HSC Physics in Month

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Neville Warren

MSc, DipEd, MACE

PASCAL

PRESS

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Publisher: Vivienne Petris Joannou Editor: May McCool

Typeset by Precision Typesetting Services, Sydney Cover by DiZign

Printed in Singapore by Green Giant Press Copying for educational purposes

The Australian Copyright Act 1968 (the Act) allows a maximum of one chapter or 10% of this book, whichever is the greater, to be copied by any educational institution for its educational purposes provided that the educational institution (or the body that administers it) has given a remuneration notice to Copyright Agency Limited (CAL) under the Act. For details of the CAL licence for educational institutions contact: Copyright Agency Limited

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Except as permitted under the Act (for example, any fair dealing for the purposes of study, research, criticism or review) no part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means without prior written permission. All inquiries should be made to the publisher at the address above.

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The total time allocated is approximately 22 hours. This includes 13 hours for the three core topics, approximately 5 hours for the option topic (depending on the topic), three hours for the exam and an hour to go through the answers. To revise in a month you will need to keep to a schedule.

For example, you might choose to follow the following timetable.

Space Gravity

Space Launch and Return

Future Space Travel Special Relativity Motors and

Generators The Motor Effect E lectromag netic Induction Electric Generators Transformers Electric Motors From Ideas to Implementation Cathode Rays Quantum Theory Solid State Devices Su percond uctivity

Do ONE option from

the following: Medical Physics Astrophysics Quanta to Quarks Sample Examination (3 hours) Check answers (1 hour)

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Check that you know the key points in each topic that you are studying. This quick test should take only 10 minutes to complete. Check your answers by referring to the bottom of the page. This is important feedback for you.

If you got any of the test questions wrong, you can quickly find an explanation and more information on this question by going to the same number in this section. You should also read the other key points for this topic to help you revise thoroughly.

These are exam-style questions that you should be able to answer in order to prepare for the exam. In this section you apply your knowledge. Make sure you have fully revised your work in the Key Points section. Complete answers are found at the back of the book. Hints to some questions are provided in case you need extra help with them. They are found at the bottom of the page.

Marks are allocated for each question. Always check the marks and use them as a guide for how much to write in your answer.

When you have completed all sections you are ready to complete the exam paper. Set aside the required time and try to do it under exam style conditions - this way you will benefit most from it.

Complete answers are provided for each question. Mark your paper to see how well you have done.

Tips for the HSC exam can be found on the inside back cover. A suggested time is given for each section. Try to follow it.

A week-by-week time plan for the month is given on the contents page to help you plan your study timetable.

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A force F acts between two masses separated by a distance d. If the masses are both doubled and their separation is halved, the new force is now:

F 2F 4F 16F

Surrounding any object with mass is a _ _ _ _ field.

The gravitational field strength of a mass m placed a distance r from the mass is g. If

the distance from the mass is halved, the new gravitational field strength is:

g/4 g/2 2g 4g

The acceleration due to gravity near the Earth's surface is approximately equal to _ _ _ _ m.s-2.

_ _ _ _ is the force on an object due to a gravitational field.

The acceleration due to gravity on Mars is 3.8 m.s-2. The weight of a 10 kg mass on Mars is:

38 m.s-2 _{38 N} _{0.38 N} _{10 N}

The mass of an object on Earth is 5 kg. Its mass on Mars (where the acceleration due to gravity is 3.8 m.s-2) is:

5 kg 5 N 19 kg 19 N

When a force is applied to a mass and the mass moves through a distance, we have done on the mass. If this force is used to move the mass vertically, we have increased the mass's _ _ _ _

The gravitational potential energy has its zero value at _ _ _ _

The gravitational potential energy Ep of an object of mass m placed a distance

r

from the Earth (mass ME) is given by:

Ep =_GmME

r

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Every mass exerts a force of attraction on every other mass in the universe in accordance with

Newton's law of universal gravitation.

This states 'the force, F, between two masses

m,

and

m

_{2 whose centres are separated by a distance r is proportional to the} product of their masses and inversely proportional to the square of their separation'. Mathematically F

=

G

m

1

_m

2

r2

A

gravitational field

surrounds the Earth. This field exerts an attractive force on objects on it and around it.

The

gravitational field strength,

9, of a mass m at a distance r from the mass is

given by: 9

=

Gm. On Earth 9 is equal to

-9.8

N.kg-'.

r2

The gravitational field strength is numerically equivalent to the

acceleration due to

gravity.

On Earth, this is equal to

-9.8

m.s-2.

Weight

is the force on an object due to a gravitational field.

The

weight

Wof a mass m on a planet where the acceleration due to gravity is 9 is given by W= mg

The

mass

of an object is independent of its location. Its weight, however, depends on where it is placed. For example a 10 kg mass has a weight of

98

N on the Earth but only 38 N on Mars (where 9 = 3.8 m.s-2). Its mass, however, is 10 kg on both planets. As we lift an object from the ground to a height above the ground we do

work

on it. This work is stored in the object as

gravitational potential energy.

The

gravitational potential energy

is a measure of the work done in moving an object from

infinity

(that is, a very large distance away) to a point in the field. At infinity, the gravitational potential energy is defined to be zero.

The gravitational potential energy of an object of mass m placed a distance rfrom the Earth (mass ME) is given by Ep

=

-G mME • The negative sign comes about because of

r

where we define the zero of potential energy to be. CHECKLIST - Can you:

1. Calculate the force between two masses using Newton's law of universal gravitation?

2. Define weight? •

3. Determine the weight force for a body on Earth and on other planets? 4. Describe an experiment to determine the acceleration due to gravity? 5. Define gravitational potential energy?

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Four planets alpha, beta, gamma and delta are shown in the figure below. alpha Radius r Mass M beta Radius r Mass 2M gamma Radius 2r Mass M

The planet with the largest acceleration due to gravity is: alpha beta gamma delta delta Radius 2r Mass 2M

The weight of a body on Earth is 2000 N. What is its weight on Mercury (where g = 3.4 m.s-2)?

The gravitational potential energy of a mass near the Earth is negative. This means: no work needs to be done to move the mass to infinity

no work needs to be done to move the mass from infinity the gravitational potential energy at infinity is zero the gravitational potential energy at infinity is positive.

