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Principles of Technology
Ch 11 MAGNETISM 3
Name________
KEY OBJECTIVES:
At the conclusion of this lecture you will be able to:
• Describe how a potential difference may be induced across a conductor moving in a magnetic field.
• State the equations that govern electromagnetic induction, and use them to solve related problems.
• Describe the construction and operation of a simple alternating- current generator.
• State Lenz’s law, and demonstrate how it applies to electromagnetic induction.
• Define the term electromotive force, state Lenz’s law, and define the term back emf
• Define the term transformer, and describe the principle upon which a transformer operates.
• State the equations relevant to transformer operation, and apply them to the solution of problems.
• Describe how electromagnetic waves may be produced from accelerating charges.
11.5 ELECTROMAGNETIC INDUCTION
A motor uses a magnetic field to convert electrical energy into mechanical energy. It is also
possible to accomplish the reverse process, that is, to use a magnetic field to convert mechanical energy
into electrical energy. Devices that accomplish this purpose are known as generators. Let’s begin by
moving a wire perpendicularly through a magnetic field (Fig. 1)
Fig. 1 (below) Moving a wire perpendicularly through a magnetic field.
Fig. 2 Focusing on one electron in the wire (above).
If we focus on one electron in the wire, indicated in the diagram below:
we can apply right hand rule 3, but we must use the left hand (why?), to show that there is a downward
force on the electron. This is true for all electrons passing through the moving segment of the wire.
These moving electrons constitute an electric current.
Since work has been done in moving the electrons through the wire, a potential difference has been
induced across the ends of the wire. This potential difference (V) depends on the strength of the
magnetic field (B), the length of the wire in the magnetic field (ℓ), and the speed (v) with which the
wire is moved. The induced potential difference is represented by this relationship:
V= Bℓv
PROBLEM
Calculate the potential difference (V) induced across the ends of a conductor that is 0.20 meter (ℓ)
long and is moved perpendicularly through a magnetic field of 4.0 x 10-1 tesla (B), with a speed of 8.0
meters per second (v).
SOLUTION
V= Bℓv = (4.0 x 10-1 T)(0.20 m)(8.0 m/s) = 6.4 x 10-1 V
Assessment Question 1
Calculate the potential difference (V) induced across the ends of a conductor that is 3.70 meter (ℓ)
long and is moved perpendicularly through a magnetic field of 0.05 tesla (B), with a speed of 58 meters
per second (v).
V= Bℓv
a) 0.90 V
b) 11 V
c) 59 V
d) 130 V
Electromotive force (emf)
Induced potential difference is also known as electromotive force (emf), symbolized as E.
To induce a potential difference across a conductor, the only requirement is that the magnetic field be
interrupted. This interruption is accomplished when the conductor “cuts through” the magnetic field
lines. However, physical motion need not be present, only a change in the magnetic field is required.
Our equation V= Bℓv is completely equivalent to the following equation: V=Δφ/Δt
This equation shows that it is the change in the magnetic flux with time that produces the potential
difference. The Greek letter (phi), Δφ, represents the magnetic flux, which is measured in webers.
Assessment Question 2
Calculate the potential difference (V) induced across the ends of a conductor that has a change in
magnetic flux 980 webers (Δφ) in 13 seconds (Δt).
V=Δφ/Δt
a) 0.8 V
b) 34 V
c) 75 V
d) 1300 V
Generators
Fig. 3 A very simple electric generator (below)
A generator is a commercial device that converts
mechanical energy into electrical energy. The source of
mechanical energy can be falling water, steam expansion, or
something as simple as a hand crank.
In a very simple electric generator, such as the one diagramed
below (Fig. 3), a coil of wire is wrapped around an iron core.
This arrangement is placed in a magnetic field and rotated in the
field.
Assessment Question 3
Which set of statements is true:
i. A motor uses a magnetic field to convert electrical
energy into mechanical energy.
ii. A generator is a commercial device that converts
mechanical energy into electrical energy
iii. Induced potential difference is also known as
electromotive force (emf), symbolized as E.
iv. To induce a potential difference across a conductor, the
only requirement is that the magnetic field be constant.
v. Physical motion is needed to cause the magnetic field to be interrupted in a conductor.
a) i , ii, iii
b) i , iii, iv
c) ii , iii, v
d) i , iii, v
Fig. 4: Coil position at different intervals in a generator
In this arrangement, it is the ends of the coil that interrupt
the field and produce the potential difference across the
ends of the coil. Let’s rotate the coil clockwise through
3600 and show the rotation at 90° intervals (Fig. 4). If we
apply right hand rule 3 to the rotating coil, we can show the
direction of the current in the coil at each position.
