VCE PHYSICS UNITS 3&4

UNIT 3 RECAP LECTURE

Presented by:Alevine Magila

OVERVIEW

2

• Introduction

• Practical Investigations

• Circular Motion

• Einstein’s Theory of Special Relativity

• Recap on Fields

• Electric Generators

• Transformers and the Transmission of

Electricity

Practical Investigations

THE PRACTICAL INVESTIGATION

4

• Experiments are at the heart of the science of

Physics.

• Year 12 physics students must demonstrate that they

are capable of planning, executing and recording a

scientific experiment in the form of a ‘practical

investigation’

• Your practical investigation will likely be presented as

a poster or a report

• The practical investigation is worth about 37% of your

Unit 4 score

ADVICE ON CHOOSING YOUR TOPIC

FOR THE EPI

5

The best advice for your EPI?

Keep it simple.

Remember – you are not trying to uncover something that’s never been

discovered before.

Investigating an overly complex topic does not mean you are going to get high

marks.

You are better off exploring something unknown to you, yet achievable and

simple, with a clear hypothesis and a well organized method.

INDEPENDENT AND DEPENDENT

VARIABLES

6

• Independent variables are variables that you control and change.

• Possible independent variables may include things like mass,

incline angle, height, supplied voltage etc.

• Dependent variables are variables that change in response to the

independent variables; a.k.a they depend on the independent

variables

• Experimenters will typically observe how a chosen dependent

variable changes in response to altering the independent variable.

• For instance: How does the time taken for an object to fall down

change with increasing drop height?

– Independent variable: Height

– Dependent Variable: Time Taken to Fall to Ground

CONTROLLED VARIABLES

7

• Controlled variables are outside variables that experimenters try to hold

constant

• By keeping controlled variables at a constant level (or ‘controlling’ them), any

influence an outside variable has on the outcome of your experiment is

reduced.

• If not all the appropriate variables are controlled, we cannot conclusively say

that the independent variable influenced the dependent variable.

• The dependent variable may have been influenced by other factors as well

• Unless controlled variables are accounted for and held constant, the

explored relationship between the independent and dependent variables

may not be accurate.

• Examples of controlled variables include temperature, mass, density, air

pressure etc.

ACCURACY VS PRECISION

8

• Accuracy is a measure of how close a

measured value is to it’s true value.

• The “precision” of a measurement refers to

how small the increment to which the

measurement was made is.

MEASURING UNCERTAINTIES

9

• Uncertainties are important indicators of how precise

our measurements are. The smaller the uncertainty,

the more precise our measurement is.

• The uncertainty of a measurement can vary

depending on the circumstances and the equipment

• Oftentimes however the uncertainty is simply taken

as half the smallest increment on the measuring

device.

• For example, if your ruler makes measurements of

length to the nearest mm, then your ruler would have

an uncertainty of half a mm, or ±0.5 mm

HOW TO CALCULATE

UNCERTAINTIES

10

• In your EPI, it is likely that you will need to perform calculations with several quantities

– all of which have uncertainties.

• The result of these calculations will also have an uncertainty based on the values

entered.

• If you are adding or subtracting two quantities – both of which have uncertainties –

then the result will have an uncertainty equal to the sum of the uncertainties of the

two values.

• Let’s say for example you want to measure the mass of water in a bowl.

𝑚 = 750 ± 10 𝑔 𝑚 = 1690 ± 10 𝑔

HOW TO CALCULATE

UNCERTAINTIES

11

• To find the mass of the water, we need to subtract the mass of the bowl from the

combined mass of the bowl and the water.

• The calculated result will have an uncertainty equal to the sum of the combined

uncertainties of the mass of the bowl, and the combined mass of bowl and water:

Mass of the water = 1690 – 750

= 940

𝑚 = 750 ± 10 𝑔𝑚 = 1690 ± 10 𝑔

± 20 g

ABSOLUTE UNCERTAINTY AND

RELATIVE UNCERTAINTY

12

• Expressing the uncertainty in the form of a plus/minus figure away from

the measured value is one way of measuring the uncertainty: for example,

5.0 ± 0.5 m.

• Uncertainty expressed in this way is referred to as an absolute uncertainty.

• A relative uncertainty is an uncertainty that is expressed as a percentage

of the measured value.

