Chapter 23 Laws of Electromagnetic Induction

CAMBRIDGE A – LEVELCAMBRIDGE A – LEVEL

PHYSICS

LAWS OF

ELECTROMAGNETIC

INDUCTION

LEARNING OUTCOMES

No. LEARNING OUTCOMEI I n t e r p r e t w h a t i s m a g n e t i c f l u x . A p p l y u n d e r s t a n d i n g o f

m a g n e t i c f l u x t o c a l c u l a t e m a g n e t i c f l u x .

ii W h a t i s m a g n e t i c f l u x l i n k a g e ?

iii A p p l y t h e k n o w l e d g e o f m a g n e t i c f l u x l i n k a g e t o

u n d e r s t a n d t h e c o n c e p t o f e l e c t r o m a g n e t i c i n d u c t i o n .

iv A p p l y F a r a d a y ’ s L a w o f E l e c t r o m a g n e t i c I n d u c t i o n t o

c a l c u l a t e t h e m a g n i t u d e o f i n d u c e d e . m . f a n d c u r r e n t i n

s i t u a t i o n s i n v o l v i n g e l e c t r o m a g n e t i c i n d u c t i o n .

v A p p l y L e n z ’ s L a w t o d e t e r m i n e t h e d i r e c t i o n o f t h e f l o w

i n d u c e d c u r r e n t i n s o l e n o i d s / c o i l s i n v o l v i n g

e l e c t r o m a g n e t i c i n d u c t i o n .

MAGNETIC FLUX

• To understand the concept of• To understand the concept ofmagnetic flux, we will use waterflowing through the mouth of awater bottle as an analogy.

• How much water flows throughthe mouth depends on theamount of water flowing and thesize of the opening.

MAGNETIC FLUX• If we instead consider the flux of a• If we instead consider the flux of a

magnetic field instead of the flow ofwater:–the amount of water flowing can be

taken to be the magnetic flux density,and

–the size of the opening of the bottlecan be considered as the surface areaof the coil.

MAGNETIC FLUX• Magnetic flux is proportional to• Magnetic flux is proportional to

these two quantities.

• What happens when we tilt thebottle? Does the amount of waterflowing into the mouth change?

MAGNETIC FLUX• Definition: “The magnetic flux, Φ• Definition: “The magnetic flux, Φ

through a coil is the product of thecomponent of magnetic flux density,

that is perpendicular to thesurface of the coil with the surfacearea, of the coil.”

• Mathematically,

MAGNETIC FLUX• Mathematically,• Mathematically,

where:o� = is the magnetic flux, weber (Wb),

o� = magnetic flux density, Tesla (T),

o� = cross sectional area of the coil, m2,

o� = angle between the normal to the coil and the magnetic field lines.

MAGNETIC FLUX

Figure 28.12, page 439, Chapter 28: Electromagnetic Induction; Cambridge

International AS and A Level Physics Coursebook, Sang, Jones, Chadha and Woodside,

2nd edition, Cambridge University Press, Cambridge, UK,2014.

MAGNETIC FLUX• The unit for magnetic flux is the• The unit for magnetic flux is the

weber (Wb).

• Definition: “One weber is equal tothe magnetic flux passing through anarea of � where the magneticflux density is equal to .”

EXAMPLESQuestions 2 and 3,

Set 59:

Electromagnetic

Induction and

Electromagnetic

Waves; page 185;

PROBLEMS IN

PHYSICS ; E.D

GARDINER, B.L

McKITTRICK;

McGraw – Hill Book

Company, Sydney

1985.

M AG N E T I C F LU X v s .

M AG N E T I C F LU X L I N K AG E

M AG N E T I C F LU X v s .

M AG N E T I C F LU X L I N K AG E• The magnetic flux is defined for the flux

� �

�� � �����

• The magnetic flux is defined for the fluxthrough one turn of a coil.• What happens if the coil has more than

1 turn?• We then use the magnetic flux linkage.• Definition: “The magnetic flux linkage

is the product of the number of turns,�and the magnetic flux, �.”• Mathematically, magnetic flux linkage =�� � �����.

