EKT 103
Magnetism & Electromagnetism
CHAPTER 2
1
By: Dr Rosemizi Abd Rahim
Learning Outcomes
• At the end of the chapter, students should be able to:–understand the theory of
magnetic and electromagnetic– understand the law of
electromagnetic induction.
2
Introduction to Magnetism
Basic Magnetism
• Effects of magnetism known as early as 800 BC by the Greeks.
• Certain stones called "magnetite or iron oxide (Fe2O3)" attracted, pieces of iron.
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Introduction to MagnetismMagnetism
• magnets do not come in separate charges • Any magnetic/magnetized object has a North
and South pole
• If you break a magnet in half, each piece will have a North and a South end
4
Introduction to MagnetismMagnetic field
• Magnetic field lines – 3D lines which tiny bar magnets lie along. Magnetic field lines run from N to S.
• A compass can be used to map out the magnetic field.
• Field forms closed “flux lines” around the magnet (lines of magnetic flux never intersect)
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Introduction to MagnetismMagnetic field
• The strength of the magnetic field is greater where the lines are closer together and weaker where they are farther apart.
• Field is strongest in regions of dense field lines.
• Field is weakest in regions of sparse field lines. Strong
Field
Weak Field
The density of field lines indicates the strength of
the field
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Introduction to MagnetismMagnetism
• Magnetism is a basic force of attraction and repulsion in nature that is created, by moving charges.
• A magnet is an object, which has a magnetic field that causes a push or pulling action.
• Similar to electric charges, unlike poles attract, while like poles repel
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Introduction to MagnetismMagnetism
• Magnetism is a basic force of attraction and repulsion in nature that is created, by moving charges.
• A magnet is an object, which has a magnetic field that causes a push or pulling action.
• Similar to electric charges, unlike poles attract, while like poles repel
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Introduction to MagnetismMagnetic flux
• Magnetic flux is measurement of the quantity of magnetism, the description of how certain materials relate to magnetic fields.
• Specifically, it describes the strength and extent of the object's interaction with the field.
• Magnetic lines of force (flux) are assumed to be continuous loops.
• Magnetic flux measured in Webers (Wb) • Symbol
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Introduction to MagnetismThe Earth is a Magnet
• A magnetic compass aligns itself along the magnetic field lines (produced by the Earth in the absence of a stronger field)
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Introduction to MagnetismThe Earth is a Magnet
• The North pole of the compass points to the Earth magnetic South pole (generally toward geographic north) and vice‐versa
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Introduction to MagnetismMagnetism
• Magnetism can be transferred or induced into other materials, this is known as Magnetic Induction
• The induction of magnetism into a material can be permanent or temporary
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Introduction to MagnetismMagnetism
• Magnetic materials (ferromagnetic): iron, steel, cobalt, nickel and some of their alloys.
• Non magnetic materials: water, wood, air, quartz.
• In an un-magnetised state, the molecular magnets lie in random manner, hence there is no resultant external magnetism exhibited by the iron bar.
wood
Non-magnetic molecules
Iron bar
Magnetic molecules
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Introduction to MagnetismMagnetism
• When the iron bar is placed in a magnetic field or under the influence of a magnetising force, then these molecular magnets start turning their axes and orientate themselves more or less along a straight lines.
Iron bar
Magnetic molecules
S N
SN
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Introduction to MagnetismMagnetism
• When the iron bar is placed in a very strong magnetic field, all these molecular magnets orientate themselves along a straight lines (saturated).
Iron barMagnetic molecules
S N
N S
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Introduction to Electromagnetism
• A simple electromagnet can be made by coiling some wire around a steel nail, and connecting a battery to it.
• A magnetic field is produced when an electric current flows through a coil of wire.
• We can make an electromagnet stronger by doing these things:• wrapping the coil around an iron core • adding more turns to the coil• increasing the current flowing through
the coil.
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Introduction to Electromagnetism
Using Electromagnets• Many objects around you contain
electromagnets They are found in electric motors and loudspeakers
• Very large and powerful electromagnets are used as lifting magnets in scrap yards to pick up, then drop, old cars and other scrap iron and steel
• They are better than magnets because the magnetism can be turned off and on
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Introduction to Electromagnetism
• A moving electric field creates a magnetic field that rotates around it
• A moving magnetic field creates an electric field that rotates around it
• The Right Hand Rule helps describe this
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The Right Hand Rule
• First define positive electric current as flowing from the positive (+) end of a battery, through an electric circuit, and back into the negative (-) end.
