Transcript induced emf

Chapter 23
Faraday’s Law
and
Induction
23.1 Michael Faraday
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1791 – 1867
British experimental
physicist
Contributions to early
electricity include
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Invention of motor,
generator, and
transformer
Electromagnetic
induction
Laws of electrolysis
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Induction
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A changing magnetic field produces an
induced current on a circuit without the
present of a battery in the circuit
There is an induced emf associated with
the induced current
Faraday’s Law of Induction describes
the induced emf
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EMF Produced by a
Changing Magnetic Field,
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When the magnet is held stationary, there is
no deflection of the ammeter
Therefore, there is no induced current
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Even though the magnet is inside the loop
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EMF Produced by a
Changing Magnetic Field,
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A loop of wire is connected to a sensitive ammeter
When a magnet is moved toward the loop, the
ammeter deflects
The deflection indicates a current induced in the wire
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EMF Produced by a
Changing Magnetic Field,
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The magnet is moved away from the loop
The ammeter deflects in the opposite
direction
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EMF Produced by a Changing
Magnetic Field, Summary
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The ammeter deflects when the magnet is
moving toward or away from the loop
The ammeter also deflects when the loop is
moved toward or away from the magnet
An electric current is set up in the coil as long
as relative motion occurs between the
magnet and the coil
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This is the induced current that is produced by an
induced emf
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Faraday’s Experiment –
Set Up
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A primary coil is connected to
a switch and a battery
The wire is wrapped around
an iron ring
A secondary coil is also
wrapped around the iron ring
There is no battery present in
the secondary coil
The secondary coil is not
electrically connected to the
primary coil
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Faraday’s Experiment –
Findings
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At the instant the switch is closed, the
galvanometer (ammeter) needle deflects in
one direction and then returns to zero
When the switch is opened, the galvanometer
needle deflects in the opposite direction and
then returns to zero
The galvanometer reads zero when there is a
steady current or when there is no current in
the primary circuit
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Faraday’s Experiment –
Conclusions
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An electric current can be produced by a timevarying magnetic field
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This would be the current in the secondary circuit of
this experimental set-up
The induced current exists only for a short time
while the magnetic field is changing
This is generally expressed as: an induced
emf is produced in the secondary circuit by
the changing magnetic field
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The actual existence of the magnetic field is not
sufficient to produce the induced emf, the field must
be changing
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Magnetic Flux
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To express
Faraday’s finding
mathematically, the
magnetic flux is
used
The flux depends on
the magnetic field
and the area:
 B   B  dA
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Faraday’s Law – Statements
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Faraday’s Law of Induction states that
the emf induced in a circuit is equal
to the time rate of change of the
magnetic flux through the circuit
Mathematically,
d B
 
dt
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Faraday’s Law – Example
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Assume a loop
enclosing an area A
lies in a uniform
magnetic field
The magnetic flux
through the loop is
B = B A cos q
The induced emf is
d
    BA cosq 
dt
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Ways of Inducing an emf
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The magnitude of the field can change
with time
The area enclosed by the loop can
change with time
The angle q between the field and the
normal to the loop can change with time
Any combination of the above can occur
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Applications of
Faraday’s Law – Pickup Coil
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The pickup coil of an electric
guitar uses Faraday’s Law
The coil is placed near the
vibrating string and causes a
portion of the string to
become magnetized
When the string vibrates at
the some frequency, the
magnetized segment
produces a changing flux
through the coil
The induced emf is fed to an
amplifier
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23.2 Motional emf
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A motional emf is one
induced in a conductor
moving through a
magnetic field
The electrons in the
conductor experience
a force that is directed
along l
FB  qv  B
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Motional emf, cont
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Under the influence of the force, the electrons
move to the lower end of the conductor and
accumulate there
As a result of the charge separation, an
electric field is produced inside the conductor
and gives rise to an electric force on the
electrons
The charges accumulate at both ends of the
conductor until the electric and magnetic
forces are balanced
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Motional emf, final
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For balance, q E = q v B or E = v B
A potential difference DV=vBl between the
two ends of the conductor is maintained as
long as the conductor 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
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A bar moving through a uniform field and the
equivalent circuit diagram
Assume the bar has zero resistance
The work done by the applied force appears as
internal energy in the resistor R
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Sliding Conducting Bar, cont
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The induced emf is
d B
dx
 
 B
 B v
dt
dt
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Since the resistance in the circuit is R,
the current is
 B v
I

R
R
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Sliding Conducting Bar,
Energy Considerations
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The applied force does work on the
conducting bar
This moves the charges through a magnetic
field
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
2
  Fappv   I B  v 
R
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AC Generators
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Electric generators take
in energy by work and
transfer it out by
electrical transmission
The AC generator
consists of a loop of
wire rotated by some
external means in a
magnetic field
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Induced emf
In an AC Generator
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The induced emf in
the loops is
d B
  N
dt
 NABw sinw t
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This is sinusoidal,
with max = N A B w
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23.3 Lenz’ Law
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Faraday’s Law indicates the induced
emf and the change in flux have
opposite algebraic signs
This has a physical interpretation that
has come to be known as Lenz’ Law
It was developed by a German physicist,
Heinrich Lenz
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Lenz’ Law, cont
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Lenz’ Law states the polarity of the
induced emf in a loop is such that it
produces a current whose magnetic
field opposes the change in magnetic
flux through the loop
The induced current tends to keep the
original magnetic flux through the circuit
from changing
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Lenz’ Law – Example 1
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When the magnet is moved toward the stationary
loop, a current is induced as shown in a
This induced current produces its own magnetic field
that is directed as shown in b to counteract the
increasing external flux
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Lenz’ Law – Example 2
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When the magnet is moved away the stationary loop,
a current is induced as shown in c
This induced current produces its own magnetic field
that is directed as shown in d to counteract the
decreasing external flux
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