at first but

decreases rapidly.

3 The current and magnetic field in coil A both reach their

maximum value. The rate of change of magnetic flux in coil B is

now zero, so the induced emf and current are also zero.

4 Coil A is disconnected by opening the switch. The current in coil A

decreases rapidly, but does not stop immediately because there is

normally a brief spark in the switch that allows current to continue

flowing briefly.

5 The current in coil A, and therefore the magnetic field it produces,

rapidly decreases. The changing magnetic flux from coil A causes a

changing magnetic flux in coil B that, in turn, induces an emf and

therefore a current. The rate of change of magnetic flux in coil B is

negative, initially high but rapidly decreases. Therefore, the induced

current is negative, high at first but decreases rapidly to zero.

The example above illustrates our previous conclusions that it is the

change in the magnetic field (more precisely, the changing magnetic flux)

passing through a wire coil that induces a current, and the induced current is

proportional to the rate of change of magnetic flux. Now we can see that the

direction of the induced current is determined by whether the magnetic flux

is increasing or decreasing.



Describe generated potential

difference as the rate of

change of magnetic flux

through a circuit.

layers of copper coil

interwound with

cotton and calico



soft

iron

ring



switch



+



G



–



coil B

coil A



Figure 5.1.4 Basic set-up of Faraday’s experiment



IA



BA



IB

2

1



3



5

4



Figure 5.1.5 The behaviour of currents and

magnetic fields in Faraday’s

iron ring experiment

103



5



Induction:

the influence of

changing magnetism



Checkpoint 5.1

1 Outline Faraday’s discovery of induction by a moving magnet and summarise his conclusion.

2 Define magnetic flux in terms of magnetic flux density.

3 Using the term magnetic flux, explain why removing a magnet quickly from a coil induces a relatively large current.



5.2 Lenz’s law

Heinrich Lenz (1804–1865) independently made many of the same discoveries

as Faraday. He also devised a way to predict the direction of an induced current

This method

in a closed conducting loop due to a changing magnetic field.

is called Lenz’s law and it states that an induced current in a closed conducting

loop will appear in such a direction that it opposes the change that produced it.

This means that the induced magnetic field from a wire loop will oppose the

change in magnetic flux that causes the induced current. Let us look at the

example shown in Figure 5.2.1 to understand this better.

a



direction of

movement



b



S



direction of

movement



N



S

N

N



B



I



Figure 5.2.1 (a) Bar magnet moves towards a wire loop.

(b) The magnetic field due to the induced current



S



As the north pole of the magnet gets closer to the wire loop in Figure 5.2.1a,

the magnetic flux passing through the coil increases. This change in flux induces

a current in the wire loop. Now let’s find the direction of the current to agree

with Lenz’s law.

The north pole of the magnet is coming towards the coil, so the magnetic

flux pointing downwards through the coil is increasing. Lenz’s law says that the

magnetic field produced by the induced current should oppose this change in

flux, so the induced flux should point upwards through the coil. Using the

right-hand grip rule for a wire coil or solenoid, we see that the current would

need to flow in the direction shown in Figure 5.2.1b, to produce an upwardspointing magnetic field within the loop. This field is pointing in the opposite

direction to the changing magnetic flux, so it reduces the changing magnetic flux

from the approaching magnet. Simply, you can think of the interaction of these

two magnetic fields as if the north poles of two bar magnets are facing each

other. The two north poles repel each other, and in this way the induced field

acts to minimise the increasing magnetic flux within the coil.

104



motors and

generators

Now, let’s look at what would happen when you move a magnet away from

the loop with its north pole facing the loop (Figure 5.2.2).

In this case the magnetic flux in the coil is decreasing and pointing

downwards. The induced magnetic field should therefore be also pointing

downwards to add to the reducing field and try to minimise the change. Using

the right-hand grip rule, we see that we need a current as shown to produce a

downwards-pointing induced magnetic field. Again, you can think of the

interaction of these two magnetic fields as the interaction of two magnets in

which a north pole is facing a south pole. The two ends of the magnets are

attracted to one another and in this way the induced field acts to add to the

decreasing flux within the coil. These examples leave us with Lenz’s law as

a tool to determine the direction of an induced current in a wire coil due to

a changing magnetic flux.



