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Chapter 29 Electromagnetic Induction
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•
•
•
Consider Faraday’s Law
Consider Lenz’s Law
Study motional emf
Explore induced electric
fields
• Eddy currents
• Displacement current
• Superconductivity and
Magnetism
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Induced EMF Experiments
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Induced Current Phenomenon
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Faraday’s Law of Induction
The induced emf is proportional to the rate
of change of magnetic flux ,  B ,through
the coil.
•B, the magnetic field can change with
time.
•A, the area can change with time
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Faraday’s Law Area and Magnetic Flux Direction
Regardless of what moves, knowing the magnetic
flux around a conducting entity will allow
determination of current induced.

B
  B  d A   BdA cos 
For a uniform B field

B
Faraday’s Law of Induction
 B  A  BA cos 
d
   B
dt
5
dB
 0.020T / s
dt
A = 120 cm2
R (loop resistance) = 5 
Determine induced voltage (VEMF = Vab).
Determine induced current (I).
Verify current direction using Lenz’s Law.
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Lenz’s Law
•The direction of any magnetic induction effect is such as to oppose the
cause of the effect.
•The “cause” can be a change flux, or the motion of a conductor.
•In all cases the induced current tries to prevent the status quo by opposing
motion or change of flux.
•The induced current due to the
change in B is clockwise as seen
from above the loop. (RHR
opposite direction of fingers)
•The Binduced that it caused is
downward, opposite the change
in the upward field B.
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Lenz’s Law I – Counter clockwise induced current
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Lenz’s Law II – clockwise induced current
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Changing the Coil Shape
Change the shape of the coil and you change the shape
of the magnetic flux. The rate at which you change the
shape is the rate of change of the magnetic flux
This induces a current in the coil to oppose the change
in flux.
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A Simple Alternator (generator)
 = t, where  is the angular velocity of the loop.
 B  BA cos   BA cos t (B is the total magnetic flux penetrating area A )
d B
  Vab  
 BA sin t
dt
d B
 NBA sin t
For an N-turn coil, Vab   N
dt
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DC generator
• A dc generator produces an emf of the same sign (only positive)
• Slip rings and brushes reverses the polarity negative of the negative
cycle
• Commercial dc generators have a large number of coils and
commutator segments-smoothes out the emf approaching a constant dc
  Vab   N
dB
 N BA sin t
dt
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Motor average back emf
• The motor’s back emf is the emf induced by the changing magnetic
flux through the rotating coil.
  Vab   N
dB
 N BA sin t
dt
Back emf
proportional to
motor speed
Slow speed could
burn out motor
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Motional Electromotive Force
•As the rod moves the magnetic field causes positive
free charge to go to move to one end and negative
charge to the other.
•Equilibrium is established when the magnetic force
equals the electric force.
B
E

 
FB  q(v xB)
At equilibrium
qE  qvB sin 
E  vBsin 
FE  FB
FB  qvB sin 


FE  qE
FE  qE
for  = 90°
  Vab  EL  vBL
(29.6)
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A conducting rod moving in a uniform magnetic field
dA
dA  Lvdt
 
 B   B  dA   B cos dA
cos   1
d B  B cos dA  BdA
d B  BdA  BLvdt
d B
 BLv  VEMF
dt
Figure 29-10
Faraday’s Law of Induction
The induced emf () in a closed loop equals the negative of the time rate of
change of magnetic flux through the loop.
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Eddy currents
• Induced currents produce
eddy currents that oppose the
induced currents (and the
motion of the disk)
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Displacement current and Maxwell’s equations
• A varying electric field will give rise to a magnetic field.
• Explains electromagnetic waves.
Displacement current iD
between plates
Proof of iD is the
measure magnetic field
between plates
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Superconductivity and the Meissner effect
• When cooled
below the critical
temperature,
superconductive
materials lose all
resistance to
electrical current.
• Refer to Figures
29.24 and 29.25 at
right.
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Q29.1
A circular loop of wire is in a region of
spatially uniform magnetic field. The
magnetic field is directed into the
plane of the figure. If the magnetic
field magnitude is constant,
A. the induced emf is clockwise.
B. the induced emf is counterclockwise.
C. the induced emf is zero.
D. The answer depends on the strength of the field.
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Q29.2
A circular loop of wire is in a region of
spatially uniform magnetic field. The
magnetic field is directed into the
plane of the figure. If the magnetic
field magnitude is decreasing,
A. the induced emf is clockwise.
B. the induced emf is counterclockwise.
C. the induced emf is zero.
D. The answer depends on the strength of the field.
Q29.3
A circular loop of wire is placed next
to a long straight wire. The current I in
the long straight wire is increasing.
What current does this induce in the
circular loop?
A. a clockwise current
B. a counterclockwise current
C. zero current
D. not enough information given to decide
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Q29.4
A flexible loop of wire lies in a
uniform magnetic field of magnitude
B directed into the plane of the
picture. The loop is pulled as shown,
reducing its area. The induced
current
A. flows downward through resistor R and is proportional to B.
B. flows upward through resistor R and is proportional to B.
C. flows downward through resistor R and is proportional to B2.
D. flows upward through resistor R and is proportional to B2.
E. none of the above
Q29.5
The rectangular loop of wire is being moved
to the right at constant velocity. A constant
current I flows in the long straight wire in
the direction shown. The current induced in
the loop is
A. clockwise and proportional to I.
B. counterclockwise and proportional to I.
C. clockwise and proportional to I2.
D. counterclockwise and proportional to I2.
E. zero.
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Q29.6
The loop of wire is being moved to the right
at constant velocity. A constant current I
flows in the long straight wire in the
direction shown. The current induced in the
loop is
A. clockwise and proportional to I.
B. counterclockwise and proportional to I.
C. clockwise and proportional to I2.
D. counterclockwise and proportional to I2.
E. zero.
Q29.7
The rectangular loop of wire is being moved
to the right at constant velocity. A constant
current I flows in the long wire in the
direction shown. What are the directions of
the magnetic forces on the left-hand (L) and
right-hand (R) sides of the loop?
A. L: to the left; R: to the left
B. L: to the left; R: to the right
C. L: to the right; R: to the left
D. L: to the right; R: to the right
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Q29.8
The drawing shows the uniform magnetic field
inside a long, straight solenoid. The field is
directed into the plane of the drawing, and is
increasing.
What is the direction of the electric force on a
positive point charge placed at point a?
A. to the left
B. to the right
C. straight up
D. straight down
E. misleading question — the electric force at this point is zero
Q29.9
The drawing shows the uniform magnetic field
inside a long, straight solenoid. The field is
directed into the plane of the drawing, and is
increasing.
What is the direction of the electric force on a
positive point charge placed at point b?
A. to the left
B. to the right
C. straight up
D. straight down
E. misleading question — the electric force at this point is zero
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