Induced EMF
Generators , Transformers
Physics 114
4/12/2020
Lecture VIII
1
Concepts
• Electric generator
• Magnetic flux
• Induced EMF
4/12/2020
Lecture VIII
2
Electric motor  electric generator
• Electric motor:
– electric energy mechanical.
• Electric generator:
– Current loop rotates in
– mechanical  electric energy.
magnetic field
– conductor loop rotating in
magnetic field produces
electric current
4/12/2020
Lecture VIII
3
Magnetic flux
• If magnetic field is rain –
magnetic flux is the amount of
water in a bucket accumulated
per unit of time:
  B A  BA cos



 B   B  dA
• Magnetic flux is measured in
Weber:
1Wb=1T.m2
4/12/2020
Lecture VIII
Three ways to change flux
•Change B
•Change A
•Change 
4
Faraday’s Law of induction
• Changing magnetic flux
induces emf (voltage),
• Acts like a battery!
4/12/2020
Lecture VIII
d
Ε -N
dt
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  internal Bint (created by the induced
current) is in the same direction as the external Bext
– Flux increases  Bint – in the opposite direction to Bext
– Determine current direction using 1st right hand rule
4/12/2020
Lecture VIII
6
Moving conductor
• A conducting rod is moving
to the right on a U-shaped
conductor in a uniform
magnetic field  flux is
increasing
d  B dA  Blvdt
• Induced emf:
• Induced electric field:
d
Ε
 Blv
dt
4/12/2020
Ε
E   vB
l
Lecture VIII
7
Electric generator
• Electric generator:
– conductor loop rotating
in magnetic field
produces
– Alternating electric
current AC
4/12/2020
  2f


Angle between B and A   t
  BA cost
d
d cost
Ε  N
  NBA
dt
dt
Ε  NBA sin t
Lecture VIII
8
Alternating current (AC)
• Emf changes sign  current changes the direction
Ε  Ε0 sin t
Ε0  NBA
I  I 0 sin t
I 0  Ε0 / Req
I
Req
~
4/12/2020
Lecture VIII
Ε0 sin t
9
Transformer
• If all flux goes through the core:
d
Vp  N p
dt
d
Vs  N s
dt
Vs N s

Vp N p
4/12/2020
Lecture VIII
10
Transformer
• If energy is conserved
I pV p  I sVs
Is N p

I p Ns
• If efficiency e<100%
I sVs  eI pV p
4/12/2020
Lecture VIII
11
Power transmission
• High voltage  low current  power loss in power line
resistance is lower:
2
Ploss  I R
Power is dissipated only in resistors!!!
4/12/2020
Lecture VIII
12
Power transmission
• 65kW is transmitted over two 0.100 Ohm lines.
• V=1201200V120V, e=99%
• Compare losses to power transmission at 120V
Ploss (resistor )  I R
2
Ploss (transformer )  (1  e ) P
4/12/2020
Lecture VIII
13
Moving conductor – eddy currents
• A increases   increases 
Induced current creates Bint
opposite to external Bext
• I down
• Now we have a current in
magnetic field  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
4/12/2020
Lecture VIII
14
Electric generator –counter torque
• Loop is rotating cw
• Induced currents experience force in magnetic field 
resultant torque on the loop ccw – counter torque
• Nature resists change.
4/12/2020
Lecture VIII
15
Electric motor – counter emf
• Current loop in magnetic field
• Magnetic field creates a torque
that rotates the loop
• Changing flux  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.
4/12/2020
Lecture VIII
16