Transcript Ch. 22

Ch. 28
Electromagnetic Induction
Chapter Overview
 Motional EMF
 Faraday’s Law
 Lenz’s Law
 Magnetic Flux
 Electric Generator
 Transformers
Motional EMF
 If a conductor moves perpendicular to a
magnetic field, a potential difference is
induced across the conductor
 Moving the conductor in the B-field
produces magnetic force
 Charge separation from magnetic force
produces electric force
 At equilibrium electric force balances
magnetic force
Motional EMF
 qvB = qE
 Multiply both sides by
L
 vBL = qEL
 ΔV = vBL
A bar of length 10 cm closes a circuit as shown. The
bar moves at 2.0 m/s perpendicular to a B-field of
strength .25 T. a) Find the current in the circuit if the
light bulb has a resistance of 5.0 Ω. b) Ignoring the
resistance of the connecting wires find the potential
difference across the light bulb. Label the higher and
lower potential side of the light bulb.
Faraday’s Law
 In 1820 Oersted demonstrated that a
current could create a magnetic field – i.e.
that an E-field could produce a B-field
 Almost immediately Faraday asked the
opposite question – Could a B-field
produce an E-field?
Faraday’s Law
 Faraday worked on the question for 11
years until he accidentally found his
answer while disconnecting an
unsuccessful experiment
 Faraday had been searching for a current
produced by a steady field, but it was a
changing field that produced the current
and he produced the changing magnetic
field as he disconnected his experiment
Magnetic Flux
 Magnetic flux
through a single
surface
 ΦB = BA cosφ
 If a coil has N
turns
 ΦB = NBA cosφ
Faraday’s Law
 An EMF (potential difference) is
induced when the magnetic flux
through a surface changes in time
d
V  
dt
Which of the following can produce
a changing magnetic flux?
1.
2.
3.
4.
5.
1
A changing B-field
A changing area
A changing angle
1,2, and 3
None of the above
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Lenz’s Law
 What pole is induced near coil when a N
pole of a bar magnet is inserted into a
coil? (OBS)
 What pole is induced if the N pole is
removed form a coil? (OBS)
 Reverse the magnet. What poles are
observed now? (OBS)
Lenz’s Law
 The induced EMF is produced so as to
oppose the change in magnetic flux
producing it.
A conducting coil is placed over an AC
electromagnet. When the magnet is
turned on what will the coil do?
1. Nothing
2. It will attract to the
magnet
3. It will repel from the
magnet
4. Cannot be determined
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Lenz’s Law Tube
 Two identically sized disks are dropped.
One is dropped inside a tube in which it
fits. Which will hit the ground first?
A coil is oriented perpendicular to a B-field
directed into the page. The coil is at rest.
What is the direction of the induced current?
1. Clockwise
2. Counterclockwise
3. There is no induced
current
4. Cannot be
determined
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For the situation depicted, what will
be the direction of the induced
current?
1. Clockwise
2. Counterclockwise
3. There is no induced
current
4. Cannot be
determined
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A wire is formed into a loop of radius .050
m. The coil is oriented perpendicular to a
uniform B-field of strength .075 T. a)
Sketch the situation. b) The ends of the
wire are pulled so that the wire collapses in
a time of .060 s. Is an EMF induced?
Explain. c) Find the magnitude of the
induced EMF. d) If a 2.0 Ω resistor is
connected across the ends of the wire, how
much power is dissipated. Where did the
power come from?
Applications of Faraday’s Law
 Pick up coils
 Generators
 Transformers
Pick up coils
Generators
 In a generator, a coil
is turned at a constant
angular frequency in
a B-field
 What produces the
changing flux to
generate the EMF?
(GR)
Generators
 Flux is produced by changing angle
 θ = ωt
 ΦB = NAB cos ωt
 ΔV = -dΦ/dt = NABω sin ωt
 What does the output of a generator look
like? (GR)
AC Generators
 Output of AC
Generator is sine
wave
 Can we make a DC
Generator?
(BRST)
DC Generator
 To create a DC generator
(such as Genecon) use a
split ring
 Output for a simple DC
generator is shown
 Output can be made
smoother by more
sophisticated
combinations of rings and
magnets
a) What must be the magnetic
field strength so that a
generator consisting of 1000
turns of a coil of radius 25 cm
produces a peak output of 160
V when turned at a frequency of
60 Hz? b) Sketch a graph of
the output of the generator.
Why AC?
 In the early days of electrification, there
was a debate of whether power
companies should supply ac or dc
 Edison favored dc whereas Westinghouse
favored ac
 Clearly Westinghouse won the debate.
Why?
Transformers
 Electromagnetic induction can be used to
change ac electric potential from one
value to another
Transformers
 Flux through one coil is the same