EXAMPLESQuestions 7, 8 and

9, page 441,

Chapter 28:

Electromagnetic

Induction;

Cambridge

International AS

and A Level Physics

Coursebook, Sang,

Jones, Chadha and

Woodside, 2nd

edition, Cambridge

University Press,

Cambridge,

UK,2014.

E L EC T R O M AG N E T I C

I N D U C T I O N

E L EC T R O M AG N E T I C

I N D U C T I O N• Electromagnetic induction is the• Electromagnetic induction is the

process of generating a potentialdifference across then ends of aconductor by changing themagnetic flux through it.

• We will look at a few examples ofelectromagnetic induction in thenext few slides.

E L EC T R O M AG N E T I C

I N D U C T I O N

E L EC T R O M AG N E T I C

I N D U C T I O N

Figure 28.3, page 436, Chapter 28: Electromagnetic Induction; Cambridge

International AS and A Level Physics Coursebook, Sang, Jones, Chadha and

Woodside, 2nd edition, Cambridge University Press, Cambridge, UK,2014.

E L EC T R O M AG N E T I C

I N D U C T I O N

E L EC T R O M AG N E T I C

I N D U C T I O N• The diagram above show a• The diagram above show a

possible situation where an e.m.fcan be induced.• An e.m.f is induced across the

ends of the coil when the needleof the meter deflects.• When e.m.f is induced, the coil

acts like a battery.

E L EC T R O M AG N E T I C

I N D U C T I O N

E L EC T R O M AG N E T I C

I N D U C T I O N

Diagram 29.1(b), Chapter 29: Electromagnetic Induction, Section 29.1, page 958, Sear’s

and Zemansky’s University Physics, Young and Freedman, 13th edition, Pearson

Education, San Francisco, 2012.

• The solenoid is attached to a

galvanometer and has no power source.

• However, the needle of the meter

deflects when the bar magnet is moved

towards or away from the coil.

• The magnetic field lines around the bar

magnet will pass through the opening

of the solenoid.

• This produces a magnetic flux linkage

between the turnings of the

coil/solenoid.

E L EC T R O M AG N E T I C

I N D U C T I O N

E L EC T R O M AG N E T I C

I N D U C T I O N• The movement(s) of the bar magnet

causes a change in the magnetic flux

linkage between the turnings in coil.

• What happens to the deflection of the

needle when the following changes

are made?

I. The speed at which the magnet

is moved is changed?

II. We use a stronger bar magnet?

III. We change the cross sectional

area of the solenoid?

IV. We vary the number of turns in

the solenoid?

E L EC T R O M AG N E T I C

I N D U C T I O N

E L EC T R O M AG N E T I C

I N D U C T I O N

Figure 28.4, page 436, Chapter 28: Electromagnetic Induction; Cambridge

International AS and A Level Physics Coursebook, Sang, Jones, Chadha and

Woodside, 2nd edition, Cambridge University Press, Cambridge, UK,2014.

E L EC T R O M AG N E T I C

I N D U C T I O N

E L EC T R O M AG N E T I C

I N D U C T I O N• Another way to look at• Another way to look at

electromagnetic induction is bydetermining whether there aremagnetic field lines being “cut”by a conductor.• The horizontal movement of the

conductor “cuts” magnetic fieldlines thus inducing an e.m.facross the ends of the conductor.

E L EC T R O M AG N E T I C

I N D U C T I O N

E L EC T R O M AG N E T I C

I N D U C T I O N• Electromagnetic induction in this• Electromagnetic induction in this

case is due to relative motionbetween the magnetic field andthe conductor, either:• the conductor is moved to “cut”

the magnetic field lines, or• the magnetic field is moved so that

the lines are “cut” by theconductor

E L EC T R O M AG N E T I C

I N D U C T I O N

E L EC T R O M AG N E T I C

I N D U C T I O N

Figure 28.5, page 437, Chapter 28: Electromagnetic Induction; Cambridge

International AS and A Level Physics Coursebook, Sang, Jones, Chadha and

Woodside, 2nd edition, Cambridge University Press, Cambridge, UK,2014.

• The magnitude of the

motional e.m.f. depends on:

� the speed of the

relative motion of the

conductor,

� the length of conductor,

and

� the magnetic flux

density.

