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Chapter
14
Electromagnetism
Topics Covered in Chapter 14
14-1: Ampere-turns of Magnetomotive Force (mmf)
14-2: Field Intensity (H)
14-3: B-H Magnetization Curve
14-4: Magnetic Hysteresis
14-5: Magnetic Field around an Electric Current
© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
Topics Covered in Chapter 14
 14-6: Magnetic Polarity of a Coil
 14-7: Motor Action between Two Magnetic Fields
 14-8: Induced Current
 14-9: Generating an Induced Voltage
 14-10: Relays
McGraw-Hill
© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
14-1: Ampere-turns of
Magnetomotive Force (mmf)
 The strength of a coil’s magnetic field is proportional to
the amount of current flowing through the coil and the
number of turns per given length of coil.
 Ampere-turns = I × N = mmf
 I is the amount of current flowing through N turns of
wire.
 This formula specifies the amount of magnetizing force
or magnetic potential (mmf).
14-1: Ampere-turns of
Magnetomotive Force (mmf)
 The SI abbreviation for
ampere-turn is A · t.
 The cgs unit of mmf is the
gilbert, abbreviated Gb.
 1 A.t = 1.26 Gb
Fig. 14-1: Two examples of equal ampereturns for the same mmf. (a) IN is 2 × 5 = 10.
(b) IN is 1 × 10 = 10.
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14-2: Field Intensity (H)
 The length of a coil influences the intensity of a
magnetic field. Intensity is different from mmf.
 Equation: H = mmf/length
 Units: A·t/m
ampere-turns per meter
 A·t/m is the mks unit
 The cgs unit for H is the oersted (Oe), which equals 1
gilbert per centimeter.
 Shorter magnetic circuits produce a greater field
intensity
14-2: Field Intensity (H)
The field intensity in the core is inversely related to length.
Fig. 14-2: Relation between ampere-turns of mmf and the resultant field intensity H for different
cores. Note that H = mmf/length. (a) Intensity H is 1000 A · t/m with an air core. (b) H = 1000 A ·
t/m in an iron core of the same length as the coil. (c) H is 100 / 2 = 500 A · t/m in an iron core
twice as long as the coil.
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14-2: Field Intensity (H)
 Permeability (μ)
 Permeability is a measure of the ability to concentrate
magnetic fields. Materials with high permeability can
concentrate flux, and produce large values of flux
density B for a specified H.
 The amount of flux produced by H depends on the
material in the field.
 These factors are reflected in the formulas:
 B=μ×H
 μ=B/H
Permeability (μ)
 In cgs system, μ = 1 G/Oe for air or space
 i.e. B and H have the same value for air
 Relative permeability, μr is equal to absolute permeability
B/H or μ
 In SI system, the permeability of air is μ0 = 1.26 x 10-6
 So, μ = μ0 x μr = 1.26 x 10-6 x μr
T
 The unit is teslas per ampere-turn per meter:
A. t
m
14-2: Field Intensity (H)
Permeability drops drastically
at saturation.
+B
+ Bmax
Slope of
B/H is large
+H
Slope of
B/H is small
-H
- Bmax
-B
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14-3: B-H Magnetization Curve
 The B-H magnetization
curve shows how
much flux density B
results from increasing
field intensity H.
 Saturation is the effect
of little change in flux
density when the field
intensity increases.
Fig. 14-3: B-H magnetization curve for
soft iron. No values are shown near
zero, where μ may vary with previous
magnetization.
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14-4: Magnetic Hysteresis
 Hysteresis refers to a situation where the magnetic flux
lags the increases or decreases in magnetizing force.
 Hysteresis loss is energy wasted in the form of heat
when alternating current reverses rapidly and molecular
dipoles lag the magnetizing force.
 For steel and other hard magnetic materials, hysteresis
losses are much higher than in soft magnetic materials
like iron.
14-4: Magnetic Hysteresis
 Hysteresis Loop
 BR is due to retentivity,
which is the flux density
remaining after the
magnetizing force is
reduced to zero.
 Note that H = 0 but B > 0.
 HC is the coercive force
(needed to make B = 0)
Fig. 14-4: Hysteresis loop for magnetic materials.
This graph is a B-H curve like Fig. 14-3, but H
alternates in polarity with alternating current.