What is the gravitational potential energy of a 1000 kg satellite in low Earth orbit 300 km above the Earth's surface? (The radius of the Earth is 6380 km and its mass is 5.983

x

1024 _kg)

As part of your course you determined a value for the acceleration due to gravity. Clearly explain how you did this and account for any variation from the accepted value of 9.8 m.s-2.

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A _ _ _ _ is any object moving only under the influence of gravity.

_____ motion can be best analysed by breaking it into two components. The horizontal component is motion with constant . The vertical component is motion with constant _ _ _ _

Two objects are released from the same height. Object A falls straight down and object 8 follows a curved path as shown in the figure. It is true that:

8 hits the ground before A

A hits the ground first only if it is heavier than 8

~" ObjectB

A hits the ground before 8

!

(Jf!&i Object A

A and 8 hit the ground at the same time. Falling masses

The equations linking the horizontal displacement

x,

the horizontal component of velocity

v

_x' the time t, the acceleration due to gravity a_gand the vertical displacement

11y, are given by

x

= and 11y = . The path followed by a projectile

has the shape of a _ _ _ _

The minimum velocity required for an object to leave the gravitational pull of a planet is called its velocity. This is of the mass of the object leaving the planet.

Newton was the first to propose the idea of artificial _ _ _ _

The acceleration of an object moving in a circular path with constant speed is directed towards the of the circle.

Astronauts in spacecraft and patrons of fun park roller coasters both experience significant _ _ _ _

As a rocket is launched, fuel is burned and the resulting are expelled downwards. Conservation of results in the rocket moving up. As the fuel is consumed, the acceleration . Rockets fired into space are fired in a/an _____ direction to take advantage of the Earth's _ _ _ _

The orbit of a satellite with a period of 24 hours is called a orbit.

Low Earth orbit satellites travel faster than satellites further from the Earth. True or false? _ _ _ _

The movement of spacecraft through the solar system is aided by using 'gravity-assist trajectories', also called the effect.

Safe re-entry of spacecraft to Earth is restricted to a narrow _ _ _ _ _ MOPU!M :).o4s6ulIs

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A projectile

is any object moving under the influence of gravity only. Examples include a golf ball after it has been hit, artillery shells fired from guns, 'dumb bombs' dropped by warplanes '"

Projectile motion

is composed of two independent motions: a horizontal component with

constant velocity

and a vertical component with

constant acceleration.

The independence of the two components of projectile motion is easily illustrated as shown in the figure on the right. The two objects fall at the same rate and hit the ground at the same time regardless of the horizontal motion.

::

c

The independence of motions The horizontal motion is described by D.x

=

uxt;

the vertical

motion is described by

.6.y

=

~age. The curved path followed by a projectile is called its

trajectory.

This curve is a

parabola.

The

escape velocity

is the velocity needed for an object to escape from the Earth (or other planet or moon). It depends on the radius and mass of the planet and the gravitational constant according to vescape

=

~2GME

. It follows that as the mass ofthe

RE

planet increases, the escape velocity increases; similarly as the radius decreases, the escape velocity increases. It is independent of the mass of the object trying to escape. Newton first proposed the idea of

artificial satellites.

He reasoned that if a cannon was fired horizontally from a high mountain, a speed could be reached where the shell would go into orbit around the Earth.

The motion of an object in a circular path of radius

r

with Artificial satellites constant speed v is called

uniform circular motion.

For an

?

object moving with uniform circular motion, the

centripetal acceleration a

_cis directed

2

towards the centre of the circle and is given by a_c

=~.

For a satellite orbiting the

r

Earth, the centripetal force is supplied by the gravitational attraction of the Earth to the satellite.

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g-forces

are measured in units ofthe Earth's gravitational acceleration, g. They arise whenever there are accelerations, such as in rocket launches and roller-coaster rides. Humans can withstand accelerations up to -10g when the acceleration is directed parallel to a line drawn between the person's front and back. Early astronauts experienced these forces as they reclined in specially moulded chairs. In today's Space Shuttle the g-forces are limited to -3W.

mg

Roller coaster ride

Consider a roller coaster ride as shown. As the rider moves through a bottom curve, the reaction force of the seat up on the rider must supply the necessary centripetal force, that is:

mv2

N-mg=--R mv2

N=mg+--R

The g-forces are found from the 'normal force' divided by the weight. That is:

9 felt by rider =

~

mg

mv2

mg+--_ R

mg

v

2

=1+-gR

It can be seen that the g-forces increase as the speed increases and/or the radius of the curve decreases.

Rockets are placed into Earth orbit by launching the spacecraft vertically and then tilting the trajectory parallel to the Earth's surface when the correct orbital speed is reached. By tilting in the easterly direction scientists can take advantage of the

Earth's

rotation

(from west to east).

A

geostationary orbit

is one in which the satellite has a period of 24 hours. If the orbit is in the equatorial plane, the satellite appears to stay above the same point on the Earth. Satellites placed in geostationary orbits allow communication signals to be 'bounced' around the world.

Kepler's laws

describe the motion of satellites according to

r:

=

G~

. For a constant

T 4n

mass it follows that as the radius decreases, the period must also decrease. Consequently the speed must increase so satellites in low Earth orbits travel faster than satellites further out in space.

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'Gravity-assist' trajectories (also called the

'slingshot' effect) are used to send

space probes to distant planets. A space probe approaching a planet picks up some of the planet's angular momentum resulting in a speeding up of the spacecraft relative to the Sun.

Outgoing velocity

spacecraft. Velocity of Venus Outgoing velocity relative to the Sun. of spacecraft relative

Venus The incoming speed and the outgoing speed are the same relative to Venus (but direction is changed). ~ ~~ to Venus. Outboun~ velocity relative to the Sun. Velocity of Venus

relative to the Sun.<III<!III(IIII----Venus Venus moves around the Sun. The spacecraft gains most of Venus s Incoming velocity velocity through gravitat" nal of spacecraft. attraction.

Gravity-assist trajectories

Incoming velocity of spacecraft relative to the Sun.

Safe re-entry

to Earth is limited to a small 'window'. This ensures that the spacecraft does not 'bounce' off into space if it comes in too shallow and the g-forces are not too high for the astronauts if it comes in too steep. It also means that the heat from re-entry is not too high. The Space Shuttle uses a variety of materials capable of withstanding the tremendous temperatures, as high as 1300°C. The 'allowed' angle of re-entry is -6.2° ± 1 ° relative to the Earth's horizon.