• Next define a magnetic field as always pointing away from a North pole and towards a South pole.
• Curl your fingers in the direction of the rotating field.current
field
Current
Field Lines
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The Right Hand Rule
• Extend your thumb. It now points in the direction of the other field.
• If your fingers are curling along with a rotating electric field, your thumb will point in the direction of the magnetic field and vice versa.
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The Right Hand Rule
• Wire carrying current out of page
• Wire carrying current into page
Representing Currents
X
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The Right Hand Rule
• Wire carrying current out of page
• Wire carrying current into page
The magnetic field of two wires
X
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The Right Hand Rule
• Wire carrying current out of page
• Wire carrying current into page
The magnetic field of two wires
X
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The Right Hand Rule
• Both of the wire carrying current out of page
The magnetic field of two wires
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The Right Hand Rule
• The overall field around a coil is the sum of the fields around each individual wire
The magnetic field of a coil
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The Right Hand Rule
• The magnetic field around a solenoid resembles that of a bar magnet.
• Inside the solenoid the field lines are parallel to one another. We say it is a uniform field.
The magnetic field of a solenoid
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The ElectromagnetismBy the Right Hand Rule, a coil of wire with current
flowing in it will create a magnetic fieldThe strength of the magnetic field depends on
The amount of current in a wire – More current means stronger magnetic field
The number of turns in the coil – More turns means stronger magnetic field
The material in the coil – Magnetic materials like iron and steel make the magnetic field stronger
In other word, the magnetic field only exists when electric current is flowing
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The Electromagnetism• The lines of flux, formed by current flow
through the conductor, combine to produce a larger and stronger magnetic field.
• The center of the coil is known as the core. In this simple electromagnet the core is air.
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The Electromagnetism• Iron is a better conductor of flux than air.
The air core of an electromagnet can be replaced by a piece of soft iron.
• When a piece of iron is placed in the center of the coil more lines of flux can flow and the magnetic field is strengthened.
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The Electromagnetism
• Notice that a carrying-current coil of wire will produce a perpendicular field
Magnetic field - wire coil
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The ElectromagnetismMagnetic field - wire
coil
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Magnetic Field
Flux Ф can be increased by increasing the current I,
I
Ф I
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Magnetic Field
Flux Ф can be increased by increasing the number of turns N,
I
Ф N
N
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Magnetic Field
Flux Ф can be increased by increasing the cross-section area of
coil A,
I
Ф A
N
A
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Magnetic Field
Flux Ф can be increased by increasing the cross-section area of
coil A,
I
Ф A
N
A 35
Magnetic Field
Flux Ф is decreased by increasing the length of coil l,
I
Ф
N
A
1
ll
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Magnetic Field
Therefore we can write an equation for flux Ф as,
I
Ф
N
A
NIA
ll
or
Ф =μ0 NIA
l
37
Where μ0 is vacuum or non-magnetic material permeability
μ0 = 4π x 10-7 H/m
Magnetic Field
Ф =μ0 NIA
l
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Magnetic Field: Coil
• Placing a ferrous material inside the coil increases the magnetic field
• Acts to concentrate the field also notice field lines are parallel inside ferrous element
• ‘flux density’ has increased
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Magnetic Field
By placing a magnetic material
inside the coil,
I
N
A
lФ =
μ NIA
l
Where μ is the permeability of the magnetic material
(core).
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Magnetic Field
By placing a magnetic material
inside the coil,
I
N
A
lФ =
μ NIA
l
Where μ is the permeability of the magnetic material
(core).
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Flux Density
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Permeability
• Permeability μ is a measure of the ease by which a magnetic flux can pass through a material (Wb/Am)
• Permeability of free space μo = 4π x 10-7 (Wb/Am)
• Relative permeability:
43
Reluctance• Reluctance: “resistance” to flow
of magnetic flux
Associated with “magnetic circuit”
– flux equivalent to current
44
The relationship between current and magnetic field intensity can be obtained by using Ampere’s Law.
Ampere’s Law
Ampere’s Law states that the line integral of the magnetic field intensity, H around a closed path is equal to the total current linked by the contour.
idl.H
H: the magnetic field intensity at a point on the contour
dl: the incremental length at that pointIf θ: the angle between vectors H and dl then
icosHdl45
Ampere’s Law
Consider a rectangular core with N winding
NiHlc
Nii cldl
Therefore
cl
NiH
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H - magnetic field intensity
Relationship between B-HThe magnetic field intensity, H produces a magnetic flux density, B everywhere it exists.