The law behind Lenz’s law: the law of conservation

of energy

While we were learning about Lenz’s law you may have wondered why the

current needs to produce a magnetic field to oppose the change in flux? Well the

This law states that

answer lies in the law of conservation of energy.

energy cannot be created or destroyed, only converted from one form to another.

In the case of Lenz’s law, it is the fact that energy cannot be created that is

important.

If the induced current in Figure 5.2.1 was in a direction that added to the

changing flux through the coil there would be an attractive force on the magnet.

This would mean that the magnet’s motion would cause it to be pulled through

the coil. The amount of energy you could get from the induced current (heat

from electrical resistance) and the induced magnetic field would be much more

than that put in initially to move the magnet and change the flux through the

coil. This would mean you would be getting something (energy) for free

(without doing any work), which is not possible.

Energy must be ultimately converted from the work done to move the

magnet into heat energy from the electrical resistance within the wire coil.

There must be a balance between the energy that goes into a system and

the energy that comes out. So, whether you push the magnet towards the loop

or pull it away from the loop, you will always experience a force that resists the

motion. This force is an attraction or a repulsion between the magnetic fields

of the magnet and the wire loop.

So far in this chapter we have explained the cause of magnetic induction

using Faraday’s law, used Lenz’s law to find the direction of an induced current,

and the right-hand grip rule to find the direction of this current’s magnetic field.

Keep these ideas in mind, as we will apply them in the next two chapters.



direction of

movement



S

N



Figure 5.2.2 Induced current due to a

decreasing magnetic field in

accordance with Lenz’s law



Account for Lenz’s law in terms

of conservation of energy and

relate it to the production of

back emf in motors.



Checkpoint 5.2

1

2

3



Define Lenz’s law.

Describe the induced current and magnetic field in Figure 5.2.2 if the south pole of the permanent magnet is

pointing towards the wire coil.

Justify the current and magnetic field shown in Figure 5.2.1b in terms of the law of conservation of energy.



105



5



Induction:

the influence of

changing magnetism



5.3 Eddy currents

Explain the production of eddy

currents in terms of Lenz’s Law.



We have seen that charges moving in a magnetic field experience a force in

accordance with the right-hand palm rule (sections 4.2 and 4.3). This effect

occurs for free charges and charges within conductors. When a current-carrying

wire experiences a force within an external magnetic field, we call this the motor

effect. When charges within a wire experience a force within a changing

magnetic field, inducing a current, we call this electromagnetic induction.

Many conductors that experience a changing magnetic field and produce an

induced current are much larger than a wire. We call these induced currents

eddy currents.

Eddy currents can be produced by the relative motion of a conductor

and a magnetic field. These eddy currents are small loops of current within the

conductor. They are the same as induced currents in wires subjected to changing

magnetic flux, except that the currents are not confined to a loop of wire. These

currents are set up in accordance with Lenz’s law and produce magnetic fields

that act to minimise the change in magnetic flux within the path of the current.

Figure 5.3.1 shows a square piece of copper sheet swinging like a pendulum

through a magnetic field. When this piece of metal moves through the magnetic

field, we notice that there is a braking effect, slowing its swing. After a few

swings it comes to rest. It stops much more quickly than it does when we remove

the magnetic field. To explain this situation we can use the right-hand rules or

approach the problem in terms of Lenz’s law. When we use Lenz’s law, we use the

right-hand grip rule for solenoids or coils to predict the direction of magnetic

fields and eddy currents.

As the copper square swings into the magnetic field on the left of Figure

5.3.1 let’s consider what happens to a positive charge (as shown) on the leading

edge of the square. If this positive charge was within a piece of wire it would

experience a force F1 upwards as shown. If this was a square loop of wire, this

force would generate a conventional current moving anticlockwise around the

loop. As this charge is not confined to a wire, the charge moves upwards initially

and then loops around to form a complete circuit (an eddy current). Using the

right-hand grip rule, we can see that the eddy current (I1) shown would produce



direction of swing



I1



F2 causing

braking effect



F1



N



+



F3



S



I2



+

F4 causing

braking effect



Figure 5.3.1 A square metal sheet is swung through a uniform magnetic field between two bar

magnets. A braking effect is observed due to induced currents and their magnetic

fields, in accordance with Lenz’s law.



