Chapter 7 Magnetism Electromagnetism
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Topics
Magnetic Field
Electromagnetism
Electromagnetic Devices
Magnetic Hysteresis
Electromagnetic Induction
DC Generators
DC Motors
Chapter 7 Magnetism Electromagnetism
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Magnetic Quantities
Magnetic fields are described by
drawing flux lines that represent the
magnetic field.
Where lines are close
together, the flux
density is higher.
Where lines are further
apart, the flux density
is lower.
Flux Lines Always go from N to S
Chapter 7 Magnetism Electromagnetism
The Magnetic Field
Magnetic fields are
composed of
invisible lines of
force that radiate
from the north pole
to the south pole of a
magnetic material.
Field lines can be visualized with the aid of iron filings
sprinkled in a magnetic field.
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Chapter 7 Magnetism Electromagnetism
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Earth’s Magnetic Poles
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Magnetic Quantities
• Magnetic flux lines surround a current carrying wire.
• The field lines are concentric circles.
• As in the case of bar magnets, the effects
of electrical current can be visualized with
iron filings around the wire – the current
must be large to see this effect.
Iron filings
Current-carrying wire
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Magnetic Quantities
• Recall that magnetic flux lines surround a current-carrying
wire. A coil reinforces and intensifies these flux lines.
• The cause of magnetic flux is called magnetomotive
force (mmf), which is related to the current and number of
turns of the coil.
Fm = NI
Fm = magnetomotive force (A-t)(ampere-turn)
N = number of turns of wire in a coil
I = current (A)
Chapter 7 Magnetism Electromagnetism
Magnetic Quantities
• Lets calculate’s the magnetomotive force (mmf)
• N= 450 turns in the coil I = 5A
Fm = NI
Fm = magnetomotive force (A-t)(ampere-turn)
N = number of turns of wire in a coil
I = current (A)
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Magnetic Quantities
The magnetomotive force (mmf) is not a true force in the
physics sense, but can be thought of as a cause of flux in
a core or other material.
Iron core
Current in the coil causes flux
in the iron core.
What is the mmf if a 250
turn coil has 3 A of current?
750 A-t
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Factors Influencing Electromagnetic
Strength in an Coil
1. Number of
turns of
Wire
2. Amount of
Current
3. Reluctance
of the
material in
the core
(conductance)
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The Hall effect is an occurrence of a very small voltage that
is generated on opposite sides of a thin current-carrying
conductor or semiconductor (the Hall element) that is in a
magnetic field.
The Hall effect is widely
employed by various sensors
for directly measuring
position or motion and can
be used indirectly for other
measurements.
Hall element
(semiconductor)
Current
N
+
Hall voltage _
Magnetic field
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The Hall Effect
• Hall sensors are commonly used to measure
parameters associated with rotating devices (e.g.
wheels and shafts)
–
–
–
–
internal combustion engine ignition timing
tachometers
anti-lock braking systems
brushless DC electric motors to detect the position of the
permanent magnet
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Solenoids
A solenoid is a magnetic device that produces mechanical
motion from an electrical signal.
Stationary core
Sliding core
(plunger)
Spring
One application is valves that can
remotely control a fluid in a pipe,
such as in sprinkler systems.
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Relays
A relay is an electrically controlled switch; a small control
voltage on the coil can control a large current through the
contacts.
Structure
Contac t points
Arm ature
Spring
Elec trom agnetic
c oil
Term inals
Term inals
Schematic
symbol
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Relays
A relay is an electrically controlled switch; a small control
voltage on the coil can control a large current through the
contacts.
Contac t points
StructureAlternate
schematic symbol
Schematic
Arm ature
Term inals
Spring
symbol
Fixed
contact
NC
contacts
CR1 -1
CR1
Movable contact
NO
contacts
Elec trom agnetic
c oil
CR1 -2
Fixed
Term inals
contact
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Magnetic Quantities
The unit of flux is the weber (Wb). The unit of flux
density is the weber/square meter, which defines the unit
tesla, (T), a very large unit.
j

