1. ELECTRICAL TECHNOLOGY EET 103/4
Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve
Define and explain magnetic equivalent circuit, electromagnetic induction, Sinusoidal excitation, Lenz’s law.
Analyze and explain magnetic losses, eddy current, hysterisis

2. ELECTROMAGNETIC FIELD
(CHAPTER 11)

3. Magnetic Fields
In the region surrounding a permanent magnet there exists a magnetic field, which can be represented by magnetic flux lines similar to electric flux lines.
Magnetic flux lines differ from electric flux lines in that they don’t have an origin or termination point.
Magnetic flux lines radiate from the north pole to the south pole through the magnetic bar.

4. Magnetic Fields
Flux distribution for a permanent magnet

5. Magnetic Fields
Continuous magnetic flux lines will strive to occupy as small an area as possible.
The strength of a magnetic field in a given region is directly related to the density of flux lines in that region.
If unlike poles of two permanent magnets are brought together the magnets will attract, and the flux distribution will be as shown below.

6. Magnetic Fields
Flux distribution for two adjacent, opposite poles

7. Magnetic Fields
If like poles are brought together, the magnets will repel, and the flux distribution will be as shown.

8. Magnetic Fields
If a nonmagnetic material, such as glass or copper, is placed in the flux paths surrounding a permanent magnet, there will be an almost unnoticeable change in the flux distribution.

9. Magnetic Fields

10. Magnetic Fields
This principle is put to use in the shielding of sensitive electrical elements and instruments that can be affected by stray magnetic fields.

11. Magnetic Fields
A current-carrying conductor develops magnetic fields in the form of concentric circle around it.

12. Magnetic Fields
If the coil is wound in a single-turn coil, the resulting flux flows in a common direction through the centre of the coil.

13. Magnetic Fields
A coil of more than one turn produces a magnetic field that exists in a continuous path through and around the coil.

14. Magnetic Fields
The flux distribution around the coil is quite similar to the permanent magnet.
The flux lines leaving the coil from the left and entering to the right simulate a north and a south pole.
The concentration of flux lines in a coil is less than that of a permanent magnet.

15. Magnetic Fields
The field concentration (or field strength) may be increased effectively by placing a core made of magnetic materials (e.g. iron, steel, cobalt) within the coil – electromagnet.

16. Magnetic Fields
The field strength of an electromagnet can be varied by varying one of the component values (i.e. currents, turns, material of the core etc.)

17. Magnetic Fields
The direction of the magnetic flux lines can be found by placing the thumb of the right hand in the direction of conventional current flow and noting the direction of the fingers (commonly called the right hand rule).

18. Magnetic Fields

19. 11.2 Magnetic Fields Flux and Flux Density
In the SI system of units, magnetic flux is measured in webers (Wb) and is represented using the symbol .

20. Wilhelm Eduard Weber (1804 – 1891) Prof
Wilhelm Eduard Weber (1804 – 1891) Prof. of Physics, University of Göttingen

21. 11.2 Magnetic Fields 1 tesla = 1 T = 1 Wb/m2
The number of flux lines per unit area is called flux density (B). Flux density is measured in teslas (T).
Its magnitude is determined by the following equation:
1 tesla = 1 T = 1 Wb/m2

22. Nikola Tesla (1856 – 1943) Electrical Engineer and Inventor Recipient of the Edison Medal in 1917.

23. Magnetic Fields
The flux density of an electromagnet is directly related to:
the number of turns of
the current through
the coil
The product is the magnetomotive force:

24. 11.2 Magnetic Fields Permeability
Another factor affecting the field strength is the type of core used.
If cores of different materials with the same physical dimensions are used in the electromagnet, the strength of the magnet will vary in accordance with the core used.
The variation in strength is due to the number of flux lines passing through the core.

25. Magnetic Fields
Magnetic material is material in which flux lines can readily be created and is said to have high permeability.
Permeability () is a measure of the ease with which magnetic flux lines can be established in the material.

26. 11.2 Magnetic Fields Permeability of free space 0 (vacuum) is
Materials that have permeability slightly less than that of free space are said to be diamagnetic and those with permeability slightly greater than that of free space are said to be paramagnetic.

27. Magnetic Fields
Magnetic materials, such as iron, nickel, steel and alloys of these materials, have permeability hundreds and even thousands of times that of free space and are referred to as ferromagnetic.
The ratio of the permeability of a material to that of free space is called relative permeability:

28. 11.2 Magnetic Fields In general for ferromagnetic materials,
For nonmagnetic materials,
Relative permeability is a function of operating conditions.

