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8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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For NJC internal use only; No parts of these slides shall be reproduced without prior permission from NJC.
EMI Lecture
26 Mar 2010
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
2/45
For NJC internal use only; No parts of these slides shall be reproduced without prior permission from NJC.
Worked Example 6.1
The original field is INTO the plane.
This flux is now decreasing.
EMF is induced and current flows.
Induced current flows to maintain
this flux.
Induced current flows in theclockwise direction to set up a Bfield that points INTO the page.
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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For NJC internal use only; No parts of these slides shall be reproduced without prior permission from NJC.
Worked Example 6.1
Original field is pointing OUT of
the page.
Now the flux is decreasing.
To maintain the flux, instead ofcausing further decrease, theinduced current flows in anti-clockwise direction to set up a Bfield pointing OUT of the page.
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
4/45For NJC internal use only; No parts of these slides shall be reproduced without prior permission from NJC.
Lets go back to Page 13
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
5/45For NJC internal use only; No parts of these slides shall be reproduced without prior permission from NJC.
Lenzs Law is a consequence of the law
of conservation of energyP
Q
By simply moving the rodPQ in a magnetic field, we
create a current,I, flowingthrough the resistor R.
In a way, the rod PQ acts
as a source of emf,providing current =I= /R.
Electrical power, P,delivered to R =I2R = 2/R= B2l2v2/R
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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No free lunch in this world
Emf represents theamount of energy
converted from otherforms to electrical. For instance, chemcial ->
electrical in battery
For instance, solar ->electrical in solar panel
So the electrical powerfrom the induced emfdissipated in R must havebeen converted fromother forms.
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
7/45For NJC internal use only; No parts of these slides shall be reproduced without prior permission from NJC.
No free lunch in this world The electrical power from
the induced emfdissipated in R must havebeen converted from thework done by Fapp, thepulling force.
The rod is pulled at
constant velocity i.e. KEof rod is constant.
This means there is a
force opposing Fapp suchthat Fnet = 0 Induced current flows in therod surrounded by magneticfield. This results in a
magnetic force FB2 actingon rod.
FB2
This is Lenzs Law at work!The induced current has toflow in a direction to opposethe change that causes it.
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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No free lunch in this world
Fapp = FB2.
Hence Fapp = BIL (or is it BLv?) What is the rate of work done by
Fapp? Fapp v
BILv = BLv (/R) =
B2L2v2/ R
What happens to this power?
FB2
Mechanical
work done by
Fapp
Electrical
Energy
dissipated
in R
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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Lenzs Law
Used to predict andexplain polarity of
induced emf or direction
of induced current;
Arises from conservationof Total Energy
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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Faradays law
To produce aninduced e.m.f.
Rate of change ofmagnetic fluxlinkage
Rate of flux-cutting
Magnitude ofthe emf is
proportional to
Magnitude ofthe emf is
proportional to
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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Page 16
Emf is induced in a circular loop conductor
when flux through it changes. Emf is induced across a straight conductor
when it cuts across a magnetic field. Now what if a loop conductor moves in a
magnetic field?
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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What happens when a loop conductor cuts themagnetic field?
VL inducedcurrent
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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What happens when a loop conductor cuts themagnetic field?
V
Net induced e.m.f.= zero
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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What happens when a loop conductor cuts themagnetic field?
V
inducedcurrent
Wh h h l d h
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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What happens when a loop conductor cuts themagnetic field?
VLinducedcurrent
Looking at the magnetic flux instead
Area of the coil withinthe magnetic flux density
This area (i.e.magnetic flux) is
increasing as the coilmoves into the field.
Hence, rate of
change of magneticflux induced e.m.f.
Wh t h h l d t t th
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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What happens when a loop conductor cuts themagnetic field?
VLinducedcurrent
Considering fluxcutting by QR
= BLv
P Q
RS
Wh t h h l d t t th
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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What happens when a loop conductor cuts themagnetic field?
V
Looking at the magnetic flux instead
The magnetic flux of coilremains unchanged.Hence, by Faradays
law, no induced e.m.f.
P Q
RS
Wh t h h l d t t th
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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What happens when a loop conductor cuts themagnetic field?
V
If consider flux cutting
Sides PQ and RS
do not cut the Bfield and hence noemf is induced
across PQ or RS.
