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Lecture 10-1
Motional EMF
Most of the worlds electric energy is produced by electric generators, not by batteries.
Motional emf is the principle behind the electric generator. Motional emf occurs
whenever a conductor moves, cutting through magnetic fields.
Assume that a conducting rod of length L moves with
velocity v in magnetic field B . This creates a force on
the conduction electrons in the rod.
L
v
F 
B
av
 qv  B
per electron on average
FB accumulates conduction electrons near bottom.
 In response E develops, opposing the accumulation.
Equilibrium is reached when
F E  qE   F B
 E  v  B
Potential difference
between the ends of rod
induced emf
More generally,
V  EL  vBL


V  EL  v  B  L
Lecture 10-2
Motional EMF of Sliding Conductor
Induced EMF
+
v
FM
  vBL
L  Direction of current is as if the
induced emf were due to a battery.
counter-clockwise here
(later: Lenz’s Law)
Rod slides as before, but there is a
complete circuit instead of a rod.
• Induced emf moves
electrons (current flows).
• emf (and current) is
maintained as long as the
rod is sliding with v.
 Magnitude of induced current I

vBL
I 
R
R
 Magnetic force FM acts on this I
vB 2 L2
FM  I LB 
R
FM decelerates the bar
Lecture 10-3
Faraday’s Law
(See Giambattista V.2 Ch.20, p726-744)
Hans C. Oersted discovered that electric current produces a magnetic field. Michel
Faraday showed the reverse: Magnetic field
produces an electric current.
Induced emf of ε=vBL turns out to be
just an example of a more general result:
Faraday’s Law of Induction:
The magnitude of the induced
emf in conducting loop is equal to
the rate at which the magnetic
flux through the surface spanned
by the loop changes with time.
 B
 
t
Magnetic flux
 B   BdA
S
  B cos  dA
S
1 Wb = 1 T m2
• First decide on which way the loop is to be taken
Fixes sign of B by RHR
• The positive direction for emf  is relative to the
chosen loop direction
Lecture 10-4
Kinds of Ways to Change Magnetic Flux?
 B  BA cos
• Changing the magnitude of the field within a conducting loop (or coil).
• Changing the area of the loop (or coil) that lies within the magnetic field.
• Changing the relative orientation of the field and the loop.
motor
generator
Lecture 10-5
Conducting Loop in a Changing Magnetic Field
Induced EMF has a direction such that it opposes the change in
magnetic flux that produced it.
approaching
 Magnetic moment 
created by induced currrent
I repels the bar magnet.
Force on ring is repulsive.
moving away
 Magnetic moment 
created by induced currrent
I attracts the bar magnet.
Force on ring is attractive.
Lecture 10-6
Faraday’s and Lenz’s Laws
Faraday’s Law of Induction: The magnitude of the
induced emf in conducting loop is equal to the rate at
which the magnetic flux through the surface spanned
by the loop changes with time.
 B
 
t
Lenz’s Law: The direction of induced emf and current opposes
the change that produced them.
 At 1, 3, and 5, B is not changing.
So there is no induced emf.
 At 2, B is increasing into page. So emf is
induced to produce a counterclockwise current.
 At 4, B in decreasing into
page. So current is clockwise.
Lecture 10-7
Applications
Ground fault interupter
Audio tape playback head
Moving coil microphone
Lecture 10-8
Examples of Induction
+
-
Switch has been
open for some time:
Switch is just closed:
Nothing happening
EMF induced in Coil 2
+
-
Switch is just opened:
EMF is induced again
Switch is just closed:
EMF is induced in coil
-
+
Back emf
(counter emf)
Lecture 10-9
Physics 219 – Question 1 – Sept. 26. 2016.
There are two circular loop wires with z-axis going through
their centers perpendicularly as shown. A current I1 flows
in the top loop, clockwise as viewed from +z direction and
its magnitude is increasing. Which statement is true about
I2, the induced current in the bottom loop?
z
a) Clockwise
b) Counter-clockwise
c) I2 is zero.
I1
y
x
I2
Lecture 10-10
Transformer
• AC voltage can be stepped up or
down by using a transformer.
•AC current in the primary coil creates a
time-varying magnetic flux through the
secondary coil via the iron core. This
induces emf in the secondary circuit.
2
1
N1
N2
ideal transformer (no losses and magnetic
flux per turn is the same on primary and
secondary).
(With no load)
 B
2  N2
t
 B
 1   N1
t
2 N2

 1 N1
N1  N 2  V1  V2
turns ratio
N1  N 2  V1  V2
step-up
step-down
Lecture 10-11
Energy Transfer in a Transformer
With switch S closed:
conservation of energy
proportional to
average power
I1
I1V1  I 2 V2

N1 V1

N 2 V2
I2
N1 I 2

N 2 I1
Lecture 10-12
Eddy Current
A current induced in a solid conducting
object, due to motion of the object in an
external magnetic field.
The pattern of eddy currents is usually
complicated, but Lenz’s Law implies that
the resultant force opposes the motion
which caused it.
• The presence of eddy current in the object
results in dissipation of electric energy
that is derived from mechanical motion
of the object.
• The dissipation of electric energy in turn
causes the loss of mechanical energy of
the object, i.e., the presence of the field
damps motion of the object.