1. Chapter 2 Electromagnetism Dr. Mohd Junaidi Abdul Aziz

2. Aim: impart an understanding of electromagnetic principles
Electromagnetism
Aim: impart an understanding of　electromagnetic principles
Important as electromagnetism underpins the operation of many electrical machines
Linkage between electrical and mechanical worlds
Dr. Mohd Junaidi Abdul Aziz

3. Describes the relationship between electricity and magnetism
Electromagnetism
Describes the relationship between electricity and magnetism
Is essentially the foundation for all of electrical engineering
Use electromagnets to generate electricity, store memory on our computers, generate pictures on a television screen, diagnose illnesses,
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4. Electromagnetism
Electromagnetism works on the principle that an electric current through a wire generates a magnetic field
In a bar magnet, the magnetic field runs from the north to the south pole.
In a wire, the magnetic field forms around the wire.
If we wrap that wire around a metal object, we can often magnetize that object. In this way, we can create an electromagnet.
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5. Electromagnetism
Magnetism is a force field that acts on magnetic materials but not on other materials.
Magnetic field around a bar magnet
Two “poles” dictated by direction of the field
Opposite poles attract (aligned magnetic field)
Same poles repel (opposing magnetic field)
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6. Electromagnetism
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7. Field Detector Electromagnetism
Can use a compass to map out magnetic field
Field forms closed “flux lines” around the magnet
Magnetic flux measured in Webers (Wb)
Symbol
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8. Electromagnetism Magnetic Flux
Magnetic flux lines are assumed to have the following properties:
Leave the north pole (N) and enter the south pole (S) of a magnet.
Like magnetic poles repel each other.
Unlike magnetic poles create a force of attraction.
Magnetic lines of force (flux) are assumed to be continuous loops.
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9. Magnetic Field conductor
Electromagnetism
Magnetic Field conductor
A magnetic field also forms round a conductor along which a current is flowing
Field can be described using “right hand screw rule”
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10. Right Hand Rule Electromagnetism
Thumb indicates direction of current flow
Finger curl indicates the direction of field
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11. Wire Coil Electromagnetism
Notice that a coil of wire will produce a perpendicular field
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12. Magnetic Field: Coil Electromagnetism
A series of coils produces a field similar to a bar magnet – but weaker!
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13. Magnetic Field : Coil Electromagnetism
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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14. Electromagnetism
Flux Density
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15. Electromagnetism- 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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16. Electromagnetism- Reluctance
Reluctance: “resistance” to flow of magnetic flux @
Associated with “magnetic circuit” – flux equivalent to current
What’s equivalent of voltage?
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17. Magnetomotive Force Electromagnetism
Coil generates magnetic field in ferrous toroidal
Driving force F needed to overcome toroidal reluctance
Magnetic equivalent of ohms law
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18. Electromagnetism
Circuit Analogy
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19. Electromagnetism- Magnetomotive Force
Magnetomotive Force (MMF)
The MMF is generated by the coil
Strength related to number of turns and current, measured in Ampere turns (At)
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20. Electromagnetism- 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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21. Electromagnetism
Free space, electrical conductors (aluminium or copper), insulators:
= unity.
Ferromagnetic materials (iron, cobalt and nickel):
= several hundred - several thousand
A large value of : a small current can produce a large flux density
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22. Electromagnetism Ampère’s Law:
Magnetic Field Intensity and Ampère’s Law
Ampère’s Law:
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23. Faraday’s law of magnetic induction:
Electromagnetism
Flux Linkages and Faraday’s Law
Faraday’s law of magnetic induction:
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24. Electromagnetism
Ampere’s Law
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25. Electromagnetism Magnetic Field Around a Long Straight Wire
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26. Electromagnetism
Ampere’s Law
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27. Electromagnetism
Lenz’s Law states that the polarity of the induced voltage is such that the voltage would produce a current (through an external resistance) that opposes the original change in flux linkages
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28. Electromagnetism Lenz’s Law
Voltages Induced in Field-Cutting Conductors
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29. Electromagnetism- magnetic circuit
In many engineering applications, we need to compute the magnetic fields for structures that lack sufficient symmetry for straight-forward application of Ampère’s law. Then, we use an approximate method known as magnetic-circuit analysis.