P Q
RS
Sides PS and QRcut the B field and
hence emf isinduced across PSor QR.
What happens when a loop conductor cuts the
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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What happens when a loop conductor cuts themagnetic field?
V
inducedcurrent
Looking at the magnetic flux instead
The magnetic flux of coilis now decreasing. Hence,
by Faradays law, there is
induced e.m.f.
What happens when a loop conductor cuts the
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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What happens when a loop conductor cuts themagnetic field?
V
inducedcurrent
This induced e.m.f. = Blv
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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Example 7.1
180 ms-150 m
The wingspan cuts the Earths fieldand induces an emf across it.
V
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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What happens if the loop conductorrotates within the B Field?
Ch i th l
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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Changing the angle
Ch i th l
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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Changing the angle
When increases from 0 to 90
Ch i th l
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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Changing the angle
When increases from 0 to 90
Changing the angle
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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Changing the angle
When increases from 0 to 90
Changing the angle
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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Changing the angle
When increases from 0 to 90
Themagnetic fluxdecreases
Changing the angle
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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Changing the angle
How does the induced current flow?
When increases from 0 to 90
Changing the angle
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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Changing the angle
When increases from 90 to 180
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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Changing the angle If the coil rotates constantly (i.e. with
angular frequency ), the magnetic flux
linkage is given by
= NBA cos
= NBA cos (
t)Induced e.m.f. = - (rate of flux change)
=
tNBA
tdt
dNBA
sin
)(cos
=
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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Example 7.3
= NBA cos (t) or
NBA sin (t)
depending if ismax or min at t = 0
At t = 0
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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= NBA cos (t) or NBA sin (t)
= NBA sin(t) or -NBA cos (t) What is important to note is that the
induced emf is sinusoidal! This is the AC voltage you have studied
last year end.
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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Example 7.2
(b) Spinning the coil faster increases and so does
(c) Increasing the magneticfield
B increases and so does
(a) Replacing the coil wirewith one of lowerresistance
No change to ;
R is smaller and henceinduced ,I, increases.
(d) Increasing the number ofturns of wire on the coil
N increases and so does ;
I may not increase. Do you
know why?
How to increase the induced emf, = NBA sin(t) ?
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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Eddy Current
When a conductor is exposed to a changingmagnetic field, circulating current flows withinthe body of the conductor.
This current is called eddy current.
Eddy current flows in a direction that opposesthe change of flux due to Lenz's law, causingdrag forces between the conductor and the
magnet.
Larger the current, the larger the drag force.
http://en.wikipedia.org/wiki/Conductor_(material)http://en.wikipedia.org/wiki/Magnetic_fieldhttp://en.wikipedia.org/wiki/Electric_currenthttp://en.wikipedia.org/wiki/Lenz%27s_lawhttp://en.wikipedia.org/wiki/Lenz%27s_lawhttp://en.wikipedia.org/wiki/Electric_currenthttp://en.wikipedia.org/wiki/Magnetic_fieldhttp://en.wikipedia.org/wiki/Conductor_(material)8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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Demo 1
The flux through the copper ring increases
and decreases as the falling magnetapproaches and recedes from the ring.
Emf is induced.
Induced (eddy) current flows in the ring soas to oppose the change.
What exactly happens to the magnet asthe current flows to oppose the change?
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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Applications of Eddy Current
Magnetic Braking
S
N
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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Applications of Eddy Current
Magnetic Braking see Example 8.1
S
N
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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A li i f Edd C
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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Applications of Eddy Current
Magnetic Braking see Example 8.1
S
N
How to slow down the plateeven more?
Strengthen the field;
Use a plate with lowerresistance;
E l 8 1
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Massbalance
Metal plate moving upand down between
magnetic poles
Example 8.1
A li ti
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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Applications
Metal Detector
See Animation of how VLF metal detectorswork:
http://home.howstuffworks.com/metal-
detector2.htm
Induction Stovetops
A li ti
http://home.howstuffworks.com/metal-detector2.htmhttp://home.howstuffworks.com/metal-detector2.htmhttp://home.howstuffworks.com/metal-detector2.htmhttp://home.howstuffworks.com/metal-detector2.htm8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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Applications
A li ti
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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Application
Speakers and microphones
8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)
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inducedcu
rrent
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The End