Points A, B, C, and D, are shown in order to orient the coil
during each 90° rotation. At positions 2 and 4 in the
diagram the current in the coil is zero because the ends of
the coil do not interrupt the magnetic field. We also note
that the direction of the current in position 3 is opposite to
the direction of the current in positions 1 and 5. This type
of generator is known as an alternating-current (ac)
generator because it produces a current that reverses its
direction regularly. Until this point, we considered currents
that have only one direction and are known as direct currents (dc).
This alternating current is a direct result of the fact that the potential difference across the ends of the
coil has reversed direction. If we included all the intermediate positions of the coil, we would find that
the potential difference (or current) varies as shown in the diagram (Fig. 5). This variation traces out a
cosine or sine wave. The speed with which the coil is rotated determines the “frequency” of the ac
potential difference. In the United States alternating current is produced at 60 hertz (Hz), indicating that
the current reverses its direction 60 times each second.
Fig. 5: Potential Difference and Current v. time in a coil (below)
11.6 LENZ’S LAW
Fig. 6: A bar magnet being brought towards a coil (above)
Suppose a bar magnet is brought toward a coil of wire as shown above.
Since the coil will interrupt the magnetic field, a potential difference will be induced across the ends of the coil and a
current will be established in it. What is the direction of the current in the coil?
Obviously, there are only two choices. In either case the coil will behave as an electromagnet with a north and a south pole.
Fig. 7 (above): The direction of the current in a coil when a bar magnet is brought towards a coil.
In the upper part of the diagram above (Fig. 7), the magnets repel each other; in the lower part, they attract each other. The
magnets attracting cannot be correct because the attraction would eliminate the need to use mechanical energy to induce
electrical energy—a clear violation of the law of conservation of energy. In the upper, however, the repulsion ensures
that outside work will be required in order to induce electrical energy. In 1834, the German physicist H.EE. Lenz
recognized this principle and stated it as follows:
When a potential difference is induced across a conductor, its direction must oppose the motion that induced it.
Whenever a motor is operated, a secondary potential difference is established that reduces the effective potential difference
of the circuit used to operate the motor. This secondary potential difference, which is a result of Lenz’s law, is known as
back emf.
Assessment Question 4
Which set of statements is true:
i. A coil of wires interrupting a magnetic field will cause a potential difference to be induced across
the ends of the coil and a current will be established in it
ii. The repulsion between magnets ensures that outside work will be required in order to induce
electrical energy.
iii. When a potential difference is induced across a conductor, its direction must be the same as the
motion that induced it.
iv. Whenever a motor is operated, a secondary potential difference is established that reduces the
effective potential difference of the circuit used to operate the motor.
v. Primary potential or front emf is a result of Lenz’s law.
a) i , ii, iii
b) i , ii, iv
c) ii , iii, iv
d) i , iii, v
Transformers
When electricity is transmitted across long distances, high voltages are used to reduce losses due to heat At the power
plant the electricity is first generated at a low potential difference and it must be stepped up for transmission.
When electricity enters a building or home, however, its potential difference must be reduced or stepped down.
A transformer is a device that allows the potential difference to be increased or decreased. A diagram of a transformer is
shown below (Fig. 8 ).
Assessment Question 5
Which set of statements is true:
i. Existing transformers are electronic or mechanical devices that turn into robots
ii. When electricity is transmitted across long distances, high voltages reduce losses due to heat.
iii. At the power plant the electricity is first generated at a low potential difference and it must be
stepped up for transmission.
iv. When electricity enters a building or home, however, its potential difference must be reduced or
stepped down.
v. The voltage of electricity remains constant when electricity is transferred from the power plant to
your home.
a) i , ii, iii
b) i , iii, iv
c) ii , iii, iv
d) i , iii, v
Fig. 8: A Transformer (above)
Fig. 9: Transformer Voltage
One of the coils, known as the primary coil, is attached to an alternating- current source, and the other, the secondary coil,
to the circuit that requires the stepped-up or stepped-down voltage. The alternating current in the primary coil produces a
changing electric field that, in turn, produces a changing magnetic field. The changing magnetic field is carried by the iron
core and induces a changing electric field in the secondary coil.
The ratio of the voltages in the primary and secondary coils depends on the relative numbers of turns of wire in these coils,
as indicated in this equation (Fig. 9): Vp/Vs = Np/Ns
If the voltage is increased, that is, if the number of turns is greater in the secondary coil, the transformer is termed a
step-up transformer. If the voltage is decreased (the number of turns in the secondary coil is less), the transformer a stepdown transformer.