CHECKLIST - Can you:

Re-entry corridor

5.20

Re-entry 'window'

7.20

1. Analyse and solve problems of projectile motion in terms of its horizontal and vertical components? 2. Explain the concept of escape velocity and discuss the factors that affect it?

3. Analyse the forces involved in uniform circular motion? 4. Compare g-forces on astronauts and roller coaster riders? 5. Analyse the acceleration of a rocket during launch? 6. Compare low Earth orbits with a geostationary orbit? 7. Describe the slingshot effect used to assist space probes? 8. Relate Newton's laws to the motion of satellites.

9. Discuss issues associated with safe re-entry of spacecraft to Earth including the optimum angle for re-entry and the consequences of not achieving this?

10. Describe the contributions of Tsiolkovsky, Oberth, Goddard, Esnault-Pelterie, O'Neill or von Braun to

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A projectile is fired with an initial speed of 500 m.s-1 _{at an angle of 30° to the ground.}

Find:

the maximum height reached by the projectile the time to reach the maximum height

the distance travelled horizontally.

The escape velocities for Earth and Mercury are shown in the table below.

Planet Earth Mercury

Escape _{11.2 km.s-}1 _{4.3 km.s-l}

velocity

What is meant by escape velocity? What factors affect the escape velocity?

The period of revolution of the Martian moon Demos is 1.09 x 105 _{s. What is the radius} of its orbit given that the mass of Mars is 7.1 x 1023 _kg?

Describe the changes that occur in a rocket/s acceleration as it is launched into space. Be sure to explain the causes of the accelerations and the causes of any changes.

Astronauts in the Space Shuttle experience forces up to 3Wwhere W is the weight of the astronaut. Explain how it is possible for riders in a roller coaster to experience similar forces.

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Current rockets work by ejecting _____ formed by the combustion of a _ _ _ _ and oxygen. Conservation of means that the rocket will move in the opposite direction to the exhaust _ _ _ _ _

Scientists have been able to manufacture spacecraft that are able to travel at hundreds of thousands of kilometres per hour. True or false? _ _ _ _ _

The relatively _ _ _ _ speeds of spacecraft mean that travel times to distant planets would be very _ _ _ _

The engines of spacecraft are operating all the time. True or false? _ _ _ _ _ Three factors that affect communication between the Earth and distant space probes

are and _ _ _ _ _

_ _ _ _ radiation travels at the ultimate speed of 3.0 x 108 _m.s-1.

The reduction in strength of microwave signals as they travel through space from distant sources is a result of a/an square law. This weakening of strength is referred to as _ _ _ _ _ _ _ _ _ _

Sunspots are relatively _ _ _ _ areas on the surface of the Sun. They have magnetic fields thousands of times than the Earth/s magnetic field.

The solar wind consists of: a stream of positive particles a stream of negative particles

a stream of positive and negative particles a stream of neutral particles.

The Van Allen radiation belts are two belts of energetic _ _ _ _ particles. They can

be disrupted by intense activity. The resulting storms can affect

communication on Earth.

Communication with satellites or other spacecraft relies on electromagnetic radiation in the region of the electromagnetic spectrum.

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Rockets operate by expelling gases formed by combustion of the fuel and oxygen. These are ejected at very high velocities.

Conservation of momentum

ensures that the rocket travels in the opposite direction to the exhaust gases.

Scientists are not yet able to produce speeds of spacecraft more than a few

tens of

thousands of kilometres per hour.

For example, the

1969

Mariner 6 space probe to Mars took

157

days to travel

92,800,000

km, an average speed of

-25,000

km.h-1.

The relatively slow speeds of spacecraft mean that

travel times

to even the closest planets are long. A round trip to Mars for example, would take up to two years and eight months. Currently, extended manned space travel is not feasible.

The

engines of spacecraft

are designed for manoeuvring the spacecraft, to bring it into orbit around a planet (or moon), and in the most extreme situation, of leaving the planet (or moon). At all other times they are turned off.

Distance,

the

Van Allen radiation belts

and

sunspots

affect communication between the Earth and distant space probes.

Even though

electromagnetic radiation

travels at the enormous speed of

3.0

x

10

8 _ms1,

nevertheless the time for a signal to travel from distant objects is not insignificant, especially for very distant objects. For example, it takes 4 years for light to travel to us from our nearest star (other than the Sun).

The intensity of the electromagnetic radiation decreases as the square of the distance from the source (an

inverse square law).

This loss of signal strength is referred to as

space loss.

The dimensions of space are so vast that the electromagnetic energy able to be detected from distant objects (be they emissions from a spacecraft with a relatively low power transmitter or those from a star), are tiny.

Sunspots

are relatively cool areas on the surface of the Sun with strong local magnetic field strengths some thousands of times stronger than the Earth's magnetic field. Sunspots vary in activity. In an eleven-year cycle, the number of sunspots varies from a minimum up to a maximum and back to a minimum.

Sunspots are also associated with the

solar wind.

This wind consists of a

stream of

charged particles,

mostly protons and electrons that flow out from the Sun in all directions at a speed of

-400

km.s-1. The number of these particles increases following increases in sunspot activity. The solar wind affects the Earth's magnetic field and this in turn affects radio communication.

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The Van Allen radiation belts are two belts of energetic charged particles, mainly electrons and protons, lying at right angles to the equator of the Earth.

Solar wind particles (as well as particles from interactions between the Earth's upper atmosphere and energetic cosmic rays) become trapped in the Van Allen radiation belts. Intense solar activity can disrupt the belts. This in turn is associated with auroras and magnetic storms which can lead to interference of short wave radio communication, errors in communication satellites and even failure of electrical transmission lines.

Inner belt

Van Allen radiation belts

Communication with satellites and other spacecraft relies on electromagnetic radiation in the radio frequency part of the electromagnetic spectrum. In particular, microwaves in the frequency range 1000 MHz to 300,000 MHz are the major carriers of data between earthbound stations and between Earth stations and satellites and space probes.

1. Explain how space travel is limited by the current maximum speed of spacecraft? 2. Describe the factors affecting reliable satellite communication?

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What is the most significant problem making extended space travel not feasible at the present time? Clearly explain your answer.

Communication with space probes to distant planets such as Mars is not instantaneous but is always delayed. Explain why this delay occurs.