EXAMPLESEXAMPLESQuestion 1, page 438, Chapter

28: Electromagnetic Induction;

Cambridge International AS and

A Level Physics Coursebook,

Sang, Jones, Chadha and

Woodside, 2nd edition,

Cambridge University Press,

Cambridge, UK,2014.

FARADAY’S LAW

• To summarise, the factor that• To summarise, the factor thatdetermines the magnitude of theinduced e.m.f is the rate at whichmagnetic flux linkage is changed.

• This is stated as Faraday’s Law ofelectromagnetic Induction.

• Definition: “Faraday’s Law of• Definition: “Faraday’s Law ofElectromagnetic Induction statesthat the magnitude of theinduced e.m.f is directlyproportional to the rate ofchange of magnetic flux linkage.”

FARADAY’S LAW

• Mathematically, Faraday’s Law is• Mathematically, Faraday’s Law isgiven as:

• The negative sign is due to Lenz’slaw. If we need to calculate themagnitude of the induced e.m.f, weignore the negative sign.

FARADAY’S LAW

• Recall that :

�

• Recall that :

• Hence we can get an induced e.m.f,, by varying w.r.t time, by

varying:o the magnetic flux density, �,o the cross sectional surface area, �,o the angle between B – field and the

normal to the surface, �.

FARADAY’S LAW

�

�

�

• We can use Faraday’s Law to find the

e.m.f, � across a long straight conductor

that “cuts” across a magnetic field:

� � ���

where:� � = the speed of the conductor, m s-1

� �= length of conductor, m

� � = magnetic flux density, T

FARADAY’S LAW

EXAMPLESEXAMPLES

Question 4, page 440, Chapter 28: Electromagnetic Induction; Cambridge

International AS and A Level Physics Coursebook, Sang, Jones, Chadha and

Woodside, 2nd edition, Cambridge University Press, Cambridge, UK,2014.

EXAMPLESEXAMPLESQuestion 5 and Figure 28.14, page

440, Chapter 28: Electromagnetic

Induction; Cambridge International

AS and A Level Physics Coursebook,

Sang, Jones, Chadha and Woodside,

2nd edition, Cambridge University

Press, Cambridge, UK,2014.

EXAMPLESEXAMPLESQuestions 10 and 11,

page 442, Chapter 28:

Electromagnetic

Induction; Cambridge

International AS and A

Level Physics

Coursebook, Sang,

Jones, Chadha and

Woodside, 2nd edition,

Cambridge University

Press, Cambridge,

UK,2014.

EXAMPLESEXAMPLESExample; Page

340, Chapter 12:

Electromagnetism

; Section 12.3:

Electromagnetic

Induction,

International

A/AS Level

Physics, by Mee,

Crundle, Arnold

and Brown,

Hodder

Education, United

Kingdom, 2008.

EXAMPLESEXAMPLESQuestion 15, Set

59:

Electromagnetic

Induction and

Electromagnetic

Waves; page 186;

PROBLEMS IN

PHYSICS ; E.D

GARDINER, B.L

McKITTRICK;

McGraw – Hill

Book Company,

Sydney 1985.

EXAMPLESEXAMPLESQuestions 16 and 17,

Set 59:

Electromagnetic

Induction and

Electromagnetic

Waves; page 186;

PROBLEMS IN

PHYSICS ; E.D

GARDINER, B.L

McKITTRICK;

McGraw – Hill Book

Company, Sydney

1985.

EXAMPLESEXAMPLESQuestion 3, Set 59:

Electromagnetic

Induction and

Electromagnetic Waves;

page 186; PROBLEMS IN

PHYSICS ; E.D

GARDINER, B.L

McKITTRICK; McGraw –

Hill Book Company,

Sydney 1985.

EXAMPLESEXAMPLESQuestion 6, Set 59:

Electromagnetic Induction

and Electromagnetic Waves;

page 186; PROBLEMS IN

PHYSICS ; E.D GARDINER, B.L

McKITTRICK; McGraw – Hill

Book Company, Sydney 1985.

