Induced EMF
Generators , Transformers
Physics 122
10/29/12
Lecture XVI
1
Concepts
•  Electric generator
•  Magnetic flux
•  Induced EMF
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Lecture XVI
2
Electric motor ßà electric generator
•  Electric motor:
–  electric energy àmechanical.
•  Electric generator:
–  Current loop rotates in
–  mechanical à electric energy.
magnetic field
–  conductor loop rotating in
magnetic field produces
electric current
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Lecture XVI
3
1
Magnetic flux
•  If magnetic field is rain –
magnetic flux is the amount of
water in a bucket accumulated
per unit of time:
Φ = B⊥ A =BA cos
 θ
Φ B = ∫ B ⋅ dA
•  Magnetic flux is measured in
Weber:
1Wb=1T.m2
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Three ways to change flux
• Change B
• Change A
• Change θ
Lecture XVI
4
Faraday’s Law of induction
•  Changing magnetic flux
induces emf (voltage),
•  Acts like a battery!
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emf = - N
dΦ
dt
Lecture XVI
5
Lenz’s Law: conservatism of nature
•  An induced emf always gives rise to a current whose
magnetic field opposes the original change in flux:
–  Flux decreases è internal Bint (created by the induced
current) is in the same direction as the external Bext
–  Flux increases è Bint – in the opposite direction to Bext
–  Determine current direction using 1st right hand rule
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2
Moving conductor
•  A conducting rod is moving
to the right on a U-shaped
conductor in a uniform
magnetic field è flux is
increasing
dΦ = B⊥dA = Blvdt
•  Induced electric field:
•  Induced emf:
emf =
dΦ
= Blv
dt
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E=
emf
= vB
l
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7
Electric generator
•  Electric generator:
–  conductor loop rotating
in magnetic field
produces
–  Alternating electric
current AC
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ϖ = 2πf


Angle between B and A θ = ϖt
Φ = BA cosϖt
emf = −N
dΦ
d cos ϖ t
= −NBA
dt
dt
emf = NBAϖ sin ϖ t
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Alternating current (AC)
•  Emf changes sign è current changes the direction
emf = emf0 sin ϖ t
V = V0 sin ϖ t
V0 = NBAϖ
I = I0 sin ϖt
I 0 = V0 / Req
I
Req
~
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Lecture XVI
V0 sin ϖ t
9
3
Transformer
•  If all flux goes through the core:
dΦ
dt
dΦ
Vs = N s
dt
Vp = N p
Vs N s
=
Vp N p
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Lecture XVI
10
Transformer
•  If energy is conserved
I pV p = I sVs
Is N p
=
I p Ns
•  If efficiency ε<100%
I sVs = εI pV p
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Lecture XVI
11
Power transmission
•  High voltage à low current à power loss in power line
resistance is lower:
2
Ploss = I R
Power is dissipated only in resistors!!!
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4
Power transmission
•  65kW is transmitted over two 0.100 Ohm lines.
•  V=120à1200Và120V, ε=99%
•  Compare losses to power transmission at 120V
Ploss (resistor ) = I 2 R
Ploss (transformer ) = (1 − ε ) P
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Lecture XVI
13
Moving conductor – eddy currents
•  A increases è Φ increases à
Induced current creates Bint
opposite to external Bext
•  I down
•  Now we have a current in
magnetic field è there is a force
acting on it
•  The direction of this force is
opposite to v
•  Conservatism of nature
•  Currents created in conductors
moving through the magnetic
field – eddy currents – work to
resist the change
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Lecture XVI
14
Electric generator –counter torque
•  Loop is rotating cw
•  Induced currents experience force in magnetic field è
resultant torque on the loop ccw – counter torque
•  Nature resists change.
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5
Electric motor – counter emf
•  Current loop in magnetic field
•  Magnetic field creates a torque
that rotates the loop
•  Changing flux è emf
•  Based on conservatism – this emf
will try to create a current in the
opposite direction to the original
current - counter emf.
•  Current is large at the beginning
and is decreased later on.
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6