notes for chapter 20
TRANSCRIPT
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BMoving magnetic fields inducecurrents
B
Change the strength of B:Induced current
Induced EMF!
vB
Chapter 20.1 Induced EMF and magnetic flux
Moving current loop induces currents
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Fig. 20.2
Chapter 20.1 Induced EMF and magnetic flux
SI units: weber (Wb)
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20.2&20.4 Faradays law of induction
Michael Faraday1791-1867
Faradays law:The induced emf, , in a closed wire is
equal to the time rate of change of the
magnetic flux, B.
An induced emf,
, always gives rise to acurrent whose magnetic field opposes the
original change in magnetic flux.
Lenzs law
Faradays Law and Lenzs Law both
state that a loop of wire will want its
magnetic flux to remain constant.
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2. A circular loop with a radius of 0.20 m is placed in a
uniform magnetic field B=0.85 T. The normal to the loop
makes an angle of 30o with the direction of B. The field
increases to 0.95 T what is the change in the magnetic flux
through the loop?
B=0.85T
B=0.95T
30o
Change in flux?
' 'cos ' cosB
B A BA =
2'
' 30oA A R
= =
= =
2
2
2
cos ( ' ) cos30( ' )
(0.2) cos30(0.95 0.85)
1.1 10
B
B
B
A B B R B B
x Wb
= =
=
=
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8. A circular coil with a radius of 20 cm is in a field of 0.2 T
with the plane of the coil perpendicular to the field. If the
coil is pulled out of the field in 0.30 s find the average
emf during this interval
B
cos 0B BAN Nt t
= =
2 2
2
0.2 (0.2)
0.3
8.4 10
B R
t
x V
= =
=
N=
cos=A=
1
1R2
B=0
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20.3 Motional emf
x x x x x
x x x x x
x x x x x
x x x x x
A voltage is produced by a conductor moving ina magnetic field
B into the page
v
Charges in the conductor
experience a force upward
F
L
The work done in moving
a charge from bottom to
top
W FL qvBL= =
F qvB=
The potential difference is
WV vBL
q = =
V
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x x x x x
x x x x x
x x x x x
x x x x x
A voltage is produced by a conductor moving in
a magnetic field
B into the page
v
Charges in the conductorexperience a force upward
F
L W FL qvBL= =
F qvB=
The potential difference is
W
V vBLq = =
V
V
olt
a
g
e
velocity
20.3 Motional emf
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20.3 Motional emf
x x x x x
x x x x x
x x x x x
x x x x x
B into the page
vF
L
V
The potential difference can drive a current through a circuit
The emf arises from changing flux due to changing areaaccording to Faradays Law
wire
R
I
Bx AB
V vLB LBt t t
= = = = =
BLvIR R
= =
Changing Magnetic Flux
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x x x x x
x x x x x
x x x x x
x x x x x
B into the page
vF
L
V
18. R= 6.0 and L=1.2 m and B=2.5 T. a) What
speed should the bar be moving to generate a currentof 0.50A in the resistor? b) How much power is
dissipated in R? c) Where does the power come from?
wire
R
I 0.5(6.0)
2.5(1.2)
1.0 /
BLvIR R
IRv
BL
v m s
= =
= =
=
a)
b) 2 2(0.5) (6.0)
1.5
P I R
P W
= =
=
c) Work is done by the
force moving the bar
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Lenzs Law
The polarity of the induced emf is such that it
induces a current whose magnetic field opposes the
change in magnetic flux through the loop. i.e. the
current flows to maintain the original flux through theloop.
NS
V
B Bin
B increasing in loop
Bin acts to oppose thechange in flux
Current direction thatproduces Bin is as
shown (right hand rule)I
+
-
Emf has the polarity shown.
drives current inexternal circuit.
20.4 Lenzs law revisited
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Now reverse the motion of the magnet
NS
V
B
Bin
B decreasing in loop
Bin acts to oppose the
change in flux
Current direction that
produces Bin is as
shown (right hand rule)I
+
-
Emf has the polarity shown.
The current reverses direction
20.4 Lenzs law revisited
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N S
Lenzs Law and Reaction Forces
NS
V
B Bin
I
A force is exerted by the
magnet on loop to produce thecurrent
A force must be exerted by
the current on the magnet tooppose the change
The current flowing in the direction shown
induces a magnetic dipole in the current loop
that creates a force in the opposite direction
FmcFcm
20.4 Lenzs law revisited
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B
The flux through the loop
cosB BA =t =
= angular velocity (radians/s)
Normal to the plane
Flux through a rotating loop in a B field20.5 Generators
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B
t
t
B
t
B
t
sinB
BA tt
=
cosB
BA t =
BA
-BA
BA
-BA
BRelation between
Band
proportional to
20.5 Generators
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The emf generated by a loop of N turns rotating at constantangular velocity is
sinNBA t =
t
NBA
-NBA
0
BN
t
=
20.5 Generators
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35. In a model ac generator, a 500 turn rectangular coil
8.0 cmx 20 cm rotates at 120 rev/min in a uniform magnetic
field of 0.60 T. a) What is the maximum emf induced in the
coil?
sinNBA t =
The maximum value of
max
max
(120 2 )
(500)(0.6)(0.08 0.2) 6060
NBA
x
x V
=
= =
20.5 Generators
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Direct Current (DC) generator
20.5 Generators
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DC motor
drives rotation
A generator is motor acting in reverse
I
20.5 Generators
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20.6 Self-Inductance
a property of a circuit carrying a current
a voltage is induced that opposes the change in current
used to make devices called inductors
Self- inductance of a circuit a reverse emf is produce
by the changing current
B
t =
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Self-inductance of a coil
I
Current
increasing
B
B increases,
changes magnetic flux in
the coil,
B A B
t t
=
B
t
Produces emf in coil
B A BN Nt t
= =
The direction of the induced emf opposes the change in
current.
+ -
20.6 Self-Inductance
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InductanceL
is a measure of theself-induced emf
I
Current
increasing
BN
t
=
I
L t
=
The self-induced emf is
L is a property of the coil, Units of L , Henry (H)Vs
A
proportionality constant is L
but B I
t t
20.6 Self-Inductance
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Inductance of a solenoid with N turns and length ,
wound around an air core (assume the length is much
larger than the diameter).
2
o
NL A=
l
B o
NBA IA = =l
B
o
N IA
t t
=
l
2
Bo
N I IN A L
t t t
= = =
l
l
A
I
t
B
t
inductance proportional to N squared x area/length
20.6 Self-Inductance
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An air wound solenoid of 100 turns has a length of 10 cm
and a diameter of 1 cm. Find the inductance of the coil.
2 2 2
7 2 25
4
4 10 (100) (0.01)1.0 10
0.1(4)
o o
N N dL A
L x H
= =
= =
l l
I
l= 10 cm
d=1 cm
20.6 Self-Inductance
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20.7 RL circuits
The inductor prevents therapid buildup of current
But at long time does notreduce the current,
IL
t
=
0I
t
=
at t=
t
oI I (1 e )
=
L
R
=
Applications of Inductors:Reduce rapid changes of
current in circuits
Produce high voltages in
automobile ignition.
f
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20.8 Energy stored in a magnetic field
Energy is stored in a magnetic field of an inductor.
I I=Io
B=0 BoB increasing
Work is done against to produce the B field.
This produces a change in the PE of the inductor
21
2L
PE LI=
This stored PE can be used to do work