everywhere
dΦB/dt is the same for each coil
Vp = -Np dΦB/dt and
Vs = -Ns dΦB/dt
After a little algebra
N s Vs

N p Vp
Transformers
 If the number of turns in the secondary is
greater than in the primary, is the
secondary potential greater or less than
the primary? (GR)
 If the number of turns in the secondary is
less than in the primary, is the secondary
potential greater or less than the primary?
(GR)
Transformers
 If the number of turns in the secondary is
greater than in the primary, the secondary
potential is greater. This is called a step
up transformer
 If the number of turns in the secondary is
less than in the primary, the secondary
potential is less than the primary. This is
called a step down transformer
Ex. To operate a neon sign a
potential difference of 12000 V is
needed. What must be the ratio
of turns if the primary potential is
120 V?
A DC potential of 100 V is applied to the
primary of a step-up transformer with
turns ratio of 500. What is the potential
difference across the secondary?
25% 25% 25% 25%
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2.
3.
4.
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.2 V
50,000 V
0V
Not enough information
given
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120 V ac is applied across the primary of a step
down transformer with turns ratio 1/50. How does
the power applied at the primary compare to that
at the secondary? (Assume a lossless
transformer)
1.
2.
3.
4.
It is 1/50 th as big
It is 50 x bigger
It is the same
Not enough information
to answer
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Power and Current in Transformers
 Conservation of Energy implies
power at primary is the same as
power at secondary
 What happens to current?
 IsVs = IpVp so
is V p

i p Vs
Current in Transformers
 In a step up transformer, current is
decreased
 Is step down transformer current is
increased
Application to Power Generation
 Need to minimize losses in transmission
 Losses given by i2R, so lower current means
less loss
 Transmitting at higher potential decreases
current
Self Inductance
 If you apply current to a coil,
you will induce an EMF
A
A
 V = - dΦ/dt = -d(μ0niNA)/dt =
- μ0nINA di/dt
 The induced EMF is
proportional to the change in
current V = -Ldi/dt
 Where L = μ0n2Al is called
the inductance of the coil
l
RL Circuits
EX. a) Use
Kirchhoff’s Voltage
Law to find an
equation for the
current in the circuit.
b) Find a solution if
I(0) = 0.
Current grows
with exponential
asymptote to
steady value of
E0/R.
Time Constant is
given by L/R
Ex. An RL circuit w/o a battery
has an initial current I0. Sketch
the circuit. b) Use KVL to find
an equation for the current. c)
Find I(t).
Magnetic Energy
 Circuits do not turn on or off
instantaneously.
 Inductance means that circuits turn on and
off with a time constant L/R
 This is due to the fact that energy is stored
in the inductor. It takes time to initially store
the energy in the inductor when the switch
is closed, it takes time to remove the
energy from the inductor when the switch is
opened.
Energy in an Inductor
 P = IV = I LdI/dt
dI
1 2
Energy   Pdt   LI dt  LI
dt
2
 For a coil I = B/(μ0N/l)
and L = μ0N2Al
 So Energy =
1/(2μ0)B2LA