1. SEE 2053 Teknologi Elektrik Chapter 2 Electromagnetism

2. Electromagnetism 1. Understand magnetic fields and their interactions with moving charges. 2. Use the right-hand rule to determine the direction of the magnetic field around a current-carrying wire or coil.

3. Electromagnetism 3. Calculate forces on moving charges and current carrying wires due to magnetic fields. 4. Calculate the voltage induced in a coil by a changing magnetic flux or in a conductor cutting through a magnetic field. 5. Use Lenz’s law to determine the polarities of induced voltages.

4. Electromagnetism 6. Apply magnetic-circuit concepts to determine the magnetic fields in practical devices. 7. Determine the inductance and mutual inductance of coils given their physical parameters. 8. Understand hysteresis, saturation, core loss, and eddy currents in cores composed of magnetic materials such as iron.

5. Electromagnetism Magnetism is a force field that acts on some materials (magnetic materials) but not on other materials (non magnetic 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)

6. By convention, flux lines leave the north- seeking end (N) of a magnet and enter its south-seeking end (S). Electromagnetism

7. Magnetic flux lines form closed paths that are close together where the field is strong and farther apart where the field is weak. Electromagnetism N N SS Strong field weak field

8. Magnetic materials (ferromagmagnetic): iron, steel, cobalt, nickel and some of their alloys. Non magnetic materials: water, wood, air, quartz, silver, copper etc. Electromagnetism

9. The basic source of the magnetic field is electrical charge in motion. In magnetic materials, fields are created by the spin of electrons in atoms. These fields aid one another, producing the net external field that we observe. In most other materials (non magnetic materials), the magnetic fields of electrons tend to cancel one another. In a current-carrying wire, the moving electrons in the wire create magnetic fields around the wire. Electromagnetism

10. Iron bar Magnetic molecules In an unmagnetised state, the molecular magnets lie in random manner, hence there is no resultant external magnetism exhibited by the iron bar. wood Non-magnetic molecules

11. Electromagnetism Iron bar Magnetic molecules 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. S N SN

12. Electromagnetism Iron bar Magnetic molecules When the iron bar is placed in a very strong magnetic field, all these molecular magnets orientate themselves along a straight lines (saturated). S N N S

13. Electromagnetism

14. Field Detector Can use a compass to map out magnetic field Field forms closed “flux lines” around the magnet (lines of magnetic flux never intersect) Magnetic flux measured in Webers (Wb) Symbol

15. 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.

16. Magnetic Field Conductor Magnetic fields also exist in the space around wires that carry current. Field can be described using “right hand screw rule”

17. Right Hand Rule Thumb indicates direction of current flow Finger curl indicates the direction of field

19. Right-Hand Rule

20. Wire Coil Notice that a carrying-current coil of wire will produce a perpendicular field

21. Magnetic Field: Coil A series of coils produces a field similar to a bar magnet – but weaker!

22. Magnetic Field: Coil

23. Magnetic Field Flux Ф can be increased by increasing the current I, I Ф I

24. Magnetic Field Flux Ф can be increased by increasing the number of turns N, I Ф N N

25. Magnetic Field Flux Ф can be increased by increasing the cross-section area of coil A, I Ф A N A

26. Magnetic Field Flux Ф can be increased by increasing the cross-section area of coil A, I Ф A N A

27. Magnetic Field Flux Ф is decreased by increasing the length of coil l, I Ф N A 1 l l

28. Magnetic Field Therefore we can write an equation for flux Ф as, I Ф N A NIA l l or Ф = μ 0 NIA l

29. Where μ 0 is vacuum or non-magnetic material permeability μ 0 = 4π x 10 -7 H/m Magnetic Field Ф = μ 0 NIA l

30. 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

31. Magnetic Field By placing a magnetic material inside the coil, I N A l Ф = μ NIA l Where μ is the permeability of the magnetic material (core).

32. Magnetic Field By placing a magnetic material inside the coil, I N A l Ф = μ NIA l Where μ is the permeability of the magnetic material (core).

33. Flux Density

34. 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 μ o = 4π x 10-7 (Wb/Am) Relative permeability:

35. Reluctance Reluctance: “resistance” to flow of magnetic flux Associated with “magnetic circuit” – flux equivalent to current What’s equivalent of voltage?

36. Magnetomotive Force, F Coil generates magnetic field in ferrous torroid Driving force F needed to overcome torroid reluctance Magnetic equivalent of ohms law

37. Circuit Analogy

38. Magnetomotive Force The MMF is generated by the coil Strength related to number of turns and current, measured in Ampere turns (At)

39. 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:

40. 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

41. Hysteresis The relationship between B and H is complicated by non-linearity and “hysteresis”

44. = Φ x l μ A = 0.16 1.818 x 10 -3 x 2 x 10 -3 = = 44004.4

45. = Φ x = 4 x 10 -4 x 44004.4 = 17.6 I = F N = 17.6 400 = 44 mA

48. Circuit Analogy

52. Leakage Flux and Fringing Leakage flux fringing

53. Leakage Flux 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. Leakage coefficient λ = Total flux produced Useful flux available

54. Fringing Spreading of lines of flux at the edges of the air-gap. Reduces the flux density in the air- gap.

55. Forces on Charges Moving in Magnetic Fields

57. Forces on Current-Carrying Wires

58. 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. N S

59. 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. N S

60. 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. 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

61. 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, 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

62. 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. 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

63. Force on a current-carrying conductor 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. 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

64. 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.

65. Faraday’s Law Second Law. The magnitude of the induced emf (voltage) is equal to the rate of change of flux-linkages. where

66. Direction of Induced emf The direction (polarity) of induced emf (voltage) can be determined by applying Lenz’s Law. Lenz’s law is equivalent to Newton’s law.

67. 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. Lenz’s Law

68. N S I

70. SELF INDUCTANCE, L i e Φ From Faraday’s Law: By substituting Ф = μ NIA l v

71. SELF INDUCTANCE, L i e Φ Rearrange the equation, yield v

72. SELF INDUCTANCE, L i e Φ or where v

73. MUTUAL INDUCTANCE, M i e1e1 Φ From Faraday’s Law: v1v1 v2v2 e2e2 Ф = μ N1i1Aμ N1i1A l substituting

74. MUTUAL INDUCTANCE, M i e1e1 Φ v1v1 v2v2 e2e2 rearrange

75. MUTUAL INDUCTANCE, M i e1e1 Φ v1v1 v2v2 e2e2 or where

76. MUTUAL INDUCTANCE, M For M 2, = L 1 x L 2

77. MUTUAL INDUCTANCE, M M 2 = L 1 x L 2 M = √(L 1 x L 2 ) or M = k√(L 1 x L 2 ) k = coupling coeeficient (0 --- 1)

79. Dot Convention Aiding fluxes are produced by currents entering like marked terminals.

80. Hysteresis Loss Hysteresis loop Uniform distribution From Faraday's law Where A is the cross section area

81. Hysteresis Loss Field energy Input power : Input energy from t 1 to t 2 where V core is the volume of the core

82. 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

83. Hysteresis Loss Empirical equation Summary : Hysteresis loss is proportional to f and A BH

84. Eddy Current Loss Eddy current Along the closed path, apply Faraday's law where A is the closed area Changes 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

85. Eddy Current Loss How to reduce Eddy current loss – Use high resistivity 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

86. Eddy Current Loss Calculation of eddy current loss – Finite element analysis Use software: Ansys®, Maxwell®, Femlab®, etc – Empirical equation

87. Core Loss