• The relative uncertainty is the absolute uncertainty divided by the

measured value.

• The relative uncertainty for the example above would be 0.5

5= 10%. Thus,

we would express this as an uncertainty by writing 5.0 ± 10% m

HOW TO CALCULATE

UNCERTAINTIES

13

• The length of the table is 75.0 ± 0.5 cm and the width of the table is 40.0 ± 0.5 cm.

• The area will be 74 x 40 = 3000 cm2 – but what is the uncertainty for that result?

• To find the uncertainty of the result, we add the relative uncertainties of the

multiplied values: 0.5

75+0.5

40= 0.01916 = 1.916%

• Thus, the surface area of the table is 3000 ± 2 % cm2

• Multiply a relative uncertainty by it’s corresponding value to turn it into an absolute

value:

• 3000 x 1.916% = 57.5

• Hence, the surface area of the table is 3000 ± 60 cm2

• When multiplying or dividing two numbers, the relative

uncertainties need to be added to find the uncertainty of

the result.

• For example, finding the surface area of a table:

= (3.00 ± 0.06) x 103 cm2

HOW TO STRUCTURE YOUR REPORT

14

• The main features of your final experimental report/

poster include:

– Title/ Question

– Aim

– Hypothesis

– Equipment

– Method

– Results

– Discussion

– Conclusion

– References

APPROACHING AN EXPERIMENT

15

• When presenting your collected data in your report,

your data should be clear, readable and easy to

understand

• Let’s consider a hypothetical experiment:

• You have a spring hanging vertically from the ceiling

and wish to observe how the mass affects the

extension of the spring

HOW TO STRUCTURE YOUR REPORT

16

– Title/ Question: If a weight is attached to a standard spring, what is the

relationship between the weight’s mass and the spring’s extension?

– Aim: To determine the relationship between the mass attached to a

hanging spring and the spring’s extension.

– Hypothesis: Increasing the mass attached to the spring will increase the

extension of the spring. Springs with a higher spring constant will be

stretched less.

– Equipment: [List equipment used]

– Method [Outline each step clearly and in third person. Writing should be

concise, but with sufficient detail such that another year 12 physics

student would be equipped to repeat the experiment themselves]

RESULTS - COLLECTING DATA

17

Data that is poorly presented:

Mass Spring 1 Mass spring 2 Mass spring 3 spring Extension

500.0 500 5 x 102 0.05 m

800 1 x 103 1.0 x 103 10

1100 1500 1500 14 cm

1500 2.00 x 103 2000 18 cm

1900 2500 2.50 x 103 24 cm

Confusing Title

Inconsistent

Sig. Figs

No units

No uncertainty in

measurements?

Different masses used for

different springs?

Inconsistent

units

RESULTS - COLLECTING DATA

18

Data that is presented well:

Unit and uncertainty in

title

Consistent weights used

for each of the three

springs Clear titles

Consistent precision

RESULTS - GRAPHING DATA

19

• TextAppropriate scale

Axis titles and units

Meaningful

Graph Title

Error Bars to indicate

uncertainty

Trendline

WHAT TO TALK ABOUT IN THE

DISCUSSION

20

• The discussion is arguably the most important part of

your report. A lot of the marks for the EPI are in the

discussion.

• Essential things to include:

– An analysis of your results and an interpretation of their

meaning

– Link the outcome of your experiment to the hypothesis and

established theory

– A discussion of possible errors in the experiment and the

influence they may have had on the accuracy of your results

– The limitations of your experiment

– Possible ways to improve the design of your experiment

Circular Motion

UNIFORM CIRCULAR MOTION

22

• An object travelling in a circular path at a constant speed is said to be

travelling in uniform circular motion.

• Uniform circular motion is the simplest form of circular motion.

• The speed of an object travelling in uniform

circular motion is given by 𝑣 =𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒

𝑡𝑖𝑚𝑒, which,

for an object travelling in a circle, is equal to

𝑣 =2𝜋𝑅

𝑇

…where

• R is the radius of the object’s circular path in

m, and

• T is the period of the object i.e the time it

takes to move around the circle once in s

CENTRIPETAL ACCELERATION

23

• ALL objects moving in circular motion experience a centripetal acceleration. Centripetal acceleration

constantly changes the direction of an object’s velocity. (Compare this to linear acceleration which

changes the speed/ magnitude of an object’s velocity)

• Centripetal acceleration is given by the equation

𝑎 =𝑣2

𝑅• The direction of an object’s centripetal acceleration always points towards the center of the circle.

