ekt 103 magnetism & electromagnetism chapter 2 1 by: dr rosemizi abd rahim
TRANSCRIPT
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EKT 103
Magnetism & Electromagnetism
CHAPTER 2
1
By: Dr Rosemizi Abd Rahim
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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.
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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
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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
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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
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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:
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Reluctance• Reluctance: “resistance” to flow
of magnetic flux
Associated with “magnetic circuit”
– flux equivalent to current
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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
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Ampere’s Law
Consider a rectangular core with N winding
NiHlc
Nii cldl
Therefore
cl
NiH
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H - magnetic field intensity
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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
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The H-field is defined as a modification of B due to magnetic fields produced by material media
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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)
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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
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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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= Φ x
l
μ A=
0.16
1.818 x 10-3 x 2 x 10-3
=
= 44004.4
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= 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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Circuit Analogy
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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
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Fleming’s Left Hand Rule
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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.
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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.
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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.
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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.
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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,
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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.
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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.
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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
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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
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Mutual Inductance, M
i
ΦFrom Faraday’s Law:
v1 v2e1
e2
dt
dNe
22
Ф =μ N1i1A
l
substituting
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Mutual Inductance, M
i
Φ
v1 v2rearrange
dt
l
AiNd
Ne
11
22
dt
di
l
ANNe 1
122
e1
e2
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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
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Mutual Inductance, M
M 2 = L1 x L2
M = √(L1 x L2)
or
M = k√(L1 x L2)
k = coupling coeeficient (0 --- 1)
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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
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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
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Hysteresis Loss• Empirical equation
Summary : Hysteresis loss is proportional to f and ABH
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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
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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
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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
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Core Loss
• Core Loss
losscurrenteddyP
losshysteresisPwhere
PPP
e
h
ehc
Hysteresis loss + eddy current loss = Core loss
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