Tesla 2 or)m/weber(HB
T 20 or)m/wb(HB r
- Permeability of the medium
0 - Permeability of free space, m.t.Awb-710 x 4
0 r - Relative permeability of the
mediumFor free space or electrical conductor (Al or Cu) or insulators,
is unityr
47
The H-field is defined as a modification of B due to magnetic fields produced by material media
Assumption:
• All fluxes are confined to the core
• The fluxes are uniformly distributed in the core
Magnetic Equivalent Circuit
The flux outside the toroid (called leakage flux), is so small (can be neglected)
Use Ampere’s Law,
Nidl.H
Nir.H 2
NiHl FNiHl
F = Magnetomotive force (mmf)
48
Magnetic Equivalent Circuit
)m/At(l
NiH
HB
)T(l
NiB
Where;N – no of turns of coil
i – current in the coil
H – magnetic field intensity
l – mean length of the core
49
Magnetomotive Force, F• Coil generates magnetic
field in ferrous torroid• Driving force F needed to
overcome torroid reluctance
• Magnetic equivalent of ohms law
Circuit Analogy
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Magnetomotive Force• The MMF is generated by the coil• Strength related to number of turns and
current, measured in Ampere turns (At)
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Field Intensity
• The longer the magnetic path the greater the MMF required to drive the flux
• Magnetomotive force per unit length is known as the “magnetizing force” H
• Magnetizing force and flux density related by:
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Magnetomotive Force• Electric circuit: Emf = V = I x R
• Magnetic circuit:
mmf = F = Φ x
= (B x A) x
l
μ A
= (B x A) x
l
μ= B x = H x l
= H x l
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54
55
= Φ x
l
μ A=
0.16
1.818 x 10-3 x 2 x 10-3
=
= 44004.4
56
= Φ x
= Φ x
= 4 x 10-4 x 44004.4
= 17.6
I = F
N =
17.6
400= 44 mA
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58
59
Circuit Analogy
60
61
62
63
Leakage Flux and Fringing
Leakage flux
fringing
• It is found that it is impossible to confine all the flux to the iron path only. Some of the flux leaks through air surrounding the iron ring.
• Spreading of lines of flux at the edges of the air-gap. Reduces the flux density in the air-gap.Leakage coefficient λ
=
Total flux producedUseful flux available 64
Fleming’s Left Hand Rule
65
Force on a current-carrying conductor
N
S
• It is found that whenever a current-carrying conductor is placed in a magnetic field, it experiences a force which acts in a direction perpendicular both to the direction of the current and the field.
66
Force on a current-carrying conductor
N
S
• It is found that whenever a current-carrying conductor is placed in a magnetic field, it experiences a force which acts in a direction perpendicular both to the direction of the current and the field.
67
N
S
Force on a current-carrying conductor
• It is found that whenever a current-carrying conductor is placed in a magnetic field, it experiences a force which acts in a direction perpendicular both to the direction of the current and the field.
68
N
S
On the left hand side, the two fields
in the same direction
On the right hand side, the two fields in the opposition
Force on a current-carrying conductor
• It is found that whenever a current-carrying conductor is placed in a magnetic field, it experiences a force which acts in a direction perpendicular both to the direction of the current and the field.
69
N
S
On the left hand side, the two fields
in the same direction
On the right hand side, the two fields in the opposition
Force on a current-carrying conductor
• Hence, the combined effect is to strengthen the magnetic field on the left hand side and weaken it on the right hand side,
70
N
S
On the left hand side, the two fields
in the same direction
On the right hand side, the two fields in the opposition
Force on a current-carrying conductor
• Hence, the combined effect is to strengthen the magnetic field on the left hand side and weaken it on the right hand side, thus giving the distribution shown below.
71
N
S
On the left hand side, the two fields
in the same direction
On the right hand side, the two fields in the opposition
F
• This distorted flux acts like stretched elastic cords bend out of the straight , the line of the flux try to return to the shortest paths, thereby exerting a force F urging the conductor out of the way.
Force on a current-carrying conductor
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Faraday’s Law
First Law
Whenever the magnetic flux linked with a coil changes, an emf (voltage) is always induced in it.