• For an object travelling in uniform circular motion, the only acceleration that is experienced is a

centripetal acceleration. This is because –for objects moving in uniform circular motion – the net

force is equal to the centripetal force.

𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 = ∆𝑣= 𝑣𝑓𝑖𝑛𝑎𝑙 − 𝑣𝑖𝑛𝑖𝑡𝑖𝑎𝑙

−=

= + =

CENTRIPETAL FORCE

24

• The centripetal force is the force that causes objects to move in

uniform circular motion.

• In uniform circular motion, the centripetal force is equal to the

net force.

• The centripetal force is not an ‘abstract’ force; it is always

supplied by a real, tangible force. For example, the tension in a

string, the gravitational force, the sideways friction of the road

on your car tires etc.

• Since the centripetal force is equal to the net force (in uniform

circular motion), we can say that

Σ𝐹𝑐 = 𝑚𝑎𝑐 =𝑚𝑣2

𝑅

EXAMPLE QUESTION

25

A ball is tied to a string, as shown in the figure below. The ball

moves at a speed of 1.7 m s-1. What is the centripetal acceleration

of the ball?ADAPTED FROM VCAA EXAM 2016 Q2

EXAMPLE QUESTION

26

EXAMPLE QUESTION

27

A 1,200 kg car is travelling around a bend that can be modelled as a

circular arc with radius 8.0 m. Calculate the speed of the car given that it

experiences a constant centripetal force of 5400 N.

𝑣

EXAMPLE QUESTION

28

BANKED TRACKS

29

• Banked tracks are tracks that are slanted or at an incline

relative to the flat, horizontal ground.

• Banked tracks are another example of circular motion. Objects

moving around banked tracks have a centripetal force and a

centripetal acceleration.

• Normally, when we turn in a circle on flat, horizontal roads on a

bike or car, we rely on the sideways horizontal frictional force of

our tires on the road to turn. A banked track eliminates the

need for a sideways frictional force to turn.

BANKED TRACKS

30

Nmg

Σ𝐹𝑐

EXAMPLE QUESTION

31

VERTICAL CIRCULAR MOTION

33

• So far, everything that we’ve learnt about circular motion only applies to uniform

circular motion; that is, circular motion where the object travels at a constant speed

• However, not all objects travel in uniform circular motion. This is especially evident

when we consider uniform circular motion in a vertical plane – for example, the

motion of a bike rider down a half-pipe.

• In uniform circular motion, objects only experience one type of acceleration: a

centripetal acceleration.

• In non-uniform circular motion, there may be more than one type of acceleration at

play.

• The bike rider has two accelerations, the vertical acceleration due to gravity, which

causes his bike to speed up AND the centripetal acceleration, causing him to move

along a circular path.

𝑎𝑐

Σ𝑎

𝑎𝑙

VERTICAL CIRCULAR MOTION

34

• Analyzing the motion of an object moving with circular motion in a

vertical plane at any point is beyond the scope of this course.

• However, there ARE two points in a vertical circle where we CAN

analyze the motion of such an object: at the top and at the bottom of

the circle.

• At the top and at the bottom, an object (in this case, the car and the

bike) will –for an instant- move with a roughly constant speed. This

allows us to apply our tools covering uniform circular motion.

EXAMPLE QUESTION

35

Our sense of how ‘heavy’ we feel comes from the normal force.

• If the normal force is equal to our weight force, we feel normal.

• If the normal force is lower than the weight force, we feel lighter than usual.

• And if the normal force is greater than the weight force, we feel heavier than usual.

Consider the motion of the car travelling through a shallow ditch, as shown below. At the bottom of

the ditch, the car has a roughly constant speed of 6.5 m s-1. The bottom point of the ditch can be

modelled as a circle with radius of 6.0 m. The mass of the car is 1,300 kg.

Does the car feel lighter, heavier, or the same at the top of the hill? Justify your answer.

