Electromagnetic induction

Topic 12: Electromagnetic induction

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Topic 12: Electromagnetic induction
Describe the inducing of an emf by relative motion between a
conductor and a magnetic field.

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Electromagnetic Induction
N
The direction of the induced current is reversed if…
1) The wire is moved in the opposite direction
2) The field is reversed
The size of the induced current can be increased by:
1) Increasing the speed of movement
2) Increasing the magnet strength

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Electromagnetic
induction
The direction of the induced current is
reversed if…
1) The magnet is moved in the opposite
direction
2) The other pole is inserted first
The size of the induced current can be
increased by:
1) Increasing the speed of movement
2) Increasing the magnet strength
3) Increasing the number of turns on
the coil

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The north pole of a permanent bar magnet is pushed along the axis of a coil as
shown below.
V
N Saxis of coil
The pointer of the sensitive voltmeter connected to the coil moves to the right and gives a
maximum reading of 8 units. The experiment is repeated but on this occasion, the south
pole of the magnet enters the coil at twice the previous speed.
Which of the following gives the maximum deflection of the pointer of the voltmeter?
A. 8 units to the right
B. 8 units to the left
C. 16 units to the right
D. 16 units to the left (1)

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Derivation of Emf
By conservation of energy
Derive the formula for the emf induced in a straight conductor moving
in a magnetic field. Students should be able to derive the expression
induced emf = Blv without using Faraday’s law.

Magnetic flux
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Define magnetic flux and magnetic flux linkage.

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Magnetic Flux
As we said, magnetic field strength is also called magnetic flux density.
The “magnetic flux” is the amount of flux that passes through a given
area:
Magnetic flux = magnetic flux density x area Φ = BA
(in Weber, Wb) in T in m2
For a coil of N turns the total magnetic flux is NΦ
Φ
Faraday (1791-1867)
Faraday’s law:
The induced EMF for a magnet in a coil is
directly proportional to the rate of
change of flux linkage:
EMF = NΔΦ
ΔT

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Magnetic flux
Define magnetic flux and magnetic flux linkage.

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Induced e.m.f
NΦ is known as the magnetic flux linkage
Φ the magnetic flux through one coil
Faraday (1791-1867)
Describe the production of an induced
emf by a time-changing magnetic flux.

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Cutting Magnetic Fields
Consider a conductor of length l moving at speed v through a
magnetic field at 900:
From Faraday’s Law: Not on syllabus
Induced emf = -N ΔΦ
Δt
But Φ=BA and B is constant, so:
Induced emf = -NB A
t
This is a single wire, so N=1, and
A = lvt, therefore:
Induced emf = -Blv

Calculating the EMF
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Lenz’s Law
Consider a magnet in a solenoid:
The current induced by the magnet
induces a north pole that repels the
magnet again.
Lenz’s Law:
Lenz (1804-1865)
Any current driven by an induced emf opposes
the change that caused it. In other words,
emf = -NΦ/t

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Lenz’s Law
Click to play

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Lenz’s law question
• Explain why it is harder to turn a bicycle
dynamo when it is connected to a light bulb
than when it is not connected to anything.

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When a simple d.c. electric motor is connected to a battery,
the current which flows during the first few seconds
varies (approximately) as shown by the graph below.
Explain the shape of this graph.

12.2 Alternating current
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Generator
Hyperlink
Describe the emf induced in a
coil rotating within a uniform
magnetic field.
Explain the
operation of a basic
alternating current
(ac) generator.
Students should understand, without any
derivation, that the induced emf is
sinusoidal if the rotation is at constant
speed.

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Effect of changing the speed of rotation of
the coil on the induced emf
Slow rotation Faster rotation
Describe the effect on the induced emf of
changing the generator frequency.
Students will be expected to compare the
output from generators operating at
different frequencies by sketching
appropriate graphs.

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Generator question
• A rectangular coil, 2cm by 3cm, rotates in a uniform
magnetic field of flux density 0.15T. The axis around which
the coil rotates is at 90° to the flux lines.
The coil has 250 turns and its rotational frequency is 50s-
1.a)Calculate the maximum emf induced in the coil. What
is the position of the coil (relative to the flux lines) when
the induced emf has its maximum value?b)What is the
magnitude of the induced emf at a time 5×10-3s after it
has passed through its maximum value.c)Calculate the
magnitude of the induced emf at a time 2.5×10-3s after it
has passed through its maximum value.