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14-4: Magnetic Hysteresis
 Demagnetization (Also Called Degaussing)
 To demagnetize a magnetic material completely, the
retentivity BR must be reduced to zero.
 The practical way to do so is to magnetize and
demagnetize the material with a decreasing hysteresis
loop:
 A magnetic field is produced by alternating current.
 The magnetic field and the magnetic material are
moved away from each other, or the current
amplitude is reduced.
 The hysteresis loop then becomes smaller and
smaller until it effectively collapses.
14-4: Magnetic Hysteresis
 Demagnetization (Also Called Degaussing)
 This method of demagnetization is called degaussing.
 Applications of degaussing include:
 Metal electrodes in a color picture tube
 Erasing the recorded signal on magnetic tape.
14-5: Magnetic Field around an
Electric Current
 Straight Conductor
 A straight conductor can be a short but continuous
length of conducting wire with no bends.
 A magnetic field is produced by the flow of current
through a straight conductor.
 The magnetic field around a straight conductor is
circular and perpendicular to the axis of the conductor.
 The polarity of the circular field is counterclockwise
when viewed along the conductor in the direction of
electron flow, Iin.
 These requirements apply to any charge in motion.
14-5: Magnetic Field around an
Electric Current
 Clockwise and Counterclockwise Fields
 The left-hand rule for conductors:
 Grasp the conductor with your left hand so the thumb
points in the direction of electron flow. Your fingers
will encircle the conductor in the same direction as
the circular magnetic field lines.
14-6: Magnetic Polarity of a Coil
 Bending a straight conductor into the form of a
loop produces two effects:
 The magnetic field lines are more dense inside
the loop.
 All the lines inside the loop aid in the same
direction.
 This makes the loop field the same as a bar
magnet, with opposite poles at opposite faces
of the loop.
14-6: Magnetic Polarity of a Coil
 Magnetic Polarity
 A coil of wire conductor with more than one turn is
called a solenoid.
 To determine magnetic polarity for a solenoid, grasp the
electromagnet with the left hand. When the fingers of
the left hand curl around the turns of an electromagnet
in the direction of electron flow, the thumb points to the
north pole.
 The magnetic polarity depends on the direction of
current flow and the direction of winding. The current is
determined by the connections to the voltage source:
flow runs from negative to positive.
14-6: Magnetic Polarity of a Coil
Fig. 14-10: Left-hand rule for north pole of a coil with current I. The I is electron flow.
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14-7: Motor Action between Two
Magnetic Fields
 Motor action is the result of two magnetic fields
interacting with one another.
 The fields can attract or repel.
 Motion is produced from a stronger field toward a
weaker field.
14-7: Motor Action between Two
Magnetic Fields
 Current in a conductor has its own magnetic field.
 When placed in the magnetic field of a separate source,
the two can produce motor action.
 The conductor must be perpendicular to the field. It
must also be in the same plane.
 There is stronger force below the conductor, because
the fields add up, so conductor moves up.
14-7: Motor Action between Two
Magnetic Fields
Fig. 14-13: Motor action of current in a straight conductor when it is in an external magnetic
field. The HI is the circular field of the current The HM indicates field lines between the north and
south poles of the external magnet.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
14-7: Motor Action between Two
Magnetic Fields
 Torque is the effect of a force producing rotation.
 Torque is produced when opposing magnetic fields in a
loop produce an upward force on one side of the loop
and downward force on the other.
 Torque is the basis of all electric motors.
 Torque is proportional to current, so the amount of
rotation indicates how much current flows through the
coil.
14-8: Induced Current
 Generator Action
 When a moving conductor cuts across flux lines, a
voltage is induced.
 The amount of induced voltage is proportional to:
 The conductor velocity
 The amount of flux
 The number of turns of wire
 The polarity of induced voltage is determined by Lenz’s
law (discussed in section 14-9).
14-8: Induced Current
 Lenz’s law states that the direction of an induced
current must be such that its own magnetic field will
oppose the action that produced the induced current.
The direction of the induced current is
determined by the left-hand rule for electron
flow. If the fingers coil around the direction of
electron shown, under and over the winding, the
thumb will point to the left for the north pole.
Fig. 14-15: Induced current produced by magnetic flux cutting across turns of wire in a coil.
Direction of I here is for electron flow.
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14-9: Generating an
Induced Voltage
 Consider a magnetic flux
cutting a conductor that is
not in a closed circuit, as
shown in Figure 14-16.