B=
Flux density is given by the equation
A
where
B = flux density (T)
Flux lines (j
j = flux (Wb)
A = area (m2)
2
Area (m)
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Flux and Flux Density
• Magnetic Flux:
– Denoted by Greek letter (Φ, phi)
– Unit of Measurement: Weber (Wb)
– 1 Weber = 108 lines of flux
– Normally use µW = 100 lines of flux
• Magnetic Flux Density
– Denoted by B
– Unit of Measure: Tesla (T)
– 1 Tesla = 1 Weber/ SQ meter
Flux lines (j
2
Area (m )
B
 (Wb )
A( m 2 )
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Flux and Flux Density
1 Dot = 100 lines of Flux
Calculate the flux density for (a) and (b)
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Magnetic Quantities
What is the flux density in a rectangular
core that is 8.0 mm by 5.0 mm if the flux is 20 mWb?
j
B=
A
B

20  106 Wb

8.0  103 m 5.0  103 m

 0.50 Wb/m2 = 0.50 T
Express this result in gauss.
 104 G 
0.5 T 
  5000 G
 T 
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Gauss Meter
Although the Tesla (T)
Is the SI unit for Flux
Density, another unit Called the gauss (G)
From the GCS
(centimeter-gram-second)
System, is used 104 G = 1T
This instrument is used to
Measure flux density.
Chapter 7 Magnetism Electromagnetism
Operation of a typical
magnetic switch.
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Electromagnetic Field
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Lines of Force
Left Hand Rule
Current flow
Chapter 7 Magnetism Electromagnetism
• What is the flux density in a rectangular
core that is 7.0 mm by 4.0 mm if the flux is
42 mWb?
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Magnetic Quantities
• Permeability (m) defines the ease with which a
magnetic field can be established in a given material. It is
measured in units of the weber per ampere-turn meter.
• The permeability of a vacuum (m0) is 4p x 10-7 weber
per ampere-turn meter, which is used as a reference.
• Relative Permeability (mr) is the ratio of the absolute
permeability to the permeability of a vacuum.
mr 
m
m0
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Magnetic Quantities
• Permeability (µ - mu) is the ease in the establishment of a
magnetic field in a material.
• Vacuum (mo = 4*10-7 Wb/At*M (webers/amp-turn*meter)
• Relative permeability is compared to a vacuum.
•
mr 
Relative permeability, also
of the ratio permeabilities.
m
m
r

Has no units of measurement because
mo
• Reluctance (R) is the opposition to the establishment
of a magnetic field in a material. (similar to resistance)
R= reluctance in A-t/Wb
l = length of the path (meter(s))
m = permeability (Wb/A-t m).
A = area (m2)
R
l
mA
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What is the Relative Permeability of a ferromagnetic material whose absolute permeability
is 480 x 10-6 Wb/At x m?
What do we know?
m
mr 
mo
What is the Relative Permeability of a ferromagnetic material whose absolute permeability
is 560 x 10-6 Wb/At x m?
What is the Relative Permeability of a ferromagnetic material whose absolute permeability
is 720 x 10-6 Wb/At x m?
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Reluctance
R= reluctance in A-t/Wb
l = length of the path (meter(s))
m = permeability (Wb/A-t m).
A = area (m2)
l
R
mA
4. Determine the reluctance of a material with a length of 3.5 cm and a cross-sectional
area of 0.1 m2 if the absolute permeability is 120 x 10-7 Wb/At*m.
5. Determine the reluctance of a material with a length of 0.25 m and a cross-sectional
area of 0.15 m2 if the absolute permeability is 110 x 10-7 Wb/At*m.
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1. Ohm’s law for electromagnetic circuits: because the flux (φ) is analogous (comparable in
certain aspects) to________, the mmf (Fm ) is similar to __________ and Reluctance (R) is
analogous to resistance.
2.
Fm