106



motors and

generators

a magnetic field out of the page (indicated by the N for the north pole of the

current’s magnetic field). The flow of positive charges in the direction of F1 is a

current. This current experiences a force due to the uniform magnetic field. This

force F2 opposes the motion of the copper, acting as a braking effect.

As the copper square leaves the magnetic field (on the right in Figure 5.3.1)

Lenz’s law tells us that the eddy current should produce a force to slow the square’s

departure from the field. The positive charge shown experiences a force F3

upwards, as shown. This causes a flow of positive charges in the direction of F3.

This current experiences a force due to the uniform magnetic field. This force F4

opposes the motion of the metal sheet, again acting as a braking effect.

If you have access to the equipment that demonstrates the situation in Figure

5.3.1, then try observing it for yourself. You may also be able to observe the

effect of cutting slots through the piece of metal swinging in the field. The slots

limit the size of the eddy currents that can be produced and therefore the size of

the induced magnetic fields, and the braking effect is considerably less. We will

meet this idea of reducing the size of eddy currents again in chapters 6 and 7.



Try this!

Racing magnets

Find two identical magnets. Get a piece of copper or aluminium sheet

and a sheet of a non-metal, such as glass, with a surface similar in

smoothness to the surface of the metal. Place the two sheets at the

same angle (say 60º) to the table surface and place the magnets at the

same height on each sheet (see Figure 5.3.2). Now predict which

magnet is going to win the race and why. Now race! Did everyone agree?

Explain your observations to a friend.

aluminium or

copper



glass



60°



Figure 5.3.2 Which magnet will win?



107



5



Induction:

the influence of

changing magnetism



PHYSICS FEATURE





PRACTICAL

EXPERIENCES

Activity 5.2



Gather, analyse and present information to explain

how induction is used in cooktops in electric ranges.



Activity Manual, Page

39



Induction cooking



I



nduction cooktops are a great example of a growing

application of eddy currents. The main appeal of

induction cooking is its efficiency and fast heating.

Heat is not transferred to the pan from a hot plate or

flame in induction cooking. The heat is generated

within the pan itself and then flows into the food

being cooked. This means that minimal heat is lost to

the air before reaching the food, making this much

more efficient than other cooking methods.

The operation of an induction cooktop is illustrated

in Figure 5.3.3. A rapidly changing strong magnetic

field is generated in a large wire coil, using an

alternating current. Both the intensity and direction of

this field change continuously over very short periods

of time. The resulting rapidly changing magnetic flux

within the base of the frying pan induces strong eddy

currents, causing resistive heating.

Resistive heating by eddy currents occurs when the

charges flowing within the metal collide with the ions

in the metal lattice. Kinetic energy is transferred to

the metal ions as vibrations, and this increases

the temperature of the metal. The amount of heat Q

produced by resistive heating is proportional to the

resistance of the material R   and the square of the

current I  , as shown by Joule’s law:



Q = Pt = I 2Rt

where Q is in joules, power P is in watts or joules

per second (J s–1), I is in amps A, R is in ohms (Ω)

and t is in seconds (s).



eddy currents

produced in

base of frypan

ceramic surface

coil supplied with

high frequency AC



AC



rapidly changing

magnetic field

B



Figure 5.3.3 The frypan on an induction cooktop up heats due

to eddy currents.



From Joule’s law we can see that a large current

and relatively high resistance would result in a large

amount of resistive heating. This explains why

specialised cookware is required to gain maximum

efficiency from induction cooking.

Another method of heat production within

induction cookware is a process called magnetic

hysteresis losses. When a magnetic field is applied to,

and then removed from, a magnetic material such as

iron, a permanent magnetic field remains within the

material. If a magnetic field is then introduced in the

opposite direction to this remnant field, some energy

is expended reducing the remnant field to zero before

the field can build in the other direction. Energy is

dissipated in this process as heat in the material and

therefore also raises the temperature.



Checkpoint 5.3

1

2



108



Explain the formation of eddy currents in a small, flat, square metal sheet that falls between the poles of a magnet.

Describe how Lenz’s law can be used to predict the formation of eddy currents.



PRACTICAL EXPERIENCES



motors and

generators



CHAPTER 5



This is a starting point to get you thinking about the mandatory practical

experiences outlined in the syllabus. For detailed instructions and advice, use

in2 Physics @ HSC Activity Manual.



