Download Part II - TTU Physics

EMF Induced in a Moving
Conductor (“Motional EMF”)
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This figure shows another way the magnetic flux can change.
It can change if a conducting loop
is moved in a static magnetic field.
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The induced current in the figure is in a direction
that tends to slow the moving bar. That is, It takes
an external force to keep it moving.
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•The induced emf has magnitude
•This
holds ONLY if B, l, & v are
mutually perpendicular.
•If they are not, then it is true for
their perpendicular components.
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Induced emf magnitude:
Example: Does a moving plane develop a large emf?
• A plane travels at speed v = 1000 km/h
in a region where Earth’s magnetic
field B = 5  10-5 T & is nearly vertical.
• Calculate the potential difference
induced between the wing tips that
are l = 70 m apart.
Solution:
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=Blv1V
Example
Electromagnetic Blood-flow measurement
• The rate of blood flow in our body’s vessels can be
measured using the apparatus shown, since blood
contains charged ions. Suppose that the blood vessel is
2.0 mm in diameter, the magnetic field is 0.080 T, & the
measured emf is 0.10 mV.
• Calculate the flow
velocity v of the blood.
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Example: Force on a rod.
• To make the rod move to the right at speed v, you
need to apply an external force on the rod to the right.
Calculate
(a) The magnitude of the required force.
(b) The external power needed to move the rod.
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Motional emf
Motional emf is the emf
induced in a conductor
moving through a
constant magnetic field.
• Electrons in the conductor experience a
force that is directed along ℓ: .
F  qv  B
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F  qv  B
Under this force, electrons move to
the lower end of the conductor &
accumulate there. As a result of
this charge separation, an
electric field is produced
inside the conductor.
The charges accumulate at both ends of the
conductor until they are in equilibrium with regard
to the electric and magnetic forces. At equilibrium,
qE = qvB or E = vB.
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F  qv  B
As a result of this charge
separation, an electric field is
produced inside the
conductor.
qE = qvB or E = vB.
This electric field is related to the potential difference
across the ends of the conductor: V = E ℓ =B ℓ v. This
potential difference is maintained between the ends of the
conductor as long as it continues to move through the uniform
magnetic field. If the direction of the motion is reversed, the
polarity of the potential difference is also reversed.
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Sliding Conducting Bar
A conducting bar moving through a uniform field
and the equivalent circuit diagram. Assume the bar
has zero resistance. The stationary part of the circuit
has a resistance R.
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Sliding Conducting Bar
• The induced emf is
ε
dB
dx
 B
 B v
dt
dt
• Since the resistance in the circuit is R, the current is
ε Bv
I 
R
R
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Sliding Conducting Bar
ε
dB
dx
 B
 B v
dt
dt
ε Bv
I 
R
R
• The applied force does work
on the bar. It moves the
charges through a magnetic
field & establishes a current.
• The change in energy of the system during some time interval
must be equal to the transfer of energy into the system by work.
• The power input is equal to the rate at which energy is
delivered to the resistor.
ε2
P  Fappv   I B  v 
R
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More on Lenz’s Law
• Faraday’s Law says that the induced emf & the
change in magnetic flux have opposite algebraic
signs. This has a physical interpretation known as
Lenz’s Law.
Lenz’s Law:
The induced current in a loop is in the
direction that creates a magnetic field that
opposes the change in magnetic flux
through the area enclosed by the loop.
• The induced current tends to keep the original
magnetic flux through the circuit from changing.
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Lenz’ Law, Example
• The conducting bar slides on the two fixed conducting rails.
• The magnetic flux due to the external magnetic field through the
enclosed area increases with time.
• The induced current must produce a magnetic field out of the page.
So, the induced current must be counterclockwise.
• If the bar moves in the opposite direction, the direction of the
induced current will also be reversed.
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Electric Generators
A generator is the opposite of a motor. It
transforms mechanical energy into electrical
energy. The figure shows an ac generator:
The axle is rotated by an
external force such as
falling water or steam.
The brushes are in constant
electrical contact with the
slip rings.
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If the loop is rotating with constant angular
velocity ω, the induced emf is sinusoidal:
For a coil of N Loops:
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Example: AC generator.
The armature of a 60-Hz ac generator rotates in a 0.15 T
magnetic field. The coli area is 2.0  10-2 m2, Calculate the
number of loops needed for the peak output to be E = 170 V.
A dc generator is similar to an ac generator, except that
it has a split-ring commutator instead of slip rings.
AC
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DC
Automobiles now use alternators rather than
dc generators, to reduce wear.
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