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Revision of DC and AC
DC stands for “Direct Current” –
the current only flows in one
direction:
AC stands for “Alternating
Current” – the current changes
direction 50 times every second
(frequency = 50Hz)
1/50th s
240V
V
V
Time
T
Discuss what is meant by the root
mean squared (rms) value of an
alternating current or voltage.
Students should know that the rms value of an
alternating current (or voltage) is that value of
the direct current (or voltage) that dissipates
power in a resistor at the same rate. The rms
value is also known as the rating.

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Rms and peak values
What value do you use for an a.c. current?
Discuss what is meant by the root
mean squared (rms) value of an
alternating current or voltage.

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Rms calculations
This question is about rms currents and voltages.
For the circuit shown above calculate
a the rms value of the current, I
b) the maximum value of the current
c) the mean power dissipated in R1
d) the rms value of the voltage across R2.

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Coupled Inductors 12.1.4
Describe the
production of an
induced emf by a time-
changing
magnetic flux.

The national grid
Explain the use of high-voltage step-up and
step-down transformers in the transmission
of electrical power.
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Transformers
Time
Time
Time
Current through primary
Magnetic flux through core
EMF induced in secondary

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Transformers
Transformers are used to _____ __ or step down _______. They
only work on AC because an ________ current in the primary coil
causes a constantly alternating _______ ______. This will “_____”
an alternating current in the secondary coil.
Words – alternating, magnetic field, induce, step up, voltage
We can work out how much a transformer will step up or step down
a voltage:
Voltage across primary (Vp)
No. of turns on secondary (Ns)Voltage across secondary (Vs)
No. of turns on primary (Np)

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Describe the operation of an ideal
transformer.
Solve problems on the operation of
ideal transformers.

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Transformer questions
• a)Explain the operation of a step-up transformer.
• b)A transformer has 250 turns on its primary coil and 4000 turns
on its secondary coil. It is connected to a 220V supply. Under
normal operating conditions the current flowing through the
secondary coil is 25mA and the transformer is 90% efficient
(assume that the main source of inefficiency is the resistance of
the secondary coil).
• Calculate
• i)the secondary voltage when on open circuit (that is, when the
secondary coil is not connected to anything).
• ii)the current flowing through the primary coil when the current
flowing through the secondary coil is 25mA.

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Some transformer questions
Primary
voltage
Vp
Secondary
voltage
Vs
No. of turns on
primary Np
No. of turns on
secondary Ns
Step up or
step down?
12V 24V 100 ? ?
400V 200V 20 ? ?
25,000V 50,000V 1,000 ? ?
23V 230V 150 ? ?

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Energy losses in a transformer
• Energy can be lost as:
• (a) heat in the coils because of the resistance of
the wire;
• (b) incomplete transfer of magnetic field;
• (c) heating of the core due to induced currents in
it. This is reduced by making the core out of
insulated soft iron in laminated strips. If this were
not done the cores of large transformers would
get so hot that they would melt.
Outline the reasons for power losses in transmission
lines and real transformers.

Transmission of electricity
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The transmission of electricity
To minimise losses through heating, then the current should be as
low as possible i.e. make the voltage as high as possible.

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Example of power loss
Explain the use of high-voltage stepup and step-down transformers
in the transmission of electrical power.
Students should be aware that, for economic reasons, there is no ideal
value of voltage for electrical transmission.

Questions
Hamper page 218 Q’s 46,47.
IB pack Q’s 7,8,9.
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Discuss some of the possible risks involved in living and working near
high-voltage power lines.
Students should be aware that current experimental
evidence suggests that low-frequency fields do not
harm genetic material. Students should appreciate that the risks
attached to the inducing of current in the body are not fully
understood. These risks are likely to be dependent on current
(density), frequency and length of
exposure.

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Health risks
• Power cables carry a.c. currents
• These produce e-m fields
• These can induce currents in the body
• These might do harm
• Risk increases with
• Current
• Frequency
• Time of exposure.
Suggest how extra-low-
frequency electromagnetic
fields, such as those
created by electrical
appliances and power
lines, induce currents
within a human body.

Electromagnetic induction

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