Application Of Faraday’s Law
Dr Miguel Cavero
September 2, 2014
Application Of Faraday’s Law
September 2, 2014
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The PHYS120 Exam will be divided into three sections as follows:
Section A: Short Questions (20 3-mark questions)
10 Electricity and Magnetism questions
5 Optics questions
5 Atomic and Nuclear Physics questions
Section B: Electricity and Magnetism (60 marks)
Section B: Optics and Atomic and Nuclear Physics (60 marks)
Application Of Faraday’s Law
PHYS120 Exam
September 2, 2014
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Faraday’s Law
The induced emf around a closed path is the negative of the rate of
change of the magnetic flux:
E =−
dφB
dt
where the magnetic fulx φB is (B cos θ)A, the component of the
magnetic field B perpendicular to the area A multiplied by the area.
The negative sign means that the induced emf E opposes the change
in the magnetic flux φB .
Application Of Faraday’s Law
Application Of Faraday’s Law
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Changing Magnetic Flux And An Induced Emf
A wire is shaped so that it forms a square coil with 25 turns. Each side
of the square has a length of 1.80 cm. The coil is placed in the
xz-plane, in the presence of a magnetic field B which is directed
perpendicular to the plane of the coil (i.e. in the y-direction). If the
magnetic field changes uniformly from 0 T to 0.500 T in a time of
0.800 s, calculate the induced emf in the coil while the field is
changing?
Application Of Faraday’s Law
Application Of Faraday’s Law
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Changing Magnetic Flux And An Induced Emf
Faraday’s Law states that
dφB
dt
If a coil/loop contains N turns and the magnetic flux changes
uniformly, then the induced emf can be written as
E =−
E = −N
Application Of Faraday’s Law
∆φB
∆t
Application Of Faraday’s Law
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Changing Magnetic Flux And An Induced Emf
Calculate the magnetic flux, by first finding the area of the coil.
The side of the square is 1.80 cm, therefore the area is
A = (1.80 × 10−2 )2 = 32.4 × 10−4 m
To find the change in the magnetic flux, calculate the initial and final
flux.
Application Of Faraday’s Law
Application Of Faraday’s Law
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Changing Magnetic Flux And An Induced Emf
The initial and final magnetic flux values are
φIB = (B I cos θ)A
= 0
φFB
= (B F cos θ)A
= (0.500) × (32.4 × 10−4 )
= 1.62 × 10−4 Wb
Application Of Faraday’s Law
Application Of Faraday’s Law
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Changing Magnetic Flux And An Induced Emf
The change in the magnetic flux in a time of 0.800 s is
∆φB
1.62 × 10−4 − 0
=
∆t
0.0800
Application Of Faraday’s Law
Application Of Faraday’s Law
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Changing Magnetic Flux And An Induced Emf
The induced emf is therefore
E
Application Of Faraday’s Law
∆φB
∆t
1.62 × 10−4
= −(25)
0.0800
= −5.06 × 10−3 V
= −N
Application Of Faraday’s Law
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Changing Magnetic Flux And An Induced Emf
Let the resistance of the coil be 0.350 Ω. What is the induced current in
the coil?
Using Ohm’s Law, the current in the coil is
I=
E
5.06 × 10−3
=
= 1.45 × 10−2 A
R
0.350
What is the direction of this current?
Application Of Faraday’s Law
Application Of Faraday’s Law
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Lenz’s Law
The negative sign in Faraday’s Law indicates the polarity of the
induced emf.
To determine in which direction the current will flow in the loop, Lenz’s
Law is used.
Lenz’s Law states that the current caused be the induced magnetic
field travels in the direction that creates a magnetic field with a flux
opposing the change in the original flux.
If the magnetic flux through the loop becomes more positive, the
induced emf produces a current and hence a magnetic field that
produces a negative magnetic flux.
Note that the induced magnetic field does not always point in the
opposite direction to the applied magnetic field.
Application Of Faraday’s Law
Application Of Faraday’s Law
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Changing Magnetic Flux And An Induced Emf
The magnetic field B is increasing (from 0 T to 0.500 T) in the positive
y-direction. The flux therefore is positive and increasing in that
direction.
The induced magnetic field points in the −y-direction, creating a
magnetic flux that opposes the change.
Application Of Faraday’s Law
Application Of Faraday’s Law
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Changing Magnetic Flux And An Induced Emf
Using the second right-hand rule for the induced magnetic field, the
fingers curl down through the coil when the thumb points in a
clockwise direction.
The induced current I therefore flows in the clockwise direction in this
coil.
Application Of Faraday’s Law
Application Of Faraday’s Law
September 2, 2014
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AC Generator
Generators and motors operate on the principle of electromagnetic
induction.
An alternating-current (AC) generator converts mechanical energy into
electrical energy.
The generator is essentially a coil of many turns that is made to rotate
in the presence of a magnetic field.
The energy required to rotate the coil comes from an outside source
(e.g. falling water in a hydroelectric power plant).
A rotating coil results in a changing magnetic flux and therefore
induced a current in the coil.
Application Of Faraday’s Law
Generators And Transformers
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AC Generator
Let a coil have N turns and an area A, and rotate with an angular
velocity ω.
If the normal of the coil makes an initial angle α to the magnetic field,
then the angle θ between the normal and the magnetic field at a time t
is given by
θ = α + ωt
Application Of Faraday’s Law
Generators And Transformers
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AC Generator
The induced emf is then
E
Application Of Faraday’s Law
d
[AB cos(α + ωt)]
dt
= (N ABω) sin(α + ωt)
= −N
Generators And Transformers
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DC Generator
A direct-current (DC) generator works in the same way as an AC
generator, except that the rotating coil is connected to an external
circuit by means of a split ring called a commutator.
The commutator always ensures that the induced emf always has the
same polarity, giving rise to a direct current.
Application Of Faraday’s Law
Generators And Transformers
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Transformers
A transformer is made of two coils wrapped around an iron core.
An alternating emf source E1 is applied to one of the coils (the primary)
which has N1 turns.
Application Of Faraday’s Law
Generators And Transformers
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Transformers
The current I1 due to E1 creates a changing magnetic field inside the
iron core, which gives rise to a changing flux the secondary coil (with
N2 turns in it).
By Faraday’s Law, an alternating emf E2 is induced in the secondary
coil, producing a current I2 in it.
Application Of Faraday’s Law
Generators And Transformers
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Transformers
It can be shown that
E2
N2
I1
=
=
E1
N1
I2
If N2 > N1 , the transformer is a step-up transformer (since E2 > E1 ).
If N2 < N1 , the transformer is a step-down transformer (since E2 < E1 ).
Application Of Faraday’s Law
Generators And Transformers
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