How much Flux is established in a magnetic path of a coil with 500 turns
and 0.3A with a Reluctance of 2.8 x 105 At/Wb?
3. There is 0.1 ampere of current through a coil with 400 turns.
a) what is the mmf?
B.) What is the reluctance of the circuit if the flux is 250µWb?
4.How much Flux is established in a magnetic path of a coil with 350 turn and 0.2A with a
Reluctance of 3.5 x 105 At/Wb?
Chapter 7 Magnetism Electromagnetism
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Summary
Magnetic field intensity is the magnetomotive force
per unit length of a magnetic path.
H=
Fm
l
or
H = NI
l
H= Magnetic field intensity (Wb/A-t m)
Fm = magnetomotive force (A-t)
l = average length of the path (m)
N = number of turns
I = current (A)
• Magnetic field intensity represents the effort that a
given current must put into establishing a certain flux
density in a material.
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Relative motion
S
When a wire is moved across a magnetic field,
there is a relative motion between the wire and
the magnetic field.
N
S
When a magnetic field is moved past a
stationary wire, there is also relative motion.
In either case, the relative motion results in
an induced voltage in the wire.
N
Chapter 7 Magnetism Electromagnetism
Induced voltage
The induced voltage due to the relative motion
between the conductor and the magnetic field when the
motion is perpendicular to the field is dependent on
three factors:
• the relative velocity (motion is perpendicular)
• the length of the conductor in the magnetic field
• the flux density
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Chapter 7 Magnetism Electromagnetism
Faraday’s law
Faraday experimented with generating current by
relative motion between a magnet and a coil of wire.
The amount of voltage induced across a coil is
determined by two factors:
S
1. The rate of change of the
N magnetic flux with respect
to the coil.
-V+
Voltage is indicated only
when magnet is moving.
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Chapter 7 Magnetism Electromagnetism
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Summary
Faraday’s law
Faraday also experimented generating current by
relative motion between a magnet and a coil of wire.
The amount of voltage induced across a coil is
determined by two factors:
S
-V+
1. The rate of change of the
magnetic flux with respect
N
to the coil.
2. The number of turns of
wire in the coil.
Voltage is indicated only
when magnet is moving.
Chapter 7 Magnetism Electromagnetism
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Summary
Magnetic field around a coil
Just as a moving magnetic field induces a voltage,
current in a coil causes a magnetic field. The coil acts as
an electromagnet, with a north and south pole as in the
case of a permanent magnet.
South
North
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DC Generator
A dc generator includes a rotating coil,
which is driven by an external Wire Loop
mechanical force (the coil is
shown as a loop in this
simplified view). As the coil
rotates in a magnetic field, a
pulsating voltage is generated.
Brushes
Commutator
To external circuit
Mechanical drive
turns the shaft
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Wound Rotor core
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DC Motor
A dc motor converts electrical energy to mechanical
motion by action of a magnetic field set up by the rotor.
The rotor field interacts with the stator
field, producing torque, which causes the
output shaft to rotate.
The commutator serves as
a mechanical switch to
reverse the current to the
rotor at just the right time
to continue the rotation.
Mechanical
output
–
+
I
Commutator
Brushes
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Brushless DC Motor
A brushless dc motor has rotating field and a permanent
magnet rotor. An electronic controller periodically
reverses the current in the field coils. This causes the
stator field to rotate, and the permanent magnet rotor
moves to keep up with the rotating field.
Hall sensor
Permanent magnet rotor
(Courtesy of Bodine Electric Company)
Chapter 7 Magnetism Electromagnetism
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Summary
Brushless
Series
wound
DC dc
Motor
motor
•A series wound dc motor
has the field coil(s) in
series with the armature.
•The series wound motor
has very high starting
torque.
•It can run too fast if a load
is not connected; therefore
it is always used with a
load.
Internal resistance
DC Voltage
Speed control
Field coil
Armature
Interpole windings
Speed
Starting torque
Torque
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Shunt wound dc motor
•A shunt wound dc motor