(The distance to Mars is -8 x 107 _km.)

The Van Allen radiation belts surround the Earth. What are these belts?

How do these belts affect communication between Earth and orbiting satellites?

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The medium hypothesised to transmit light was:

ether air anaesthetic

The Michelson-Morley experiment was an attempt to measure: the speed of the ether

the speed of the Earth through the ether the speed of light.

An example of an inertial frame of reference is: a car accelerating from a set of traffic lights

a car travelling in a straight line with constant speed a car travelling around a corner with constant speed. Einstein hypothesised that the speed of light:

is 3.0 x 108 _m.s-1 _{is constant}

The laws of physics are the same for all inertial observers. This is the principle of

The current standard of length, the metre, is measured in terms of _ _ _ _

Because space and time are interdependent we speak of four-dimensional _ _ _ _

Two events occur at the same time for a particular observer. To an observer in a different inertial frame of reference, they occur at different times. This is called the lack of

A metre rule, 2 cm wide, moves at a speed of e/2 relative to a stationary observer. What is the length of the rule as measured by that observer?

What is the width of the rule?

A clock moves at a speed of e/2 relative to a stationary observer. If 1 hour passes for an observer travelling with the clock, how much time passes for the stationary observer? Twins A and B are separated at birth. A is sent into space and B remains on Earth. A

eventually returns to Earth. A is now:

younger than B older than B the same age as B

Relativity 'allows' for travel into the past. True or false? _ _ _ _ _

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The ether (also aether) is the medium proposed prior to Einstein to transmit electromagnetic radiation. Its beginnings go back to the ancient Greeks but the idea was also used by Hooke in 1667 and Huygens in 1678 both of whom proposed that luminous objects set up vibrations that were transmitted through the ether like sound waves through air (compression waves). The ether was supposed to permeate all matter as evidenced by the transmission of light through transparent materials.

The Michelson-Morley experiment was an attempt to detect the motion of the Earth through the ether. It used apparatus similar to that in the diagram. The presence of the ether would mean that light travelling with and against the ether would take a different time to the light travelling across the ether. This difference should be detected by a change in the interference fringes formed when the light rays are recombined. The result was totally unexpected. It showed that the speed of the Earth relative to the ether could not be detected.

A frame of reference is a coordinate Light

source )go

Ether wind

Michelson-Morley experiment

system with respect to which we take measurements. An inertial frame of reference is one moving with constant velocity (or is at rest). A non-inertial frame of reference is one that is accelerating.

As a result of his work on how the laws of electromagnetism should behave in different frames of reference, Einstein proposed that the speed of light is constant and is independent of the speed of the source or observer. He was unaware of the null result of the Michelson-Morley experiment when he made his hypothesis - it simply provided evidence for his theory.

The principle of special relativity is that the laws of physics are the same for all inertial observers. This means that it is impossible to detect motion in an inertial frame simply by doing an experiment in that frame.

The unit of length, the metre is the defined as the distance travelled by light in a vacuum in the fraction 1/299 792 458 of a second. It follows that distance is therefore defined in terms of time.

(19)

For the speed of light to remain constant it means that space and time are relative; we speak of four-dimensional

space-time.

Two or more events that are

simultaneous

for one observer are not necessarily simultaneous for observers in different inertial frames of reference. This is called the lack of

simultaneity.

This can be illustrated by one of Einstein's famous 'thought experiments'.

The

length

of a moving rod appears to

contract in the direction of motion

relative

to a stationary observer; I

=

IO~1-

V 2

. The width is unaffected. For an observer moving

c2

with the rod, no length (or width) change occurs.

Time in a moving frame appears to be

slower

relative to a stationary observer. This is

time dilation; t

=

g.

For an observer moving with the clock, no change occurs. 1

-(2

The

twin paradox

refers to where imaginary twins are born at the same time and one is sent into space while the other remains on Earth. According to special relativity the twin left behind would 'see' the twin sent into space age less. Similarly, the twin in space would 'see' the twin on Earth age slower. This is the paradox: both say the other ages slower. The paradox is resolved when it is noted that the twin sent into space must undergo accelerations to turn around and come back to Earth. He is therefore in a non-inertial frame of reference and special relativity does not apply. (General relativity, which deals with non-inertial frames of reference, indicates that

the twin who

ventures into space ages less

than the one who stays behind.)

Relativity 'allows' for

travel into the future

but not into the past. Because an astronaut who leaves the Earth ages slower than his/her contemporaries left on Earth, the astronaut will return to Earth in say 100 years of 'Earth time' but maybe only 60 years of 'astronaut time' (depends on the speed of travel). Thus he returns to the Earth's future.

1. Explain the features of the ether?

2. Describe the Michelson-Morley experiment and explain the implications of the findings? 3. Explain the meaning of an inertial frame of reference?

4. Explain the significance of the constancy of the speed of light c?

5. Explain qualitatively and quantitatively the consequences of special relativity including lack of simultaneity, equivalence of mass and energy, length contraction and time dilation?

(20)

Describe, with the aid of a diagram, how Michelson and Morley attempted to measure the speed of the Earth through the ether and the results they obtained.

Einstein first stated the basic premise of special relativity. He said that the speed of light is constant and is independent of the speed of the source of light or of the observer. Using this and Einstein's 'thought experiment' of a simple 'light clock' in a moving train, explain why time dilation occurs.

Muons are unstable short-lived subatomic particles that can be created in the upper atmosphere when cosmic rays collide with air molecules. They have a lifetime of 2.2 ~s

(in their reference frame). If they travel at 0.999c, what is their lifetime relative to an observer on Earth?

The speed of light c is constant and is equal to 3.0 x 108 _{m.s-1. Clearly explain why an} object travelling at a speed less than c cannot be accelerated to c.

Explain how special relativity makes it possible for an astronaut to travel 'into the future'. Why is this unlikely to occur?

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Moving charges in a magnetic field experience a _ _ _ _ _

The doughnut shaped region around the Earth where moving charges are trapped is called the radiation belts.

A conductor of length 50 cm is placed at right angles to a magnetic field of strength 10 T. If the conductor carries a current of 2.5 A, calculate the force acting on the conductor.