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30. Electromagnetism- magnetic circuit
Advantage of the Magnetic-Circuit Approach is that it can be applied to unsymmetrical magnetic cores with multiple coils.
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32. Magnetic leakage and Fringing
Magnetic leakage/ leakage flux
Flux not passing through in the magnetic material or in air gap
In air gap – useful fluxs
Occurs at the magnetic source
As shown in Figure 2.a
useful fluxs, a
air gap,
(useful fluxs)
magnetic
Source, NI
leakage flux, l
Total flux, T

33. Magnetic leakage and Fringing
Occurs at the air gap
Flux intends to bulge outwards
Increasing the effective area
Reduce the flux density
As shown in Figure 2.a
(still useful flux)
Contoh 1.2 page 1.11, Contoh 1.3 page 1.12, Contoh 1.4 page 1.14 and Contoh 1.5 page 1.15

34. Electromagnetism Magnetic Circuit Equivalent circuit
Analogy between magnetic circuit and electric circuit
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35. Electromagnetism Electric circuit Magnetic circuit Term Symbol
Magnetic flux F
Electric current I
Flux density B
Current density J
Magnetic field strength H
Electric field strength E
Magnetomotive force
Electromotive force
Permeability m
Permittivity e
Reluctance S
Resistance R
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36. Electromagnetism Series Magnetic Circuit with air gap
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37. Electromagnetism
Series composite magnetic circuit with different material
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38. Electromagnetism
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39. Electromagnetism
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40. Electromagnetism
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41. Electromagnetism
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42. Electromagnetism
Circuit Analogy
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43. Electromagnetism
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44. Electromagnetism
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45. Electromagnetism
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46. Electromagnetism Example 3
A coil of 200 turns is wound uniformly over a wooden ring having a mean circumference of 600mm and a uniform cross-sectional area of 500mm2. if the current through the coil is 4A, calculate
(a) the magnetic field strength
(b) the flux density
(c) the total flux
( 1330A/m, 1680µT,0.838µWb)
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47. Electromagnetism Example 4
Calculate the magnetomotive force required to produce a flux of 0.015Wb across an air gap 2.5mm long, having effective area of 200cm2
(1492At)
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48. Electromagnetism Example 5
A mild-steel ring having a cross- sectional area of 500 mm2 and a mean circumference 0f 400mm has a coil 0f 200 turns wound uniformly around it. The relative permeability of the mild steel for the respective flux density is about 380. Calculate
(a) the reluctance of the ring
(b) the current required to produce a flux of 800µWb in the ring
(1.68 x 106 At/Wb, 6.7A)
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49. Electromagnetism Example 6
The Figure represents the magnetic circuit of a relay. The coil has 500 turns and the mean core path is lc = 360 mm. When the air-gap lengths are 1.5 mm each, a flux density of 0.8 Tesla is required to actuate the relay. The core is cast steel with the field intensity 510 At/m. Find the current in the coil.
(4.19 A)
Compute the values of permeability and relative permeability of the core.
(1.57 x 10-3 Wb/Am, 1250 Wb/Am)
If the air-gap is zero, find the current in the coil for the same flux density (0.8 T) in the core. (0.368 A)
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50. Electromagnetism Example 7
A magnetic circuit comprises three parts in series
each of uniform cross-sectional area (A). They are:
(a) a length of 80 mm and A= 50 mm2
(b) a length of 60 mm and A = 90 mm2
(c) an air gap of length 0.5 mm and A = 150 mm2
A coil of 4000 turns is wound on part (b) and the flux density in the air gap is 0.3 T. Assuming that all the flux passes through the given circuit, and the relative permeability is 1300, estimate the coil current to produce such a flux density
(45.43mA)
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51. Electromagnetism Series Parallel Magnetic Circuit
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52. Electromagnetism Series Parallel Magnetic Circuit
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53. Electromagnetism Series Parallel Magnetic Circuit with Air Gap
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54. Electromagnetism- magnetic core loss
The relationship between B and H is not linear for the types of iron used in motors and transformers.