𝐹𝑔

𝑁

Σ𝐹

EXAMPLE QUESTION

36

Einstein’s Theory of Special

Relativity

Smarter VCE Tutoring

Make an appointment at tutesmart.com/book

✓ Centre access after school & weekends ✓ One-on-one time as needed

✓ Weekly classes that cover the study design ✓ Priced from just $20 per hour

REFERENCE FRAMES AND GALILEO’S

PRINCIPLE OF RELATIVITY

39

• According to Galileo, all motion is relative.

• A reference frame is essentially a coordinate axis that we can attach to

an object. Anything within a reference frame is ‘at rest’ in that reference

frame. It is assumed that any observers in a reference frame can make

accurate measurements about position, velocity, time etc.

• This is summarized nicely in Galileo’s Principle of Relativity. It states that

all motion is relative to some particular frame of reference, but that

there is no frame of reference which has an absolute zero velocity.

• This means that there is no frame of reference where we are completely

at rest with respect to space.

AN EXAMPLE OF GALILEAN

RELATIVITY

40

• Consider the situation shown below, where there is a ball thrown in a moving train.

There are two observers: Amy (A) who is inside the train, and Chelsea (C) who is

standing on the ground.

• In the situation depicted, Amy is travelling at a constant velocity of 20 m / s right.

While in the train, Amy throws the ball to the right at 10 m/s.

• In Amy’s reference frame, the ball is

moving at 10 m/s, while in

Chelsea’s reference frame, the ball

seems to move at a speed of 20 +

10 = 30 m/s

• Thus, for two observers in two

different reference frames, the

velocity of an object (in this case,

the ball) appear different. This is

what Galileo was referring to when

he said that all motion is relative.

THE MICHELSON-MORLEY

EXPERIMENT

41

• The Michelson-Morley experiment is famous for being one of the first experiments to

accurately measure the speed of light.

• In their time, light was considered to be a wave. All mechanical waves need a medium to

travel through, so it was anticipated that light too – as a wave – would need a medium

• It was proposed that light propagated through a massless, invisible medium called the

‘aether’.

• Michelson and Morley compared the time for light to travel down two perpendicular

paths using an interferometer. They measured the speed of light at two different points

in time 6 months apart.

• If an ether existed, the speed of light in each experiment

should have been different. Instead, Michelson and

Morley found the same speed of light in both trials,

suggesting that light did not need a medium or a so

called ‘aether’ to travel through space.

• The speed of light is denoted by the constant c and has

the accepted value of 2.997 924 58 x 108 m s-1. This is

often rounded off to 3.0 x 108 m s-1.

MAXWELL’S EQUATIONS

42

• Maxwell’s equations are a set of four equations

that fully and accurately describe the interactions

and behaviors of electric and magnetic fields.

Maxwell’s equations also outline how electric and

magnetic fields interact with one another.

• Maxwell’s equations predicted the existence of a

self sustaining electromagnetic wave. Maxwell

used his equations to calculate the speed of an

electromagnetic wave – if such a wave existed.

• Maxwell found that the speed of an

electromagnetic wave – if it existed – would be

given by 1

√𝜖0𝜇0=

Exactly equal to the speed of light! Maxwell

concluded that light must be an electromagnetic

wave

3.0 × 108 𝑚/𝑠

A PROBLEM IN PHYSICS?

43

• Galileo was a physics genius. According to his principle of relativity, velocity is relative.

• What Maxwell’s equations how shown however, (in addition to the M&M experiment), was

that the speed of light seemed to be constant, regardless of your relative motion to the

source.

• Returning to our train example, this means that both the observers in the train and those

on the outside platform, will perceive the speed of light to be the same: 3.0 x 108 m s-1

• These two ideas seemed to violate one another. It seemed that they were impossible to

reconcile.

• As a young Einstein pointed out – they are not.

• Einstein proposed that both ideas must be true, and that this is possible because

spacetime itself shifts and warps so that all observers – regardless of their motion –

perceive light to be the same speed of c.

EINSTEIN’S POSTULATES

44

This is where Einstein’s theory of special relativity begins. All of it

flows from two very important truths or ‘postulates’ that Einstein

developed.

These postulates are outlined below.

Postulate 1: The laws of physics are the same in all

inertial frames of reference

Postulate 2: The speed of light has a constant value for

all observers regardless of their motion or the motion of

the source

HOW DOES RELATIVITY AFFECT

TIME?

