Review: Magnetic Flux, EMF
Announcements
• Professor Reitze taking over for the rest of the semester
• Occasional classes by Professor Kumar
Magnetic flux: ΦB = B⊥A = B A cos θ
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•WebAssign HW Set 7 due the Friday
• Problems cover material from Chapters 20 and 21
Induced EMF comes from the change in
the magnetic flux
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• Tea and Cookies with Professor Kumar
• Tuesday at 5 pm, room 2165
QUESTIONS? PLEASE ASK!
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The minus sign ‘-’ is important: Lenz’s Law!
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Suppose a straight conductor of
length ℓ moves perpendicularly
with constant velocity through a
uniform field
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Recall FM = q v B
The electrons move down and pile
up at the bottom of the conductor,
leaving a net positive charge at
the top of the conductor
The induced EMF sets up a current that opposes the
change in magnetic flux Æ it fights back!!
Will say more in today’s lecture
Motional EMF
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As a result of this charge
separation, an E field (and FE
= qE is produced)…
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The electrons in the conductor
experience a magnetic force
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ΔΦ B
Δt
Faraday’s Law
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20.3 Motional EMF
ε = −N
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Electrons continue to move
down until FM = FE
qvB=qEÆE=vB
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…leading to a potential
difference, ΔV, across the
conductor
ΔV = E l = B ℓ v
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The top is at a higher potential
1
Motional EMF in a Circuit
Motional emf in a Circuit, cont
Now place the conductor on
a pair of rails and pull it
with an applied force Fapp
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assume the moving bar
has negligible resistance
The magnetic force Fapp on
the charges sets up an
induced current
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the charges are free to
move in the closed path!
The changing magnetic
flux through the loop
and the corresponding
induced emf in the bar
result from the change
in area of the loop
The induced ‘motional’
EMF acts like a battery
in the circuit
ε = Blv and I =
Lenz’ Law Revisited,
Conservation of Energy
20.4 Lenz’ Law Revisited
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Current due to the induced EMF travels in
the direction that creates a magnetic field
with flux opposing the change in the
original flux through the circuit
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Assume the induced current
I is clockwise in the figure
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φB is decreasing; current I is induced in
counterclockwise direction to increase φB
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When applying Lenz’ Law, there are two
magnetic fields to consider
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The external changing magnetic field that
induces the current in the loop
The magnetic field produced by the current
in the loop
Magnetic flux φB would
increase
Current I would increase in
clockwise direction
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If B were increasing with time, then the
induced current would travel in the
clockwise direction
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The magnetic force Fm on
the bar would be to the right
Fm causes bar to accelerate
v would increase
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In the diagram to the right, B is
decreasing with time
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Blv
R
A perpetual motion
machine?? Sorry…
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Violation of conservation of
energy is not allowed!!
Thus, current I is
counterclockwise
2
AC Generators, mathematics
20.5 Generators
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Alternating Current (AC) generator
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Converts mechanical energy to
electrical energy using induction
Consists of a wire loop rotated by
some external means
falling water (hydroelectric), heat by
burning coal to produce steam (coalfired), nuclear fission reaction
Basic AC generator operation
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Loop rotates from external force,
Magnetic flux through the loop
changes with time, inducing an EMF
and a current in the external circuit
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The ends of the loop are connected to
slip rings that rotate with the loop
Connections to the external circuit are
made by stationary brushes in contact
with the slip rings
If the loop rotates with a
constant angular speed,
ω, and N turns:
„ θ = ω t
„ v = r ω = (a/2) ω
„ A = ℓ a
ε = N B A ω sin ω t
Problem (20.37, p 693)
In a model AC generator, a 500 turn
rectangular coil 8.0 cm by 20 cm rotates
at 120 rev/min in a uniform magnetic field
of 0.60 T
Motors and Back EMF
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Motors convert electrical
energy into mechanical energy
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What is the maximum EMF induced in
the coil?
(b)What is the instantaneous value of EMF
in the coil at t = (π/32) s? Assume the
EMF is zero at t = 0
(c)What is the smallest value of t for which
the EMF will have its maximum value?
a/2
ε =2 B ℓ v⊥=2 B ℓ v sin θ
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The emf generated by
the rotating loop can be
found by:
(a)
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A motor is a generator run in
reverse
Back EMF is the self-induced
EMF that tends to reduce the
applied current
When a motor is turned on, no
back EMF initially
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The current is very large
because it is limited only by
the resistance of the coil
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Motors and Back EMF
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20.6 Self-inductance
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As the coil begins to
rotate, the induced back
emf opposes the applied
voltage
The current in the coil is
reduced
The power requirements
for starting a motor and
for running it under heavy
loads are greater than
those for running the
motor under average
loads
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Self-inductance occurs when
the changing flux through a
circuit arises from the circuit
itself
The self-induced EMF must
be proportional to the time
rate of change of the current
ε = −L
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ΔI
Δt
L is inductance of the
device
The negative sign is
important! It indicates that a
changing current induces an
EMF in opposition to that
change
Self-inductance
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The inductance of a coil depends
on geometric factors
The SI unit of self-inductance is
the Henry
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1 H = 1 (V · s) / A
The expression for L is
L=N
ΔΦ B
NΦ B
=
ΔI
I
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