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14-9: Generating an
Induced Voltage
 The motion of flux across a conductor in an open circuit




forces free electrons to move.
Since the ends are open, electrons accumulate at them,
creating a potential difference.
The potential difference is an electromotive force
(emf), generated by the work of cutting across the flux.
Induced emf increases with the number of turns in a
coil.
The polarity of the induced voltage follows from the
direction of induced current.
14-9: Generating an
Induced Voltage
 Faraday’s Law of Induced Voltage
 The amount of voltage induced by flux cutting the turns
of a coil is determined by three factors:
 The amount of flux
 More voltage is generated by a stronger magnet.
 The number of turns
 Increasing the turns generates more voltage.
 The time rate of cutting.
 Less voltage is generated when the conductor moves slowly.
 Either the flux or the conductor can move.
14-9: Generating an
Induced Voltage
 Faraday’s Law of Induced Voltage
 The amount of induced voltage can be calculated by
Faraday’s law:
dΦ (webers)
vind = N
dt (seconds)
 N = number of turns
 dΦ/dt = how fast the flux cuts across the conductor.
14-9: Generating an
Induced Voltage
Fig. 14-17: Voltage induced across coil cut by magnetic flux. (a) Motion of flux generating voltage
across coil. (b) Induced voltage acts in series with coil. (c) Induced voltage is a source that can
produce current in an external load resistor RL connected across the coil.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
14-9: Generating an
Induced Voltage
Fig. 14-18: Graphs of induced voltage produced by magnetic flux changes in a coil. (a) Linear
increase of flux Φ. (b) Constant rate of change for dΦ/dt at 2 Wb/s. (c) Constant induced voltage
of 600 V, for a coil with 300 turns.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
14-9: Generating an
Induced Voltage
 Faraday’s Law of Induced Voltage
 The amount of induced voltage is calculated by
Faraday’s law:
d(Wb)
vind = N
dt(seconds)
 The induced voltage is directly proportional to the
number of turns times d/dt.
 To generate more voltage:
 Increase the number of turns
 Increase the flux
 Decrease the time
14-9: Generating an
Induced Voltage
 Polarity of Induced Voltage
 The polarity of induced voltage is determined by Lenz’s
law.
 An induced voltage has the polarity that opposes the
change causing the induction.
 Absolute polarity depends upon three points:
 Whether the flux is increasing or decreasing;
 The method of winding;
 Which end of the coil is the reference.
14-10: Relays
 A relay is an electromechanical device that operates on




the basis of electromagnetic induction.
It uses an electromagnet to open or close one or more
sets of contacts.
Relays, like switches, have poles and throws.
Relays can switch or control high power loads with a
low amount of input power.
In remote-control applications, relays can control high
power loads long distances away more efficiently than
can mechanical switches.
14-10: Relays
 The switching contacts of a relay may be:
 Normally open (NO)
 Normally closed (NC)
 The movable arm on a relay is called the armature.
 When the coil is energized, the armature:
 Opens the contacts (NC relay)
 Closes the contacts (NO relay)
14-10: Relays
An SPDT relay has both NO and NC contacts.
When the coil is energized, the armature is attracted and opens the NC contacts and closes the
NO contacts.
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14-10: Relays
 Relay Specifications:
 The following are a relay’s most important ratings:
Pickup voltage
The minimum amount of relay coil voltage
necessary to energize or operate the relay.
Pickup current
The minimum amount of relay coil current
necessary to energize or operate the relay.
Holding current
The minimum amount of current required to keep
a relay energized or operating (less than the
pickup current).
Dropout voltage
The maximum relay coil voltage at which the relay
is no longer energized.
14-10: Relays
 Relay Specifications:
 Important ratings, cont.
Contact voltage
rating
The maximum voltage the relay contacts are
capable of switching safely.
Contact current
rating
The maximum current the relay contacts are
capable of switching safely.
Contact voltage drop The voltage drop across the closed contacts of a
relay when operating.
Insulation resistance The resistance measured across the relay
contacts in the open position.
14-10: Relays
The pickup current is greater than the hold current because of the air gap.
The armature has
moved
and the air gap is gone.
Less current is now
required to
overcome the spring
and hold the relay
closed.
There is continuity between the main contact and the NO contact.
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