29. Induced Voltage
If a conductor is moved through a magnetic field so that it cuts magnetic lines of flux, a voltage will be induced across the conductor.

30. Induced Voltage
The magnitude of the induced voltage is directly related to the speed of movement (i.e. at which the flux is cut).
Moving the conductor in parallel with the flux lines will result in zero volt of induced voltage.

31. Induced Voltage
If a coil of conductor instead of a straight conductor is used, the resultant induced voltage will be greater
Faraday’s law of electromagnetic induction
If a coil of N turns is placed in the region of the changing flux, as in the figure below, a voltage will be induced across the coil as determined by Faraday’s Law.

32. Induced Voltage

33. Induced Voltage
Changing flux also occurs in a coil carrying a variable current.
Similar voltage will be induced, the direction of which can be determined by Lenz’s Law.

34. 11.4 Induced Voltage Lenz’s law
An induced effect is always such as to oppose the cause that produced it.
The magnitude of the induced voltage is given by:
L is known as inductance of the coil and is measure in henries (H)

35. MAGNETIC CIRCUIT
(CHAPTER 12)

36. Introduction
Magnetism is an integral part of almost every electrical device used today in industry, research, or the home.
Generators, motors, transformers, circuit breakers, televisions, computers, tape recorders and telephones all employ magnetic effects to perform a variety of important tasks.

37. Reluctance
The resistance of a material to the flow of charge (current) is determined for electric circuits by the equation
The reluctance of a material to the setting up of magnetic flux lines in a material is determined by the following equation

38. 12.4 Ohm’s Law for Magnetic Circuits
For magnetic circuits, the effect is the flux .
The cause is the magnetomotive force (mmf) F, which is the external force (or “pressure”) required to set up the magnetic flux lines within the magnetic material.
The opposition to the setting up of the flux  is the reluctance .

39. 12.4 Ohm’s Law for Magnetic Circuits
Substituting:
The magnetomotive force  is proportional to the product of the number of turns around the core (in which the flux is to be established) and the current through the turns of wire

40. 12.4 Ohm’s Law for Magnetic Circuits
An increase in the number of turns of the current through the wire, results in an increased “pressure” on the system to establish the flux lines through the core.

41. Magnetizing Force
The magnetomotive force per unit length is called the magnetizing force (H).
Magnetizing force is independent of the type of core material.
Magnetizing force is determined solely by the number of turns, the current and the length of the core.

42. Magnetizing Force
Substituting:

43. Magnetizing Force
The flux density and the magnetizing force are related by the equation:

44. Hysteresis
Hysteresis – The lagging effect between the flux density of a material and the magnetizing force applied.
The curve of the flux density (B) versus the magnetic force (H) is of particular interest to engineers.

45. Series magnetic circuit used to define the hysteresis curve.

46. Hysteresis
The entire curve (shaded) is called the hysteresis curve.
The flux density B lagged behind the magnetizing force H during the entire plotting of the curve. When H was zero at c, B was not zero but had only begun to decline. Long after H had passed through zero and had equaled to –Hd did the flux density B finally become equal to zero

47. Hysteresis
Hysteresis curve.

48. Hysteresis
If the entire cycle is repeated, the curve obtained for the same core will be determined by the maximum H applied.

49. Hysteresis
Normal magnetization curve for three ferromagnetic materials.

50. Hysteresis
Expanded view for the low magnetizing force region.

51. 12.7 Ampere’s Circuital Law
Ampère’s circuital law: The algebraic sum of the rises and drops of the mmf around a closed loop of a magnetic circuit is equal to zero; that is, the sum of the rises in mmf equals the sum drops in mmf around a closed loop. or

52. 12.7 Ampere’s Circuital Law
As an example:

53. Flux 
The sum of the fluxes entering a junction is equal to the sum of the fluxes leaving a junction

54. Flux  or

55. 12.9 Series Magnetic Circuits : Determining NI
Two types of problems
 is given, and the impressed mmf NI must be computed – design of motors, generators and transformers
NI is given, and the flux  of the magnetic circuit must be found – design of magnetic amplifiers

56. 12.9 Series Magnetic Circuits : Determining NI
Table method
A table is prepared listing in the extreme left-hand column the various sections of the magnetic circuit. The columns on the right are reserved for the quantities to be found for each section

57. 12.9 Series Magnetic Circuits : Determining NI
Example 12.1
a. Find the value of I required to develop a magnetic flux of  = 4 x 10-4 Wb.
b. Determine  and r for the material under these conditions.