What is the direction of the force acting on the conductors in the diagrams? e e e e

X X X

e e e e t c X X X Current

I~

X magnetic field into page e e e e ' 0 e field out of the page X X X

e e II II

A 'current balance' can be used to determine the factors affecting the force on a current-carrying conductor in a magnetic field. Which graph below best shows the relationship between the currents and the conductor separation?

d d d 11d

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A single current-carrying coil of wire is placed in a magnetic field, What is the torque on the coil at the instant shown and in which direction will it rotate? Axis ,.B _ _ --,.... _ _ -;C I Plane of coil is parallel to magnetic field of 0.2 T Length of AB and CD

=

4 cm Length of BC = 2 cm

Electric motors convert _____ energy into _____ energy,

DC electric motors consist of four essential components, They are _ _ _ _ _

_____ and _ _ _ _ _

The direction of the current in a simple DC motor is reversed each half cycle by a _____ ring , Current is brought to (and from) this device by carbon

The field structure of a simple DC electric motor can be provided either by _ _ _ _ _ magnets or current-carrying _ _ _ _ _

The motor effect is put to good use in devices such as moving _____ meters and

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(23)

Moving charges in a magnetic field experience a force.

These moving charges interact via their associated magnetic field.

The doughnut shaped

Van Allen radiation belts

trap charged particles from space. In doing so they protect life on Earth from this dangerous radiation.

A current-carrying conductor in a magnetic field experiences a force given by F

=

BIl sin 9. This is the

motor effect.

From the equation it can be seen that the force depends upon: the magnetic induction (B), the current in the conductor

W,

the length of the conductor (l) and the angle between the field and the conductor (9). When the conductor is parallel to the field (9 = 0°) the force is zero and is a maximum when the conductor is perpendicular to the field.

The

right-hand palm rule

allows the direction of the magnetic force to be determined. This states that: If the fingers of the right hand point in the direction of the magnetic field (B) and the thumb points in the direction of the conventional current (1) then the palm points in the direction of the B force (F) as shown.

I

F

Two

parallel current-carrying conductors

exert forces on each other. The force F per unit length L between two wires

carrying current I, and 12 respectively separated by a distance d Right-hand palm rule

in a vacuum is given by

~

=k 1112 . When the currents are in the same direction, the

L d

wires attract; when the currents are in opposite directions the wires repel.

Torque

is the turning effect of a force and is given by't = Fp where F is the force and p

is the perpendicular distance from the axis to the line of action of the force.

A

current-carrying coil

in a magnetic field experiences a torque given by't = nB1A cos

9.

This is put to practical use in electric motors.

Electric motors

convert electrical energy into mechanical energy.

DC electric motors

consist of an armature (the coi!), field structure (the magnets), commutator and brushes. Current flowing through the armature interacts with the

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magnetic field to produce a torque causing the armature to rotate. In the diagram below, the armature would begin to rotate in a clockwise direction (viewed from the commutator end). Split ring commutator

,. +

~~ Carbon brush Simple DC electric motor

Armature

A split-ring commutator reverses the direction of the current in the armature sides each half cycle. This allows the armature to continually rotate in the same direction by ensuring that the current always flows in the same direction around the armature. (Without it, the armature would simply come to rest with its plane perpendicular to the plane of the magnetic field.) Carbon brushes take current to and from the armature. The field structure can be produced by permanent magnets or by current-carrying coils (electromagnets). The latter are generally stronger and so a larger torque is possible. In real motors, the 'pole pieces' that make up the field structure are generally curved. This ensures a steady torque as the armature always lies parallel to the field and so 't = nBIA where n is the number of turns (coils), B is the magnetic induction, I is the current in the armature and A is the area of the coil.

Practical examples ofthe motor effect include moving coil meters and loudspeakers. Current flowing in the meter or loudspeaker interacts with the magnetic field causing movement of the meter pointer or loudspeaker diaphragm. The moving coil meter is the basis of the ammeter and voltmeter.

1. List the factors affecting the magnitude of the force on a current-carrying conductor in a magnetic field?

2. Solve problems using F

=

BII sin

e

3. Describe an experiment to demonstrate the motor effect? 4. Use the equation

~

==k 11c/2

5. Explain the rotation of a current-carrying coil in a magnetic field and use the equation 7:

=

nB1A cos

e

6. Describe the principle of operation of a simple DC electric motor and the purpose of the armature, field structure, split-ring commutator and brushes?

(25)

x x x x x x x A charge moves in a magnetic field as shown.

The direction of the initial force on the charge x x x x x x x is:

up the page down the page _+Q x x x x x x x

into the page out of the page.

x x x x x x x

Two parallel current-carrying wires are separated by a distance d and exert a force per unit length of F newtons per metre. If the current in one of the wires is tripled and the separation doubled, the new force is:

3FI8 9FI8 3FI4 3FI2

A rectangular

current-B Current _Magnetic carrying coil ABCD is placed in a

magnetic field as shown. The side which experiences a force down the page is:

AB BC c CD

No side experiences any force since the coil is parallel to the

A

, ----;<---'~ field is perpendicular

-~,

~

?

to the plane of

~

/3"/

-

'-»> the page. Coil is

/ 0 parallel to the

/ ~ field.

Axis field.

A rectangular coil, 5 cm x 3 cm, of 1500 turns is placed in a magnetic field of intensity 0.8 T. A current of 0.1 A flows in the coil.

What is the relationship between the coil and the field when the torque is a maximum?

What is the maximum torque on the coil?

What is the torque when the coil is set at 45° to the magnetic field? A moving coil meter is shown. Briefly describe the

principle of operation of the meter.

scale

N

s

Radial

magnetic field Soft iron Fine wire

spring core

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The discoverer of the generation of an electric current by a magnet moving near a conductor was Michael _ _ _ _

When the man in 1 above used a magnet and a coil of wire, he found a current was

induced as long as there was between the coil and the magnet.

Electromagnetic induction involves the conversion of _ _ _ _ energy into _ _ _ _ energy.

Magnetic flux is a measure of

the number of lines of force per unit area the number of lines of force per unit volume the number of lines of force.

Another name for magnetic flux is magnetic induction. True or false? _ _ _ _ Faraday's law states that the induced emf is proportional to the rate of change of

Lenz's law is a consequence of the conservation of charge

conservation of energy.

conservation of momentum

The direction of the induced current in the diagram is: down the page

up the page out of the page into the page

The induced emf in an electric motor:

is called the forward emf

opposes the supply emf

is only present as the motor first starts.