EXAMPLESEXAMPLESQuestion 6, Set 59:

Electromagnetic

Induction and

Electromagnetic

Waves; page 186;

PROBLEMS IN

PHYSICS ; E.D

GARDINER, B.L

McKITTRICK; McGraw

– Hill Book Company,

Sydney 1985.

Figure 28.26, page 446, Chapter 28: Electromagnetic Induction; Cambridge

International AS and A Level Physics Coursebook, Sang, Jones, Chadha and

Woodside, 2nd edition, Cambridge University Press, Cambridge, UK,2014.

FARADAY’S LAW

Figure 28.27, page 446, Chapter 28: Electromagnetic Induction; Cambridge

International AS and A Level Physics Coursebook, Sang, Jones, Chadha and

Woodside, 2nd edition, Cambridge University Press, Cambridge, UK,2014.

FARADAY’S LAW

• The two previous slides show the• The two previous slides show theuse of a rotating coil to producean e.m.f across the ends of thecoil.

• The direction of the B – field isfixed, but the coil’s rotation willcause (in theequation) to vary sinusoidally.

FARADAY’S LAW

• This causes the magnetic flux• This causes the magnetic fluxlinkage through the coil to varysinusoidally.• Based on Faraday’s law of

electromagnetic induction, theinduced e.m.f,

��

��.

• The induced e.m.f graph is thegraph of the derivative of the fluxlinkage versus time graph.

FARADAY’S LAW

EXAMPLESEXAMPLESQuestions 8 and 9,

Set 59:

Electromagnetic

Induction and

Electromagnetic

Waves; page 186;

PROBLEMS IN

PHYSICS ; E.D

GARDINER, B.L

McKITTRICK;

McGraw – Hill Book

Company, Sydney

1985.

LENZ’S LAWLENZ’S LAW• When induction occurs, the coil /• When induction occurs, the coil /

solenoid becomes a temporarybattery.• How do we determine which end

of the coil / solenoid becomespositive, and which end becomesnegative?• We use Lenz’s Law.

• Definition: “Lenz’s Law states• Definition: “Lenz’s Law statesthat the direction of the inducede.m.f. or current is to produceeffects that oppose the changecausing it”.

LENZ’S LAWLENZ’S LAW

• In other words, the polarity will• In other words, the polarity willbe such that if an inducedcurrent flows, the inducedcurrent will produce a magneticflux that opposes the changingexternal magnetic flux.

• We will look at a few situations tounderstand this better.

LENZ’S LAWLENZ’S LAW

Figure 28.9, page

438, Chapter 28:

Electromagnetic

Induction;

Cambridge

International AS and

A Level Physics

Coursebook, Sang,

Jones, Chadha and

Woodside, 2nd

edition, Cambridge

University Press,

Cambridge, UK,2014.

LENZ’S LAWLENZ’S LAW

• In the example in the previous slide,• In the example in the previous slide,the movement of the conductordownwards will generate an e.m.facross the ends of the conductor.

• This is because the conductor will“cut” the magnetic field lines.

• No current flows as the circuit isincomplete!

LENZ’S LAWLENZ’S LAW

• How do we determine which end• How do we determine which endbecomes positive?

• Answer: Use Fleming’s right hand rule.

LENZ’S LAWLENZ’S LAW

Figure 28.8, page 438,

Chapter 28:

Electromagnetic

Induction; Cambridge

International AS and A

Level Physics

Coursebook, Sang,

Jones, Chadha and

Woodside, 2nd edition,

Cambridge University

Press, Cambridge,

UK,2014.

• The middle finger also points• The middle finger also pointstowards the positive end of theconductor.

• The conductor acts as a source ofe.m.f (like a battery), and currentflows out through the conductorfrom the end that is positive.

LENZ’S LAWLENZ’S LAW

EXAMPLESEXAMPLES

Questions 2, 3 and Figure 28.11, page 439, Chapter 28: Electromagnetic Induction;

Cambridge International AS and A Level Physics Coursebook, Sang, Jones, Chadha

and Woodside, 2nd edition, Cambridge University Press, Cambridge, UK,2014.