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55. Electromagnetism
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56. Electromagnetism- Hysteresis
The relationship between B and H is complicated by non-linearity and “hysteresis”
Can be used to calculate µ
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57. Electromagnetism- Hysteresis
Hysterisis
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58. Electromagnetism- Hysteresis Loss
Hysteresis loop
Uniform distribution
From Faraday's law
Where A is the cross section area
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59. Electromagnetism- Hysteresis Loss
Field energy
Input power :
Input energy from t1 to t2
where Vcore is the volume of the core
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60. Electromagnetism- 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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61. Electromagnetism- Hysteresis Loss
Empirical equation
Summary : Hysteresis loss is proportional to f and ABH
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62. Electromagnetism- Eddy Current Loss
Along the closed path, apply Faraday's law
where A is the closed area
Changes in B → = BA changes
→induce e.m.f 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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63. Electromagnetism- Eddy Current Loss
How to reduce Eddy current loss
– Use high resistively core material
e.g. silicon steel, ferrite core (semiconductor)
– Use laminated core
To decrease the area closed
by closed path
Lamination thickness
0.5~5mm for machines, transformers at line frequency
0.01~0.5mm for high frequency devices
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64. Electromagnetism- Eddy Current Loss
Calculation of eddy current loss
– Finite element analysis
Use software: Ansys®, Maxwell®, Femlab®, etc
– Empirical equation
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65. Electromagnetism- Core Loss
Hysterisis loss
the loss of power in the core due to the hysterisis effect
Proportional to frequency
Eddy current loss
power loss occurs when the flux density changes rapidly in the core
Proportional to the square of the frequency
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66. Electromagnetism- Core Loss
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67. Electromagnetism Electromagnetic Induction
Faraday has made the great discovery of electromagnet induction, namely a method of obtaining an electric current with the aid of magnetic flux.
When a conductor cuts or is cut by a magnetic flux, an e.m.f is generated in the conductor.
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68. Electromagnetism Direction of e.m.f Fleming’s right-hand rule
Lenz’s law
The direction of an induced e.m.f is always such that it tends to set up a current opposing the motion or the change of flux responsible for inducing that e.m.f
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69. Electromagnetism
If a conductor cuts or is cut by a flux of dΦ webers in dt seconds, e.m.f generated in conductor
The average e.m.f induced in one turn is
e.m.f induced in a coil:
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70. Electromagnetism The emf induced in electric circuit
Equating expressions of e.m.f induced in magnetic circuit and electric circuit:
L is the self-inductance in Henry, or simply the inductance.
For and
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71. Electromagnetism- Mutual Inductances
Self-inductances of A and B are
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72. Electromagnetism- Mutual Inductances
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73. Electromagnetism- Mutual Inductances
When there is flux leakage occurs
where k = is coupling coefficient = 0 – 1
k = 1 when the magnetic leakage is zero
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74. Electromagnetism- Mutual Inductances
Example 8
A ferromagnetic ring of cross-sectional 800mm2 and of mean radius 170mm has two windings connected in series, one of 500 turns and one of 700 turns. If the relative permeability is 1200, calculate the self-inductance of each coil and the mutual inductance of each assuming that there is no flux leakage.
( 0.283H, 0.552H, 0.395H)
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75. Electromagnetism Energy Stored in the Magnetic Field
Consider a current increasing at uniform rate in a coil having a constant inductance L henrys.
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76. Electromagnetism Energy Stored in the Magnetic Field
If the current increases by di amperes in dt seconds, the induced e.m.f
And if i is the value of the current at that instant, energy absorbed by the magnetic field during time dt seconds
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77. Electromagnetism Energy Stored in the Magnetic Field
Hence total energy absorbed by the magnetic field when the current increases from 0 to I amperes is
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78. ? Electromagnetism Energy Stored in the Magnetic Field
Since inductance
Hence ?
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