Field out of page

To prevent an electric motor burning out when it is first turned on a _ _ _ _ resistance is placed in series with the motor.

Changing magnetic fields induce circular currents in bulk conducting material.

The currents in Q11 above can be used in induction _ _ _ _ and in electromagenetic

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(27)

Michael Faraday is credited with the discovery of the generation of an electric current in a conductor by a moving magnet.

Coil

Magnet

Galvanometer Faraday found that when a magnet is pushed

into a coil of many turns connected to a sensitive current-measuring device (a galvanometer) a current is produced as long as the magnet is moving relative to the coil. If there is no movement between the coil and magnet, no current is produced. When the magnet is withdrawn from the coil, current is again produced but it flows in the opposite

direction to that when the magnet is inserted. Magnet moving towards _{a conducting coil}

Electromagnetic induction involves the conversion of mechanical energy into electrical energy.

Magnetic flux is a measure of the number of lines of force emerging from a given area as shown in the diagram on the right.

Magnetic flux density is synonymous with magnetic induction. The greater the density of flux lines (also called 'lines of force'), the greater the magnetic field.

Magnetic flux

Faraday's law states that the induced emf is proportional to the rate of change of magnetic flux. That is, the faster the magnetic flux through the circuit changes, the greater will be the emf induced. This can be made to happen by moving the magnet (or coil) faster, and/or increasing the magnetic induction and/or by having more coils.

Lenz's law states that the induced emfis in such a direction that the current it produces opposes its production. This is a consequence of the law of conservation of energy. If the emf (and its associated current) aided the production instead of opposing it we could create an infinite amount of energy from a finite amount of work - we would effectively get 'something for nothing'. This would violate energy conservation.

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The direction of the induced current can be found by the

right-hand palm rule.

When a motor is operating it involves relative motion between a conductor and magnetic field and so it produces a

back

emf. This

opposes the supply emf and limits the

current flowing in the motor. This in turn limits the speed of the motor - the motor is self-regulating.

When an electric motor is starting, the back emf

will be small and so the current in the coil from the supply will be large. (Remember that the back

emf opposes the supply voltage.) To keep the

current within manageable limits to prevent it burning out the motor, a

starting resistance

is

Fingers Thumb points in direction of induced current point in

l

direction .*-;~=±==7

-?

of magnetic _ field Palm points in direction of opposing force

Right-hand palm rule

placed in series with the coil. As the coil speeds up (and hence the back emf increases)

the starting resistance can be decreased and eventually removed.

Circular eddy currents

are induced in bulk conductors in the presence of changing magnetic flux. These eddy currents obey Lenz's law. They also represent a waste of energy as they cause heating of the conductor.

Eddy currents are put to good use in

induction cookers

and in

electromagnetic

braking.

AC flowing in coils placed below a glass-ceramic cook top induces eddy currents in the metal pans placed on top, heating the pan and its contents. In certain modern trains, electromagnets are brought near to the moving metal wheels inducing eddy currents in the wheels. These currents flow in a direction to oppose their cause in agreement with Lenz's law. This provides a retarding force on the wheels that stops the wheels (and hence the train). Braking is very smooth since the force is greatest when the wheels are turning fastest and gets less as the speed of the wheels gets less.

1. Describe Faraday's discovery of electromagnetic induction?

2. Define magnetic flux, magnetic flux density and magnetic induction? 3. Qualitatively and quantitatively describe Faraday's law?

4. Explain the cause of Lenz's law and relate this to back emf, eddy currents and electromagnetic braking?

(29)

Below is a schematic diagram of a simple experiment to illustrate electromagnetic induction, similar to one that you could do at school. Explain what is required for a current to be induced and give three ways in which the induced current can be made larger (assuming you had access to additional equipment). Explain your reasoning.

Coil

Magnet

Galvanometer

A physics teacher was overheard telling a class that 'Lenz's law is simply a consequence of energy conservation'.

What is Lenz's law?

How does this law relate to energy conservation.

Many electric motors, especially large ones, have a starting resistance. Clearly explain why this is needed.

A student set up an experiment similar to that in the diagram below. Explain the student's observations.

Aluminium disk spins freely on its axle

Solid disk stops spinning when magnetic

field brought close to disk A disk with slits continues to spin for much longer than a solid disk in the presence of a magnetic field

(30)

Generators use the principle of _____ induction to convert _____ energy

into energy.

AC generators have four essential features. These are:

_ _ _ _ _ _ _ _ _ _ _ _ _ _ and _ _ _ _ _ _ _ _ _ _ _ _ _ _

DC generators also have the four essential features of AC generators but they also

have a . This is used to convert into _ _ _ _ _

Generators work by moving a conducting coil to a magnetic field. As the

coil rotates, the magnetic through the coil varies and so a/an is

induced between the ends of the coil.

Maximum emf is produced when the coil passes through the horizontal plane. True or

false? _ _ _ _

In what direction is the emf induced in the generator (Lenz's law)? _ _ _ _ _

Real generators differ from the simplified idealised models discussed in class. Three ways in which they differ are:

___________________________________ and

The biggest loss of energy from where it is generated in the 'power station' to the

consumer occurs in the where some of the electrical energy is

converted into _ _ _ _ _

Electricity has impacted on society in a number of ways including:

_________________________________ and

High voltage power lines are said to be associated with increased risk of certain _ _ _ _ . There is currently evidence about these alleged health risks.

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(31)

Electric generators

use the principle of

electromagnetic induction

to convert

mechanical energy

into

electrical energy

(the reverse of electric motors). The mechanical energy can be supplied by steam derived from water heated by the combustion of fossil fuels or the heat from nuclear reactors, by the kinetic energy of falling water (hydroelectricity) or wind generators.

Generators consist of an

armature, field

structure, slip rings

and

brushes

as in the diagram.

In addition to the structures in 2 above, DC generators also have a

commutator

whose role is to

convert AC into DC.

Generators work by moving a coil

relative

to a magnetic field. Consider the simplified diagram of an AC generator. As the coil is made to rotate, the

magnetic

flux through the coil varies,

from a minimum when the coil is parallel to the field, to a maximum when the coil is

Carbon brushes held in place by springs

Field magnets

AC generator

perpendicular to the field. As a result, an emf is induced between the ends of the

coil and current can flow in an external circuit. Faraday's law says that the emf is

proportional to the

rate of change

of magnetic flux

through the circuit. Hence the emf varies from a

maximum as it passes through the horizontal plane (the rate of change is greatest here) to a minimum as it passes through the vertical plane. In agreement with Lenz's law, the emf

is induced in such a direction that its associated current flows in a direction so that its magnetic field

opposes

the cause of the induced

emf.