Or
Whenever a conductor cuts magnetic flux, an emf (voltage) is induced in that conductor.
73
Faraday’s LawSecond Law
The magnitude of the induced emf (voltage) is equal to the rate of change of flux-linkages.
dt
de
Nwhere
dt
Nd
dt
Nde
)(
ab
If a magnetic flux, , in a coil is changing in time (n turns), hence a voltage, eab is induced
e = induced voltageN = no of turns in coil
d = change of flux in coildt = time interval 74
Voltage Induced from a time changing magnetic field
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Lenz’s Law• Lenz’s law states that the polarity of the induced
voltage is such that the voltage would produce a current that opposes the change in flux linkages responsible for inducing that emf.
• If the loop is closed, a connected to b, the current would flow in the direction to produce the flux inside the coil opposing the original flux change.
• The direction (polarity) of induced emf (voltage) can be determined by applying Lenz’s Law.
• Lenz’s law is equivalent to Newton’s law.
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N S
I
Lenz’s Law
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Self Inductance, L
i
e
Φ
From Faraday’s Law:
dt
dNe
By substituting
Ф =μ NIA
l
v
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Self Inductance, L
i
Φ
Rearrange the equation, yield
dtl
NIAd
Ne
dt
di
l
ANe
2
v e
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Self Inductance, L
i
Φdt
di
l
ANe
2
dt
diLe
or
where
l
ANL
2
v e
80
Mutual Inductance, M
i
ΦFrom Faraday’s Law:
v1 v2e1
e2
dt
dNe
22
Ф =μ N1i1A
l
substituting
81
Mutual Inductance, M
i
Φ
v1 v2rearrange
dt
l
AiNd
Ne
11
22
dt
di
l
ANNe 1
122
e1
e2
82
Mutual Inductance, M
i
Φ
v1 v2
or
dt
di
l
ANNe 1
122
dt
diMe 1
2
where
l
ANNM 12
e1
e2
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Mutual Inductance, M
l
ANNM 12
For M 2,
22
12
222
l
ANNM
l
ANM 2
12
l
AN 2
2 = L1 x L2
84
Mutual Inductance, M
M 2 = L1 x L2
M = √(L1 x L2)
or
M = k√(L1 x L2)
k = coupling coeeficient (0 --- 1)
85
Dot ConventionAiding fluxes are produced by currents entering like marked terminals.
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Hysteresis Loss
• Hysteresis loopUniform distribution
• From Faraday's law
Where A is the cross section area
87
Hysteresis Loss
• Field energyInput power :
Input energy from t1 to t2
where Vcore is the volume of the core
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Hysteresis Loss• One cycle energy loss
where is the closed area of B-H hysteresis loop
• Hysteresis power loss
where f is the operating frequency and T is the period
89
Hysteresis Loss• Empirical equation
Summary : Hysteresis loss is proportional to f and ABH
90
Magnetic saturation & hysteresis in ac magnetic field
Iron becomes magnetically saturated
Magnetism increase as magnetic field magnetized unmagnetized iron
a
b
c
d
Applied field is reduced; the magnetism reduced thru diff. curve since iron tends to retains magnetized state - hence produced permanent magnet, Residual Flux, res
AC increased in negative direction, magnetic field reversed , the iron reversely magnetized until saturated again
If continue apply ac current, curve continue to follow S-shaped curve (hysteresis curve)
The area enclosed by hysteresis curve is energy loss per unit volume per cycle – heats the iron and is one reason why electric machines become hot. Therefore, it is required to select magnetic materials that have a narrow hysteresis loop.
Hm
Magnetic field density
Bm
91
Eddy Current Loss• Eddy currentAlong the closed path, apply Faraday's law
where A is the closed areaChanges in B → = BA changes
→induce emf along the closed path→produce circulating circuit (eddy current) in the
core
• Eddy current loss
where R is the equivalent resistance along the closed path
92
Eddy Current Loss
• How to reduce Eddy current lossi) Use high resistivity core material e.g. silicon steel, ferrite core
(semiconductor)ii) Use laminated core To decrease the area closed by closed path
Lamination thickness0.5~5mm for machines, transformers at line
frequency0.01~0.5mm for high frequency devices 93
Core Loss
• Core Loss
losscurrenteddyP
losshysteresisPwhere
PPP
e
h
ehc
Hysteresis loss + eddy current loss = Core loss
94