CAMBRIDGE A – LEVEL CAMBRIDGE A – LEVEL PHYSICS 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.