PRACTICE PROBLEM
How many turns should the secondary coil (Ns) have if the primary coil on a transformer has 1200 turns (Np) and it is
desired to step down the voltage from 220 volts (Vp) to 110 volts (Vs),
SOLUTION
Fig. 10: Percent Efficiciency (below)
Assessment Question 6
How many turns should the primary coil (Np) have if the secondary coil in a cell phone charger has 80 turns (Ns) and it
is desired to step down the voltage from 110 volts (Vp) to 3.33 volts (Vs),
Vp/Vs = Np/Ns
a) 200
b) 700
c) 2600
d) 5900
Before we conclude that a transformer enables us to get something for nothing, we should remember that we cannot violate
the law of conservation of energy. Specifically, the power output at the secondary coil (Ps = VsIs) cannot exceed the power
input at the primary coil (Pp = VpIp). Therefore, a step-up transformer will produce decreased current at the secondary
coil, and a step-down transformer will produce increased current at the secondary coil. The ratio of the power output to
the power input is known as the efficiency of the transformer. (Fig. 10)
(Percent efficiency = VsIs / VpIp x 100)
Generally, heat losses produce transformers with efficiencies somewhat less than 100%.
Assessment Question 7
Which set of statements is true:
i. If the voltage is increased, that is, if the number of turns is greater in the secondary coil, the
transformer is termed a step-up transformer.
ii. If the voltage is decreased (the number of turns in the secondary coil is less), the transformer a stepdown transformer.
iii. The alternating current in the primary coil produces a changing electric field that, in turn, produces a
changing magnetic field which induces a changing electric field in the secondary coil.
iv. A step-up transformer will produce increased current at the secondary coil, and a step-down
transformer will produce decreased current at the secondary coil.
v. Most transformers have efficiencies of 100%.
a) i , ii, iii
b) i , iii, iv
c) ii , iii, v
d) i , iii, v
PRACTICE PROBLEM
Calculate the percent efficiency of the transformer that steps up potential difference from 300. volts (Vp) to 600. volts
(Vs). The current in the primary coil is 6.0 amperes (Ip), while the current in the secondary coil is 2.0 amperes (Is).
SOLUTION
Percent efficiency = VsIs / VpIp x 100 = (600 V∙2.0 A) / (300 V∙6.0 A) x 100 = 67%
Assessment Question 8
Calculate the percent efficiency of the transformer that steps down potential difference from 110 volts (Vp) to 15 volts
(Vs). The current in the primary coil is 2.0 amperes (Ip), while the current in the secondary coil is 7.5 amperes (Is).
a) 25 %
b) 50 %
c) 75 %
d) 100 %
(Percent efficiency = VsIs / VpIp x 100)
Assessment Question 9
Calculate the percent efficiency of the transformer that steps up potential difference from 500. volts (Vp) to 900. volts
(Vs). The current in the primary coil is 7.0 amperes (Ip), while the current in the secondary coil is 3.0 amperes (Is).
a) 25 %
b) 50 %
c) 75 %
d) 100 %
(Percent efficiency = VsIs / VpIp x 100)
Electromagnetic Waves
Fig. 11: Electromagnetic waves (below)
We have seen that a changing
electric field produces a
changing magnetic field and vice
versa. If the changing electric
field is produced by an
accelerating charge, energy will
be radiated away from the charge
in the form of electromagnetic
waves. In an electromagnetic wave
(Fig. 11), both the electric field
and the magnetic field vary as a
sine wave and the two fields are perpendicular to each other and to their direction of motion. All electromagnetic
waves (collectively known as the electromagnetic spectrum) travel in space at the speed of light.
Assessment Question 10
Which set of statements is true:
i. A changing magnetic field produces a changing electric field.
ii. A changing electric field does not produce a changing magnetic field.
iii. If the changing electric field is produced by an accelerating charge, energy will be radiated away
from the charge in the form of electromagnetic waves. In an electromagnetic wave
iv. The electric field and the magnetic field vary as a sine wave and the two fields are perpendicular to
each other and to their direction of motion.
v. All electromagnetic waves (collectively known as the electromagnetic spectrum) travel in space at
the speed of sound.
a) i , ii, iii
b) i , iii, iv
c) ii , iii, v
d) i , iii, v
Summary
If a conductor is moved perpendicularly through a magnetic field, a potential difference is established
across the conductor. If the conductor is rotated through the field, as occurs in a generator, the potential
difference and the current will alternate in direction. Whenever potential difference is induced in a
conductor, a secondary magnetic field is established that always opposes the original motion. This
statement, known as Lenz’s law, is a consequence of the law of conservation of energy.
An application of alternating current is the transformer. This device uses a changing magnetic field to
increase or decrease the potential difference in a secondary circuit.
If a charge is accelerated, the changing electric and magnetic fields will give rise to electromagnetic
waves that are carriers of energy.