Download Lecture 18 - Iowa State University

Summary
Lecture 18
The principle of galvanometers, electric motors, and loudspeakers is based on
the interaction between (i) a magnetic field due to permanent magnet and (ii) a
magnetic field due to electric current in the loop.
Galvanometer: transforms a magnetic field due to current into the angle of the
pointer.
Electric motor: transforms magnetic field due to current into rotation.
Loudspeaker: transforms variable magnetic field in motion and sound.
Electricity and Magnetism
Electromagnetic Induction
Faraday’s Law
Lenz’s Law
A galvanometer takes advantage of the
torque on a current loop to measure current:
φ=
NIAB sin θ
k
There are three main types of materials: (1) diamagnetics, (2) paramagnetics,
and (3) ferromegnetics.
The source of a magnetic field at the atomic level is a motion of electrons
around the nuclei (orbital magnetic moment) and around own axis (spin
magnetic moment).
Ferromagnetics contains tiny regions called domains; the magnetic field
in each domain is in a single direction; the external magnetic field aligns the
direction of the magnetic field in all domains.
Physics 112, Spring 2010, Feb 24, Lecture 18
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Physics 112, Spring 2010, Feb 24, Lecture 18
Electricity and Magnetism: Electromagnetism
Electric Charge and Magnetic Field
How electricity and magnetism are related each other?
+
The interaction between the electric and magnetic fields is what we refer to
as electromagnetism.
v=0
+
B
B
Charge at rest: no effect
of magnetic field
So, electromagnetism explains how magnetic field affects the electrical
current or how the electrical current affects the magnetic field.
v
Fm = q v⊥ B
Moving charge: magnetic
field affects the charge
Magnetic field affects only moving charge!
Only moving electric charge produces a magnetic field!
Three important electromagnetic phenomena:
1. Moving charges (for example, electric current) produce a magnetic field.
v
-
+
+
2. Magnetic field affects only moving charge and a wire with electric current.
3. Electromagnetic induction: changing magnetic field induces the electric field.
Physics 112, Spring 2010, Feb 24, Lecture 18
B
I
3
Moving charge = electric current
Right-hand rule #1
Physics 112, Spring 2010, Feb 24, Lecture 18
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Energy Produced by Wind Turbines
Electromagnetic Induction
Wind turbines can
be placed at any
location.
Wind Energy Center in
Hancock County, Iowa.
Iowa is the second largest
producer of wind energy in
the USA:
Texas (9,410 MW)
Iowa (3,670 MW)
California (2,794 MW)
Washington (1,980 MW)
Minnesota (1,809 MW)
TPI Composites,
Newton, Iowa, is a
leading provider of
blades to the wind
energy movement.
5 MW (5 Megawatts) wind turbine.
Physics 112, Spring 2010, Feb 24, Lecture 18
Coil
Renewable energy obtained
by wind generators.
Amazing physics phenomenon
used in wind turbines:
electromagnetic induction.
5
Permanent
magnet
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Physics 112, Spring 2010, Feb 24, Lecture 18
Induced Electromotive Force (EMF)
Electromagnetic Induction
If magnetic field changes in some space, it results in appearance of the
electric field in this space.
Faraday’s experiment to
induce an EMF.
Wire made of copper
v
N
Effect from permanent magnet moving inside the coil.
S
v
N
S
V
Electric field lines
A moving magnet produces an
electric field in the space around it.
A moving magnet produces an
electric voltage in the coil.
Electromagnetic induction: the electric voltage induced by changing magnetic field.
Physics 112, Spring 2010, Feb 24, Lecture 18
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Physics 112, Spring 2010, Feb 24, Lecture 18
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Magnetic Flux
Induction
Magnetic flux through the area:
r
B
r
B
Φ B = BA
In addition to
changing B, the
magnetic flux will
also change if the
area of the loop
changes.
ΦB = 0
A=0
A
Magnetic flux = (magnetic field) × (area) × cosθ
Units:
Similarly, flux will
change if the angle
between the loop and
the field changes.
ΦB = B⊥ A = BAcosθ
T ⋅ m 2 = weber = Wb
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Physics 112, Spring 2010, Feb 24, Lecture 18
Faraday’s Law of Induction
For a coil containing N loops of wire:
ε = −N
ΔΦB
Δt
ΦB
t
Minus sign in Faraday’s law is there to remind us in
which direction the induced EMF acts.
ε = −N
ΔΦB
Δt
The current produced by an induced EMF moves in
a direction such that its magnetic field opposes the
original change in flux.
Note: The induced current tries to keep the flux constant.
EMF induced in coil
Units:
10
Physics 112, Spring 2010, Feb 24, Lecture 18
Lenz’s Law
The induced EMF in a closed loop is proportional to the
rate of change of magnetic flux, through the loop.
ε
Induced
current
Magnetic field increases into the
plane of the paper. In which
direction does the induced
current flow in the loop?
Induced field must point out
of the paper (to keep the total
flux inside the loop constant)
rate of change of magnetic
flux through coil
- volts
- webers
- seconds
IIND
BIND points out of
plane of paper
B increasing into
plane of paper
Hence, IIND flows counterclockwise around the loop.
Physics 112, Spring 2010, Feb 24, Lecture 18
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Physics 112, Spring 2010, Feb 24, Lecture 18
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Induction
Electromagnetic Induction
A square loop of wire 20 cm on a side contains 20 turns and rotates in a
magnetic field of 3 T making 1 revolution per 1 second. Find:
An iron loop and copper loop of equal area are placed in a changing
magnetic field.
Across which loop is an induced EMF (voltage) generated?
1. Maximum magnetic flux that can pass through the loop.
ΦB = B⊥ A = BAcosθ = A cos00 = (3T )(0.2 m× 0.2 m)(1) = 0.12 Wb
iron
Changing B
2. Minimum magnetic flux that can pass through the loop.
ε = −N
ΦB = BAcosθ = Acos900 = (3T )(0.2 m × 0.2 m)(0) = 0
1) in iron loop
2) in copper loop
3. Electromotive force induced in the coli.
ε = −N
ΔΦB
Δt
0.12Wb
ΔΦB
= (20)
= 9.6 V
0.25 s
Δt
3) in both loops
copper
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Physics 112, Spring 2010, Feb 24, Lecture 18
Physics 112, Spring 2010, Feb 24, Lecture 18
Electromagnetic Induction
14
Units
The units for magnetic flux:
A plastic loop and copper loop of equal area are placed in a changing
magnetic field.
1) farad
Across which loop is an induced EMF (voltage) generated?
2) coulomb
3) weber
plastic
4) tesla
Changing B
ε = −N
1) in plastic loop
ΔΦB
Δt
Units
The units for magnetic field:
1) farad
2) in copper loop
2) coulomb
3) in both loops
copper
3) weber
4) tesla
Physics 112, Spring 2010, Feb 24, Lecture 18
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Physics 112, Spring 2010, Feb 24, Lecture 18
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