58. 12.9 Series Magnetic Circuits : Determining NI
Example 12.1 – solution
(a)
Calculate B:
Use B–H curves to find H:

60. 12.9 Series Magnetic Circuits : Determining NI
Example 12.1 – solution (cont’d)
Apply Ampere’s circuital law;
Hence;

61. 12.9 Series Magnetic Circuits : Determining NI
Example 12.1 – solution (cont’d)
(b)
Calculate the permeability;

62. 12.9 Series Magnetic Circuits : Determining NI
Example 12.2
Determine the current I to establish the indicated flux in the core.

63. 12.9 Series Magnetic Circuits : Determining NI
Example 12.2 – solution
Convert all dimensions into metric;

64. 12.9 Series Magnetic Circuits : Determining NI
Example 12.2 – solution (cont’d)

65. 12.9 Series Magnetic Circuits : Determining NI
Example 12.2 – solution (cont’d)
Calculate the flux density B;

66. 12.9 Series Magnetic Circuits : Determining NI
Example 12.2 – solution (cont’d)
Determine H from the B–H curves;

69. 12.9 Series Magnetic Circuits : Determining NI
Example 12.2 – solution (cont’d)
Calculate Hl for each section;

70. 12.9 Series Magnetic Circuits : Determining NI
Example 12.2 – solution (cont’d)
The magnetic circuit equivalent
The electric circuit analogy

71. 12.10 Air Gaps Effects of air gaps on a magnetic circuit
The flux density of the air gap is given by;
where;
and;

72. 12.10 Air Gaps Effects of air gaps on a magnetic circuit
Assuming the permeability of air is equal to that of free space, the magnetizing force of the air gap is determined by;
And the mmf drop across the air gap is equal to Hg Lg;

73. Air Gaps
Example 12.4
Find the value of I to establish  = 0.75 x 10-4 Wb

74. 12.10 Air Gaps Example 12.4 – solution Calculate B;
Use B–H curves to determine H;

75. 12.10 Air Gaps Example 12.4 – solution (cont’d)
Calculate H for the air gap;

76. 12.10 Air Gaps Example 12.4 – solution (cont’d)
Calculate the mmf drops;

77. 12.10 Air Gaps Example 12.4 – solution (cont’d)
Applying Ampere’s circuital law;

78. 12.11 Series-parallel Magnetic Circuits
Example 12.5
Find the value of I to establish a flux of 1.5 x 10-4 Wb in the section of core indicated

79. 12.11 Series-parallel Magnetic Circuits
Example 12.5 – solution
Calculate B2;
Use B–H curves to determine H;

81. 12.11 Series-parallel Magnetic Circuits
Example 12.5 – solution (cont’d)
Draw the equivalent magnetic circuit;
Apply Ampere’s circuital law around loop 2;
Or;

82. 12.11 Series-parallel Magnetic Circuits
Example 12.5 – solution (cont’d)
Substituting values;
Use B–H curves to find B;

83. 12.11 Series-parallel Magnetic Circuits
Example 12.5 – solution (cont’d)
Substituting values;
Use B–H curves to find B;

84. 12.11 Series-parallel Magnetic Circuits
Example 12.5 – solution (cont’d)
Calculate 1;
Calculate T;

85. 12.11 Series-parallel Magnetic Circuits
Example 12.5 – solution (cont’d)
Calculate B in section efab;

86. 12.11 Series-parallel Magnetic Circuits
Example 12.5 – solution (cont’d)
Use B–H curves to determine H;
Apply Ampere’s circuit law;

88. 12.11 Series-parallel Magnetic Circuits
Example 12.5 – solution (cont’d)
Apply Ampere’s circuit law;

89. Determining 
When determining magnetic circuits with more than one section, there is no set order of steps that will lead to an exact solution for every problem on the first attempt.

90. Determining 
Find the impressed mmf for a calculated guess of the flux  and then compare this with the specified value of mmf.
Make adjustments to the guess to bring it closer to the actual value.
For most applications, a value within 5% of the actual  or specified NI is acceptable.

91. Determining 
Example 12.6
Calculate the magnetic flux 

92. 12.12 Determining  Example 12.6 – solution
Apply Ampere’s circuital law to determine H:

93. 12.12 Determining  Example 12.6 – solution (cont’d)
Use B–H curves to determine the corresponding B;
Calculate ;

95. 12.12 Determining  Assignment 1
(a) If I = 120 mA, calculate the flux .

96. 12.12 Determining  Assignment 1 (cont’d)
(b) If an air gap of 1 mm is cut across the core, calculate the current I to maintain the flux calculated in (a) above. Assume r of the core is constant.