Time

2 3 4 5

AC generator output

Real generators

differ from the simplified model used above. In general, real generators use electromagnets to produce the magnetic field rather than permanent

(32)

magnets; have hundreds of coils wound around a soft iron core; have the armature as the stator (the non-moving part) in AC generators - it is the rotor in DC generators; have three pairs of electromagnets place at 1200

to each other (producing three-phase power).

Some

energy is lost in transmission

from the power station to where it is used. This can occur because of friction in the rotor bearings;

heat generated by currents in

the transmission cables

and energy losses in the generator's iron core.

Electricity

has profoundly affected society. The discovery of how to generate large amounts of electricity and transport it to distant sites led to electricity becoming the primary source of industrial and domestic energy. This exacerbated some of the problems of the industrial revolution - the shift of the population from the country to city slums, longer working hours ... as well as the associated current environmental issues of global warming and acid rain.

Controversy exists about the alleged

harmful affects

of living close to power lines. A number of scientific investigations have been done on the relationship between the occurrence of certain cancers and the proximity of living near high voltage power lines. The results are

conflicting or inconclusive:

some investigations show a statistically valid association; others do not. The jury is still out.

1. Identify the main components of a generator? 2. Compare a generator with a motor?

3. Describe the principle of operation of AC and DC generators?

4. Compare the advantages and disadvantages of AC and DC generators?

5. Explain how energy is lost as it is transmitted from the generator to the consumer? 6. Describe the effect of electricity on society and the environment?

(33)

The device that changes the direction of the current in a DC generator is the:

armature brush

commutator slip rings

In a simple AC generator, a coil of wire is placed between the poles of two magnets and is rotated in an anticlockwise direction as shown. Sketch the expected output on the axes provided at the positions indicated by the numbers 1-5. Repeat on the second set of axes for a DC generator.

~

0 5;:>

~

0 5;:>

_~

2 3 4 5 OJ OJ OJ OJ .l!l .l!l ~ ~ Time

The first continuous current-generating device was invented by Michael Faraday and was called Faraday's disk dynamo. It consisted of a copper disk that could be rotated between the poles of a strong magnet. Copper brushes carried current away. Briefly explain how this works.

Clearly describe the effects of the development of AC and DC generators on society and the environment.

Copper brushes

(34)

Transformers are used to electrical energy from one circuit to another. They can also be used to change the AC _ _ _ _

Transformers consist of three essential features, a _____ coil, a _____ coil

and a soft core.

_____ voltages in the coil induce changing voltages in the _ _ _ _ _ coil by the process of mutual induction.

Transformers operate on only.

In a step-down transformer:

the current in the secondary is less than the current in the primary the voltage in the secondary is greater than the voltage in the primary the voltage in the secondary is less than the voltage in the primary.

In a step-up transformer there are more coils in the primary than in the secondary. True or false? _ _ _ _ _

In an ideal transformer, the power in the secondary is same/different from the power in the secondary? _ _ _ _ _

In a step-up transformer, compared to the secondary, the voltage and current in the primary are respectively:

bigger and bigger bigger and smaller smaller and bigger

A transformer has a primary of 1000 turns and is used to step-up the voltage from 12 V to 240 V.

How many turns are needed in the secondary? (Assume 100% efficiency.) What current flows in the primary if the secondary is operating at 12 W?

To minimise energy losses in transmission, electricity is transmitted at voltages as high

as V.

Transformers in electricity _____ are used to reduce the voltages to suitable amounts for homes and industry.

Many household appliances contain _ _ _ _

Energy losses due to eddy currents are minimised in transformers by having the soft iron core _ _ _ _

Transformers and generators have had a _ _ _ _ impact on our lives.

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(35)

Transformers are devices for transferring electrical energy from one circuit to another. They also allow AC voltages to be easily changed in magnitude.

Transformers consist of two coils the primary and the secondary both of which are wrapped around the same soft iron core. The primary coil has alternating voltages supplied to it. The secondary has alternating voltages induced in it.

Changing AC voltages in the primary sets up a changing magnetic flux in the soft iron core. This sets up a changing magnetic field in the secondary coil and so an emfis induced in it. The process is called mutual induction.

Transformers operate on AC only and not DC. This is because a changing magnetic field is required for electromagnetic induction to occur.

A step-up transformer increases the voltage in the secondary coil compared to the primary coil. Conversely, in a step-down transformer the secondary voltage is less than the primary voltage.

A step-up transformer has more coils in the secondary than in the primary. In a step-down transformer, the secondary has fewer coils than the primary.

The conservation of energy necessitates that in an ideal transformer, the power in the primary circuit is equal to the power in the secondary circuit. Since P

=

VI it follows that as voltage increases, the current decreases.

It follows that in a step-up transformer, the voltage in the secondary is larger than the voltage in the primary but the current in the secondary is less than the current in the primary.

In an ideal transformer (100% efficient) the voltage, current and number of turns

V

n

I

(coils) are related by

v

P

=

L

=

-IS

5

ns

P

Power is transmitted at extremely high voltages, as high as 500 kV (500 000 V). This is done to reduce the current and so lessen the energy losses in the transmission lines where the heating effect in the wires is proportional to the square of the current. Transformers in sub-stations are used to change the voltage (and current) to values suitable for use in industry and households by stepping the voltage down. This is generally to 240 V for household use and 415 V for industriallcommercial use.

(36)

Many home electrical appliances such as TVs and computers require voltages other than the 240 V supplied to homes. Transformers are able to

change the voltage

to the required amount.

Transformers limit eddy currents in their core by having the

core made of individual

sheets

(laminates) electrically insulated from each other. This lessens energy losses due to heating of the iron core.

The invention of transformers (along with generators) meant that electricity could be easily distributed around the country and so electricity became the energy source of the industrialised world. This has had

significant impact on the way we live.

No longer are we restricted to daylight hours for work. We can now communicate almost instantaneously via radio, TV, mobile phones (the batteries of which require charging), etc. Greenhouse gas emission from fossil-burning fuels is a significant environmental issue. Imagine your life without electricity.