E L EC T R O M AG N E T I C

I N D U C T I O N

E L EC T R O M AG N E T I C

I N D U C T I O NFigure 28.22, page

443, Chapter 28:

Electromagnetic

Induction;

Cambridge

International AS

and A Level

Physics

Coursebook,

Sang, Jones,

Chadha and

Woodside, 2nd

edition,

Cambridge

University Press,

Cambridge,

UK,2014.

E L EC T R O M AG N E T I C

I N D U C T I O N

E L EC T R O M AG N E T I C

I N D U C T I O NFigure 28.23, page 444,

Chapter 28:

Electromagnetic

Induction; Cambridge

International AS and A

Level Physics

Coursebook, Sang,

Jones, Chadha and

Woodside, 2nd edition,

Cambridge University

Press, Cambridge,

UK,2014.

EXAMPLESEXAMPLESQuestion 15 and Figure

28.24, page 445,

Chapter 28:

Electromagnetic

Induction; Cambridge

International AS and A

Level Physics

Coursebook, Sang,

Jones, Chadha and

Woodside, 2nd edition,

Cambridge University

Press, Cambridge,

UK,2014.

EXAMPLESEXAMPLES

Question 15 (cont’d), page 445, Chapter 28: Electromagnetic

Induction; Cambridge International AS and A Level Physics

Coursebook, Sang, Jones, Chadha and Woodside, 2nd edition,

Cambridge University Press, Cambridge, UK,2014.

EXAMPLESEXAMPLES

Question 16, page 445, Chapter 28: Electromagnetic Induction; Cambridge

International AS and A Level Physics Coursebook, Sang, Jones, Chadha and

Woodside, 2nd edition, Cambridge University Press, Cambridge, UK,2014.

EXAMPLESEXAMPLESQuestion 19, Set 59:

Electromagnetic

Induction and

Electromagnetic

Waves; page 186;

PROBLEMS IN

PHYSICS ; E.D

GARDINER, B.L

McKITTRICK;

McGraw – Hill Book

Company, Sydney

1985.

EXAMPLESEXAMPLESQuestion 20, Set 59:

Electromagnetic Induction

and Electromagnetic Waves;

page 186; PROBLEMS IN

PHYSICS ; E.D GARDINER,

B.L McKITTRICK; McGraw –

Hill Book Company, Sydney

1985.

EXAMPLESEXAMPLES

Question 24, Set 59: Electromagnetic

Induction and Electromagnetic Waves;

page 186; PROBLEMS IN PHYSICS ; E.D

GARDINER, B.L McKITTRICK; McGraw – Hill

Book Company, Sydney 1985.

EXAMPLESEXAMPLESFigure 12.39;

Page 339,

Chapter 12:

Electromagnetis

m; Section 12.3:

Electromagnetic

Induction,

International

A/AS Level

Physics, by

Mee, Crundle,

Arnold and

Brown, Hodder

Education,

United

Kingdom, 2008.

EXAMPLESEXAMPLES

Figure 12.39; Page 339, Chapter 12: Electromagnetism; Section 12.3:

Electromagnetic Induction, International A/AS Level Physics, by Mee, Crundle,

Arnold and Brown, Hodder Education, United Kingdom, 2008.

EXAMPLESEXAMPLES• Question 6, Paper 4, Summer 2008.• Question 6, Paper 4, Summer 2008.

EXAMPLESEXAMPLES• Question 6, Paper 4, Summer 2008 (cont’d).• Question 6, Paper 4, Summer 2008 (cont’d).

EXAMPLESEXAMPLES• Question 6, Paper 4, Summer 2008 (cont’d).• Question 6, Paper 4, Summer 2008 (cont’d).

EXAMPLESEXAMPLES• Question 6, Paper 4, Summer 2008 (cont’d).• Question 6, Paper 4, Summer 2008 (cont’d).

HOMEWORKHOMEWORK1. Question 7, Paper 4, Summer 2009.1. Question 7, Paper 4, Summer 2009.

2. Question 5, Paper 43, Winter 2010.

3. Question 3, Paper 41, Winter 2011.

4. Question 7, Paper 42, Winter 2012.

5. Question 5, Paper 43, Winter 2012.