45

Consider a similar example as the one before, except now the train is from the

future and is travelling at speed v.

Inside the train, Ana has a light clock. This is a clock where light is reflected

between two mirrors facing one another. One ‘tick’ of the clock is the time it takes

for a beam of light to return to the bottom mirror the instant after it has been

reflected from the bottom.

AMY’S TIME

46

To get a sense of how the two observers experience time, let’s

calculate the time taken for the light to travel from the bottom

mirror to the top mirror. In Amy’s frame of reference, the light clock

looks like the image shown below:

The time for light to travel the height h from the bottom to the top

is equal to

𝑡𝐴 =ℎ

𝑐

Note: This simply comes from rearranging the equation 𝑣 =𝑥

𝑡

CHELSEA’S TIME

47

• In Chelsea’s frame, the light has to travel a greater distance to reach the

top mirror of the light clock. We want to calculate the time taken for the

light to reach the top in Chelsea’s reference frame. We’ll call this time 𝑡𝑐.

• The speed is 𝑐 and the distance travelled is 𝑣𝑡𝑐2 + ℎ2 . Thus, the time

taken up, 𝑡𝑐, is

𝑡𝑐 =𝑣𝑡𝑐

2 + ℎ2

𝑐

ℎ

𝑣𝑡𝑐

LINKING THE TWO TIMES

48

• We now have two different time intervals: the time it takes for the light to go up in

Amy’s reference frame and the time it takes for the light to go up in Chelsea’s

reference frame.

• Our ultimate goal is to link these equations somehow and to see if they are the

same.

• The equations are:

• Rearranging both of the equations for the height, h, we find that

• Finally, equating these two equations (since both are equal to h), and doing a little

bit of algebra we arrive at the equation

𝑡𝐴 =ℎ

𝑐𝑡𝑐 =

𝑣𝑡𝑐2 + ℎ2

𝑐

𝑡𝑐 =𝑡𝑎

1 −𝑣2

𝑐2

ℎ = 𝑡𝐴𝑐 and ℎ = 𝑡𝑐 𝑐2 − 𝑣2

and

TIME DILATION

49

𝑡 =𝑡0

1 −𝑣2

𝑐2

• This equation shows that time is relative. In other words, your

perception of how fast or slow time ‘flows’ is dependent on your

frame of reference.

• If v = 0.95c and t0 1.0 s, the dilated time, t, would be

approximately 3.2 s.

• In other words, an event that lasts

only 1.0 second inside the train

would last 3.2 seconds for a

“stationary” observer outside.

• That means that if you were looking

from where Chelsea is inside the

train, time would appear to be

moving 3.2 times more slowly!

PROPER TIME AND DILATED TIME

50

• Loosely speaking, proper time is the time that is measured while “moving”

• The dilated time is the time measured while “stationary”

• So, in the train example, Amy was moving so she experienced the proper

time, and Chelsea was stationary so she experienced the dilated time

• These are just general rules of thumb; the formal definition for the proper

time is the time interval between two events that occur at the same point

in space.

• Any time measured between events that occur at different points in space

is a dilated time.

• On a final note, the expression 1

1−𝑣2

𝑐2

appears a lot in relativity. So much

so that physicists have assigned it a variable for shorthand: 𝛾. Thus, an

alternative way to write the equation for time dilation is

𝑡 = 𝛾𝑡0

SPACE IS ALSO WARPED

51

• Einstein reconciled Maxwell’s equations and the Galilean principle of

relativity in his two postulates. He explained that these work because

spacetime warps and shifts in a reference frame close to the speed of

light.

• So far we’ve seen how time is warped, but space itself is also warped

when we approach the speed of light.

• Space is different in different reference frames moving relative to one

another. Einstein showed that if an object were to pass a “stationary”

observer, the length of the object would be shorter than if it were at rest!

PROPER LENGTH AND

CONTRACTED LENGTH

52

• Let’s return to the train example.

• Amy is at rest with respect to the train. The length of the train that she measures is called

the proper length. To her, nothing looks contracted; everything looks normal inside the

train.

• Outside the train, in Chelsea’s frame of reference, the train appears contracted as it

moves along the tracks at 0.95c.