1. Explain the use and principle of operation of transformers? 2. Compare step-up and step-down transformers?

3. Solve problems using V p

=:2.e.. =

~

Vs ns Ip

4. Relate voltage and current changes to energy conservation?

5. Explain the role of transformers in electricity sub-stations and in the home? 6. Describe how transformers have impacted on society?

(37)

A transformer can be used: to increase voltage to decrease current both a and b

to increase power.

A schematic diagram of an electric transformer is shown.

Primary coil

What is the purpose of transformers?

Secondary coil

Output voltage

Clearly explain how a transformer works, describing the role of each of the labelled components.

If the primary has 1000 turns and the secondary has 250 turns, what is the secondary voltage if the primary voltage is 240 V? (Assume 100% efficiency.)

Eddy currents can be a problem in power generation. Discuss how these eddy currents arise and how they can be minimised to lessen their impact.

The transfer of electrical energy from electric power stations to the consumer is not 100% efficient. Briefly discuss the energy losses involved and how they are kept as low as possible.

(38)

AC electric motors have a _____ and a _ _ _ _ _

AC motors, unlike DC motors do not require a _ _ _ _ _

The most common type of AC motor is the _____ motor.

These motors work on the principle that a _____ magnetic field will exert a _____ on a stationary coil.

A rotating magnetic field can be relatively easily produced by using _ _ _ _

A field like that above will _____ a current in the coil. Interaction of the two fields results in the coil being around.

AC induction motors are widely used because of their _ _ _ _ _ _ _ _ design,

relatively cost and their _ _ _ _ _ _ _

The electric motor used in small appliances such as food processors and electric power saws is most likely to be:

a single-phase AC induction motor a three-phase AC induction motor a DC motor

an AC synchronous motor.

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(39)

AC electric motors have two essential features - a rotor (the moving part) and the stator (the stationary part). Some also have slip rings to bring electricity to and from the motor.

AC electric motors have the advantage over DC motors in that they do not require a commutator (the AC automatically reverses 50 times per second). Commutators have problems associated with sparking, ozone production from the sparking and energy loss in the brushes. In addition there are problems with the wearing of the brushes.

The most common type of AC motor is the induction motor.

AC induction motors work on the principle that a rotating magnetic field will exert a torque on a stationary coil.

AC can relatively easily produce a rotating magnetic field.

AC induction motors work by having the stator produce a rotating magnetic field. This induces (hence induction motor) an electric current in the rotor by the process of electromagnetic induction. This current produces a second magnetic field. The two magnetic fields interact with the rotating field dragging the rotor around.

AC induction motors are cheap, efficient and simple to manufacture which accounts for their wide use. In particular they are used for low power

«

1 kW) applications in homes.

95% of all electric motors are single-phase induction motors. These represent the majority of motors in the home. Industry tends to use three-phase induction motors since they can have larger power ratings.

1. Describe the main features of an AC electric motor?

2. Describe the principle of operation of AC induction motors? 3. Relate the power rating of AC motors to their uses?

(40)

In an AC induction motor:

current is induced in the rotor current is induced the stator

current is supplied to the rotor from an external source a commutator converts AC to DC.

AC induction motors have the advantage over DC motors that: they don't require a commutator

they are simple to design they are relatively cheap all of the above.

Many power tools and appliances used in the home have relatively low power -0.5-1 kW. Explain why these are most likely AC induction motors.

(41)

The German Geissler invented a pump efficient enough to reduce the pressure in a glass tube to a small fraction of normal air pressure. By placing metal _ _ _ _ in these tubes it was possible to get to flow through the tubes. As the pressure is reduced in these tubes, different patterns were produced that depended on the gas pressure.

At a low pressure of -0.01 kPa a green glow appears in the end of the glass tube opposite the negative electrode, the _ _ _ _

This glow was found by Crookes to be caused by emanating

from the negative electrode.

Charged particles can be affected by:

electric fields magnetic fields both electric and magnetic fields. Various cathode ray tubes and certain properties of cathode rays are shown. Draw a line that correctly links the tube with the property.

Cathode ray tube Property

Maltese cross rays carry energy and momentum

magnet brought near rays travel in straight lines fluorescent screen

paddle wheel i rays are deflected by magnetic fields

The nature of cathode rays, _ _ _ _ or , was long debated.

A parallel plate capacitor is a useful device because it provides a _ _ _ _ electric field, the intensity of which is calculated from the equation _ _ _ _

A charge of 3.2 x 10-19 C moves at right angles to a magnetic field of 0.1 T at a speed of

2.0 x 107 _{m.s-1. What is the magnitude of the force acting on the charge?}

J.J. Thomson successfully measured the _ _ _ _ to -,-_ _ _ ratio for cathode

rays.

A cathode ray tube has three main components _ _ _ _ _ _ _ _ _ --,-__ and Cathode ray tubes are found in _ _ _ _ _ _ _ _ and _ _ _ _

The cathode ray _ _ _ _ is a useful experimental measuring device. The _ _ _ _ nature of electrons is used in electron _ _ _ _

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(42)

In 1855 the German glassblower Heinrich Geissler invented a vacuum pump that was efficient enough to

reduce the pressure

inside a strong glass tube to 0.01 % of normal air pressure. In 1862 Julius Plucker found that by placing metal

electrodes

in the ends of one of Geissler's tubes and joining the electrodes to a high voltage source he could get

electricity to flow through the tube.

Plucker showed that as the pressure is reduced in the

discharge tube,

a series of changes progressively takes place. Gas discharge tubes produce different

striation

patterns

determined by the gas pressure.

Crookes' dark space

Negative

glow column Positive

Faraday's dark space Discharge tube Anode glow +

At a pressure of -0.01 kPa a green glow appears in the glass tube behind the anode and opposite the negative electrode

(cathode).

In 1875 Crookes deduced that the green glow was caused by

cathode rays

that travelled from the cathode.

Cathode ray tubes

allow the manipulation of moving charged particles by electric and magnetic fields.

Cathode ray tubes come in a range of types including

Maltese

cross

and a

paddle wheel.

From these tubes we can deduce

various properties of the cathode rays (see diagrams). The Maltese cross tube shows they travel in straight lines; the tubes with a fluorescent screen show they are deflected by magnetic and electric fields and the paddle wheel tube shows they carry energy and momentum.

Maltese cross