has the field coil(s) in
parallel with the armature.
•The magnetic flux is
constant because of the
parallel arrangement.
•Unlike the series wound
motor, torque tends to be
nearly constant for
different loads.
RF
RA
DC Voltage
Armature
Field
coil
Full load torque
Speed
Torque
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Magnetic units
It is useful to review the key magnetic units from this
chapter:
Quantity
SI Unit
Magnetic flux density
Flux
Permeability
Reluctance
Magnetomotive force
Magnetizing force
Tesla
Weber
Weber/ampere-turn-meter
Ampere-turn/Weber
Ampere-turn
Ampere-turn/meter
Symbol
B
f
m
R
Fm
H
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Key Terms
Magnetic field A force field radiating from the north pole to
the south pole of a magnet.
Magnetic flux The lines of force between the north pole and
south pole of a permanent magnet or an
electromagnet.
Weber (Wb) The SI unit of magnetic flux, which represents
108 lines.
Permeability The measure of ease with which a magnetic
field can be established in a material.
Reluctance The opposition to the establishment of a
magnetic field in a material.
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Key Terms
Magnetomotive The cause of a magnetic field, measured in
force (mmf) ampere-turns.
Solenoid An electromagnetically controlled device in
which the mechanical movement of a shaft or
plunger is activated by a magnetizing current.
Hysteresis A characteristic of a magnetic material
whereby a change in magnetism lags the
application of the magnetic field intensity.
Retentivity The ability of a material, once magnetized, to
maintain a magnetized state without the
presence of a magnetizing current.
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Key Terms
Induced voltage Voltage produced as a result of a changing
(vind) magnetic field.
Faraday’s law A law stating that the voltage induced across a
coil of wire equals the number of turns in the
coil times the rate of change of the magnetic
flux.
Lenz’s law A law stating that when the current through a
coil changes, the polarity of the induced
voltage created by the changing magnetic
field is such that it always opposes the change
in the current that caused it. The current
cannot change instantaneously.
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Quiz
1. A unit of flux density that is the same as a Wb/m2 is the
a. ampere-turn
b. ampere-turn/weber
c. ampere-turn/meter
d. tesla
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Quiz
2. If one magnetic circuit has a larger flux than a second
magnetic circuit, then the first circuit has
a. a higher flux density
b. the same flux density
c. a lower flux density
d. answer depends on the particular circuit.
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Quiz
3. The cause of magnetic flux is
a. magnetomotive force
b. induced voltage
c. induced current
d. hysteresis
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Quiz
4. The measurement unit for permeability is
a. weber/ampere-turn
b. ampere-turn/weber
c. weber/ampere-turn-meter
d. dimensionless
Chapter 7 Magnetism Electromagnetism
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Quiz
5. The measurement unit for relative permeability is
a. weber/ampere-turn
b. ampere-turn/weber
c. weber/ampere-turn meter
d. dimensionless
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Quiz
6. The property of a magnetic material to behave as if it
had a memory is called
a. remembrance
b. hysteresis
c. reluctance
d. permittivity
Chapter 7 Magnetism Electromagnetism
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Quiz
7. Ohm’s law for a magnetic circuit is
a. Fm = NI
b. B = mH
Fm
j

c.
R
d. R 
l
mA
Chapter 7 Magnetism Electromagnetism
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Quiz
8. The control voltage for a relay is applied to the
a. normally-open contacts
b. normally-closed contacts
c. coil
d. armature
Chapter 7 Magnetism Electromagnetism
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Quiz
9. A partial hysteresis curve is shown. At the point
indicated, magnetic flux
B
a. is zero
b. exists with no magnetizing force
c. is maximum
d. is proportional to the current
BR
H
Chapter 7 Magnetism Electromagnetism
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Quiz
10. When the current through a coil changes, the induced
voltage across the coil will
a. oppose the change in the current that caused it
b. add to the change in the current that caused it
c. be zero
d. be equal to the source voltage
Chapter 7 Magnetism Electromagnetism
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Quiz
Answers:
1. d
6. b
2. d
7. c
3. a
8. c
4. c
9. b
5. d
10. a