• Even though the speed of Amy’s train causes it’s length to contract (from Chelsea’s point

of view) no other dimensions of the train are impacted; the height and the width of the

train remain the same.

PROPER LENGTH AND

CONTRACTED LENGTH

53

The equation for the contracted length is

…where

• L is the contracted length,

• L0 is the proper length, and

• v is the speed of the object/ reference frame in m / s

This can be rewritten using 𝛾 as

L = 𝐿0 1 −𝑣2

𝑐2

𝐿 =𝐿0𝛾

Fields Recap

CHUCK US A LIKE & FOLLOW!

atarnotesvce

atarnotes-vce

atarnotes_vce

atarnotes.com/forum

GRAVITY

56

• Newton’s Law of Universal Gravitation describes the gravitational

force between two masses: 𝐹𝑔 =𝐺𝑀𝑚

𝑅2

• The magnitude of the gravitational field produced by a mass is

expressed as the force per unit mass: 𝑔 =𝐹

𝑚=

𝐺𝑀

𝑅2

• In a uniform field, the gravitational potential energy is given by the

equation 𝑈𝑔 = 𝑚𝑔∆ℎ

• Otherwise, in a non-uniform field, changes in G.P.E / K.E can be found

using the areas under force-distance graphs and field-distance

graphs.

• Gravitational fields are created by particles of

mass

• The gravitational field of a point mass is radial

and directed inwards.

ELECTRICITY

57

• Electricity is created by particles of charge.

• There are two types of electric charge: positive charge and negative

charge

• The electric field of a positive point charge is radial and directed

outwards

• The electric field of a negative point charge is radial and directed

inwards

• Coulomb’s Law describes the electric force between two particles of charge: 𝐹𝑒 =𝑘𝑞1𝑞2

𝑅2

• Opposite charges attract one another; like charges repel

• The magnitude of the electric field of a point charge is expressed as the force per unit charge:

E =𝐹

𝑞=

𝑘𝑞

𝑅2

ELECTRICITY

58

• A uniform electric field can be created using two parallel plates with equal

amounts of opposite charge

• A charge placed inside this apparatus will accelerate towards the oppositely

charged plate

• The force causing the charge to accelerate is the electric force and is given

by 𝐹 = 𝑞𝐸

• The work done in a uniform electric field (as shown above) is given by the

equation 𝑊 = 𝑞𝑉

MAGNETISM

59

• Bar magnets create magnetic fields.

• The magnetic field of a bar magnet flows around the

magnet, exiting at the north pole and entering again

at the south pole.

• Bar magnets have a north pole and a south pole

• Similar to electric charges, like poles experience

repulsive forces, whereas opposite poles attract.

B

MAGNETISM

60

• In addition to bar magnets, electric currents can also produce magnetic

fields

• The direction of the magnetic field around an electric current can be

determined by the right-hand grip rule.

• Any current-carrying wire will produce it’s own circular magnetic field. In year

12, there are three arrangements that we need to be familiar with:

– Straight rods

– Wire loops

– Solenoids

• Dots are used to represent field lines coming out of the page; crosses are

used to represent field lines going into the page.

• The ‘north pole’ of a solenoid is the side where the field lines emerge from

the solenoid; the ‘south pole’ is the side where the field lines enter the

solenoid.

MAGNETISM

61

• If an electric current is placed inside of an external magnetic field, it will

experience a magnetic force.

• If the current flows perpendicular to the field, the force will be given by

the equation 𝐹 = 𝑁 × 𝐼𝑙𝐵

• If the current flows parallel to the field, the magnetic force will be 0

• If the current flows at some intermediate angle θ with respect to the

field, the magnetic force will be given by 𝐹 = 𝑁 × 𝐼𝑙𝐵 sin(𝜃).

• In year 12, you are only required to deal with situations where the

current is parallel or perpendicular to the magnetic field.

• The direction of the magnetic force acting on a current-carrying wire can

be determined using the right-hand slap rule.

• The right-slap rule: Use your right hand to point your thumb in the

direction of the conventional current and your fingers in the direction of

the magnetic field. The resulting direction your palm faces is the

direction of the magnetic force on the current-carrying wire.

MAGNETISM

62

• A moving charge in an external magnetic field will experience a force: 𝐹 =𝑞𝑣𝐵

• This force will create a centripetal acceleration – not a linear acceleration

– causing the charge to move in a circle.