Activity 5.1: Generating electric current

Using the equipment listed, write up an investigation that will allow you to

generate alternating current. Once you have produced alternating current,

investigate how changing the distance between a coil and a magnet, the strength of

the magnet and the relative motion between the coil and the magnet will affect the

electric current produced.

Equipment: coil of wire (transformer coil), galvanometer, magnet (either

electromagnet or a series of permanent magnets).

Discussion questions

1 Describe the relationship between the distance between the coil and the

magnet and the electric current produced.

2 Determine how the strength of the magnet affects the current produced.

3 What effect does making the magnet move instead of the coil and vice

versa have on the current produced?



Activity 5.2: Making use of Eddy currents

Research induction cooktops and check to see if advertised claims about their

efficiency are true. Look at the use of eddy currents in braking. What forms of

transport use it and where could it be applied?

Discussion questions

1 Explain why AC and not DC must be used for an induction cooktop to

work.

2 Discuss the efficiency claims of induction cooktops in comparison to

traditional cooktops.

3 List the advantages and disadvantages of eddy current braking. (Hint: See

Physics Focus on page 112.)



Perform an investigation to

model the generation of an

electric current by moving a

magnet in a coil or a coil near

a magnet.

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.

Plan, choose equipment or

resources for, and perform a

first-hand investigation to

demonstrate the production

of an alternating current.

Gather, analyse and present

information to explain how

induction is used in cooktops

in electric ranges.

Gather secondary information

to identify how eddy currents

have been utilised in

electromagnetic braking.



109



5

•



•



•



•



Chapter summary



Induction:

the influence of

changing magnetism



Michael Faraday discovered that a current can be

generated by a changing magnetic field when moving

a magnet within a wire coil.

Magnetic field strength B in tesla (T) is equivalent to

magnetic flux density in webers per square metre

(Wb m–2).

Magnetic flux ΦB is a measure of the magnetic field

passing through a certain area. This is equal to the

magnetic flux density B multiplied by the perpendicular

area A⊥ through which the field is passing.

An emf produced in a coil is proportional to the rate

of change of magnetic flux and the number of turns in

the coil.



•



Induced currents are produced by changing the

magnetic flux due to relative motion, changing the flux

density or changing the perpendicular area.

Lenz’s law and the right-hand grip rule can be used to

predict the direction of an induced current.

Lenz’s law states that an induced current in a closed

conducting loop will appear in such a direction that it

opposes the change that produced it.

Lenz’s law can be explained in terms of the law of

conservation of energy.

The production of eddy currents can be explained in

terms of Lenz’s law.

Applications of eddy currents include induction

cooktops and eddy current braking.



•

•



•

•

•



Review questions

Physically speaking

The theme of this word search is induction.

There is a twist; there is no list provided, so

you have to work out the words that have been

included. Find the 10 hidden words that have to

do with induction, list them and write their

definitions.



110



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motors and

generators



Reviewing

1 Outline Faraday’s experiment that led to the discovery



11 A conductive wire is placed on rails of an electrical

circuit and forced to move to the right, as shown in

the diagram below.



of electromagnetic induction.



2 Recall the factors that affect the size of the induced



wire



emf that is created by induction.



bulb



3 Magnetic flux is a measure of the magnetic field

passing through a certain area. Use this statement to

explain how magnetic flux can be altered.



rails



4 Outline how emf can be used to produce current.

5 Describe the place of relative motion in inducing emf.

6 Explain how Lenz’s law supports the law of



a Determine which is the positive and which is the

negative end of the wire.

b Determine the direction of the current in the

circuit.



conservation of energy.



7 Compare induced current in a wire and eddy currents.

8 Explain why a solid square piece of copper swinging

through a magnetic field will slow more quickly than

one with slits in it.



12 Explain how eddy currents can be a problem.

13 Give examples of how eddy currents can be of use.

14 Predict the direction of the eddy currents in the

following examples.

a



9 Compare and contrast the use of eddy currents in

induction cooktops and electromagnetic braking.

(You may need to refer to Physics Focus on

page 112.)



square metal sheet



Solving problems



rotating metal disc





15 Justify the claim that induction cooktops need



10 Using Lenz’s law, predict the direction of current



special cookware.



in the following situations. Sketch these diagrams,

showing the induced currents.

a

c

S



N



N



A



d



X



B



expanding wire loop

Y



iew



Q uesti o



n



s



v



b



A



Re



S



b



111