• The right-hand slap rule can be used to confirm that the charge will move

in a circular path.

• The centripetal force that makes the charge move in a circular path is the

magnetic force: 𝑚𝑣2

𝑅= 𝑞𝑣𝐵

• At first glance, bar magnets and currents seem quite

different, even though they both produce magnetic fields

• Ultimately, the source of the magnetic fields in both

situations comes from the same source: moving charges.

• Any moving charge will create a circular magnetic field

perpendicular to it’s velocity.

COMPARISONS

63

Gravitational Field Electric Field Magnetic Field

Formula𝑔 =

𝐹

𝑚=𝐺𝑀

𝑅2𝐸 =

𝐹

𝑞=𝑘𝑄

𝑅2𝐵 =

𝐹

𝐼𝑙

Shape

Forces Attractive Attractive and

Repulsive

Attractive and

Repulsive

Dipoles /

Monopoles

Only Monopole Monopole or Diploe Only Dipole

Recap of Electricity

Generation

MAGNETIC FLUX

Magnetic Flux can be thought of as the number of magnetic field lines that

pass through a given area.

There are two ways the magnetic flux can be changed:

1. By changing the strength of the magnetic field

2. By changing the area through which field lines pass

65

MAGNETIC FLUX

66

Magnetic Flux is an important quantity in physics. Normally

when we look at magnetic flux, we look at the magnetic flux

through a surface. This is a crucial point.

Formally, we define magnetic flux as

…where

• Φ𝐵 is the magnetic flux in webers (Wb),

• 𝐵 is the magnitude of the magnetic field in T, and

• 𝐴⊥ is the perpendicular area

Φ𝐵 = 𝐵𝐴⊥

PERPENDICULAR AREA

67

The “perpendicular” area can be thought of as the area of the surface as seen

from the point of view of the magnetic field lines.

For example, consider the rotating disk again shown below.

From the point of view of the magnetic field lines, the area (or in this case – the

‘perpendicular’ area) of the disk looks like this:

(a) (b) (c)

EXTENSION: MOTIONAL EMF

As the rod moves, the charges contained within the rod also move. There is a

‘flow’ of charge in the direction of the rod’s motion.

In the above situation, this flow of charge is perpendicular to the magnetic field.

Whenever a charge moves perpendicular to a magnetic field, it experiences a

magnetic force.

68

Can motion induce an EMF?

Consider the situation of a neutral, straight-rod conductor immersed in a

magnetic field, as shown below. You may assume the rod is moving at a

constant speed through the field.

EXTENSION: MOTIONAL EMF

Whenever a charge moves perpendicular to a magnetic field, it

experiences a magnetic force.

The magnetic force pushes the positive charges to one end of the rod,

and the negative charges to the other end of the rod.

This separation of charge creates an induced EMF. In this case, the EMF

was induced by motion.

69

FARADAY’S LAW

70

• Michael Faraday was a physics genius

• He discovered that an EMF could be induced from a change in magnetic

flux.

• The process of inducing an EMF in a wire through a change in magnetic

flux is known as electromagnetic induction.

• Faraday’s law states that the induced EMF for a change in magnetic flux

is given by:

…where

• 𝑁 is the number of turns in the coil

• ∆Φ𝐵 is the change in magnetic flux (Wb), and

• ∆𝑡 is the time interval taken for which the change in flux takes place (s)

𝐸𝑀𝐹 = −𝑁 ×∆Φ𝐵

∆𝑡

ELECTRIC POWER GENERATORS

Modern day generators are complex, but the arrangement below illustrates the fundamental

components used in all generators to produce electrical energy.

An external source of energy (steam from burnt coal, nuclear fission reactions etc.) is typically used

to rotate a turbine, which is then used to rotate a coil through a uniform magnetic field.

The changing magnetic flux through the coil induces an EMF, thereby turning the mechanical energy

used to rotate the coil into electrical energy that can be used commercially.

The electricity is transmitted from the coil to an external circuit through either slip rings or a split-ring

commutator.

GENERATORS

An AC generator, or alternator, involves a

rotating coil in a uniform magnetic field. It

is connected to slip rings which maintain

the connection between the circuit and

the loop. The output EMF of an alternator

varies sinusoidally

A DC generator also involves the rotation

of a coil in a uniform magnetic field. It

however, is connected to a split-cylinder

commutator, which reverses the direction

of the current every half turn.

The coil of a generator can be connected to an external circuit in one of

two ways: with slip rings or with a split-ring commutator

EXAMPLE QUESTION

A 30 cm x 30 cm square coil is being rotated through a uniform magnetic field of

strength 450 mT. If the 75-turn coil is rotated by a water turbine with a uniform

frequency of 50 Hz, calculate the induced EMF in the coil after a quarter rotation from

the position shown below.

73

Diagram sourced from 2009 VCAA Physics Exam 2

BLANK SLIDE

Text here

74

Transformers and the

Transmission of Electricity

TRANSFORMERS

76

• Transformers are electrical component that are used to transform voltages

to larger or smaller values. Transformers are useful for reducing power loss

in the transmission of electricity

• A basic transformer has three main components: a primary coil, a secondary

coil and an iron core.

• Transformers that have a larger voltage in the secondary coil than in the

primary coil are known as step-up transformers.

• Transformers that have a smaller voltage in the secondary coil than in the

primary coil are known as step-down transformers.

HOW TRANSFORMERS WORK

77

• The basic operation of a transformer is in

fact fairly simple to grasp: it’s all based on

the principles of electromagnetic induction.

• An AC current is supplied to the primary coil

of a transformer. Remember how currents

produce magnetic fields? Well an AC current

produces an ‘alternating’ magnetic field (a

magnetic field that oscillates in strength).

• This changing magnetic field allows a changing magnetic flux to flow

through the core of the transformer.

• The changing magnetic flux in the core of the transformer then induces

an EMF in the secondary coil of the transformer. The magnitude of the

induced voltage in the secondary coil of the transformer depends on the

number of turns in the secondary coil.

TRANSFORMER RATIOS

78

The ratio between the number of turns in the primary

and secondary coils greatly affects the secondary

voltage and the secondary current.

A useful ratio that links the voltages, number of turns,

and currents, is

𝑁𝑝

𝑁𝑠=𝑉𝑝

𝑉𝑠=𝐼𝑠𝐼𝑝

EXAMPLE QUESTION

79

A step-down transformer has 750 turns in the primary coil and 50 turns in the secondary

coil. The primary voltage and primary current are 300 kV and 0.08 A respectively.

Calculate the

a) Secondary voltage, and

b) Secondary current

POWER LOSS ALONG

TRANSMISSION LINES

81

Power loss along transmission lines is given by the equation

𝑃𝑙𝑜𝑠𝑠 = 𝐼2𝑅

A large current significantly contributes to power loss in transmission lines! The current

must be reduced in order to minimize power loss.

Recall that the equation for power is 𝑃 = 𝐼𝑉. For a constant power, an increase in

current will result in a decrease in voltage. Likewise, an increase in voltage will result in

a decrease in current.

Power loss is reduced along transmission lines by increasing the voltage. This has the

effect of decreasing the current, thereby reducing power loss (𝑃𝑙𝑜𝑠𝑠 = 𝐼2𝑅). How are

voltages increased? Using transformers!

POWER LOSS ALONG

TRANSMISSION LINES

82

Transformers have become an essential feature of electricity

transmission. At power plants, they increase the voltages to very high

values (500 kV RMS or so) to reduce the current.

By reducing the current, power loss is minimized (𝑃𝑙𝑜𝑠𝑠 = 𝐼2𝑅). Once

the electricity has been transmitted to it’s final location (e.g a town/

city) a step-down transformer is used to reduce the voltages back to

more suitable levels for domestic use (i.e around 240 V)

AC VS DC SIGNALS FOR DOMESTIC

POWER SUPPLY

83

• AC voltages and current are preferred over DC because

AC is compatible with transformers whereas DC signals

are not.

• This is because in a DC signal, there is no changing

current, and hence no changing magnetic flux through

the core of the transformer, so an EMF in the secondary

coil can not be induced.

• AC is preferred since they can work with transformers,

which save power by increasing the voltages, and

thereby decreasing the current (and thus, the power

loss)

QUESTIONS?Still feel confused about anything? Want more of an

explanation about anything else? Feel free to email

me!

My email address is alevine@atarnotes.com