1. 1 EET 103 / EET 105 Chapter 4 Magnetic Circuits

2. 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. 2

3. Flux distribution for a permanent magnet 3

4. 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. 4

5. Flux distribution for two adjacent, opposite poles If like poles are brought together, the magnets will repel, and the flux distribution will be as shown. 5

6. If a nonmagnetic material, such as glass, is placed in the flux paths surrounding a permanent magnet, there will be an almost unnoticeable change in the flux distribution. If a magnetic material, such as soft iron, is placed in the flux paths surrounding a permanent magnet, there will be an almost noticeable change in the flux distribution. 6

7. This principle is put to use in the shielding of sensitive electrical elements and instruments that can be affected by stray magnetic fields. A current-carrying conductor develops magnetic fields in the form of concentric circle around it. 7

8. If the coil is wound in a single-turn coil, the resulting flux flows in a common direction through the centre of the coil. A coil of more than one turn produces a magnetic field that exists in a continuous path through and around the coil. 8

9. 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. 9

10. The field concentration (field strength) may be increased effectively by placing a core made of magnetic materials (iron, steel, cobalt) within the coil – electromagnet. 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.) Core 10

11. A magnetic field is present around every wire that carries an electric current. The direction of the magnetic flux lines can be found using Right Hand Rule: - thumb: Direction of conventional current flow - other fingers: Direction of magnetic flux 11

12. Flux and Flux Density In the SI system of units, magnetic flux is measured in webers (Wb) and is represented using the symbol (phi)  The number of flux lines per unit area is called flux density (B). Flux density is measured in tesla (T). Its magnitude is determined by the following equation 1 tesla = 1 T = 1 Wb/m 2 12

13. The flux density of an electromagnet is directly related to: a.the number of turns of, N b.the current through the coil, I The product is the magnetomotive force is any physical driving (motive) force that produces magnetic flux. 13

14. 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. 14

15. 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. 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. 15

16. 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. 16

17. In general : Diamagnetic material: Ferromagnetic material: Nonmagnetic material: Relative permeability is a function of operating conditions. Simplified comparison of permeabilities for: ferromagnetic (μ f ), paramagnetic (μ p ), free space(μ 0 ) and diamagnetic (μ d ) 17

18. 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. 18

19. 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. If a coil of conductor instead of a straight conductor is used, the resultant induced voltage will be greater 19

20. 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. 20

21. 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. 21

22. 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) 22

23. 23 Magnetic Materials and Circuits Magnet contains a north pole and south pole. Magnet flux leaves the magnet as the north pole and the place where the flux returns to the magnet as the south pole. Two types of magnet Permanent magnet Permanent magnet Electromagnet Electromagnet

24. 24 Ampere’s Law When a conductor carries current a magnetic field is produced around it. The relationship between current and magnetic field intensity can be obtained by using Ampere’s Law.

25. MAGNETIC CIRCUITS 25

26. A magnetic circuit is made up of one or more closed loop paths containing a magnetic flux. The flux is usually generated by permanent magnets or electromagnets and confined to the path by magnetic cores consisting of ferromagnetic materials like iron, although there may be air gaps or other materials in the path. Magnetic circuits are employed to efficiently channel magnetic fields in many devices such as electric motors, generators, transformers, relays, lifting electromagnets, galvanometers, and magnetic recording heads. MAGNETIC CIRCUITS 26

27. 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 Ampere-turns per weber 27

28. 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, . 28

29. Ohm’s Law for Magnetic Circuits Substituting: 29

30. Ohm’s Law for Magnetic Circuits The magnetomotive force (mmf),  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 30

31. 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. Ohm’s Law for Magnetic Circuits 31

32. Magnetizing Force The magnetomotive force (F) per unit length (l) is called the magnetizing force (H). Magnetizing force is independent of the type of core material. 32

33. Magnetizing Force Magnetizing force, H is determined solely by the number of turns, N the current, I and the length of the core, l: 33

34. Magnetizing Force The flux density and the magnetizing force are related by the equation: 34 Where :

35. Relationship between B-H - Permeability of the medium - Permeability of free space, - Relative permeability of the medium For free space or electrical conductor (Al or Cu) or insulators, is unity 35

36. Hysteresis Hysteresis – The lagging effect between the flux density, B of a material and the magnetizing force, H applied. 36 Series magnetic circuit used to define the hysteresis curve.

37. Hysteresis Curve 37

38. 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 –H d did the flux density B finally become equal to zero 38 Hysteresis Curve

39. Hysteresis If the entire cycle is repeated, the curve obtained for the same core will be determined by the maximum H applied. 39

40. Hysteresis curve Normal magnetization curve for three ferromagnetic materials. 40

41. 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 41

42. Ampere’s Circuital Law As an example: Steel Cobalt Iron 42

43. Flux  The sum of the fluxes entering a junction is equal to the sum of the fluxes leaving a junction 43 or Which are equivalent

44. 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 44

45. Series Magnetic Circuits : Determining current, NI case of same material types of core. Example 1: (a) Determine the secondary current I 2 for the transformer if the resultant clockwise flux in the core is 1.5 x 10 -5 Wb. 45

46. Series Magnetic Circuits : Determining NI Example 1 – solution 46

47. Determine H from B-H curve 47

48. Example 1: – solution (cont’d) Based on B- H curve: Using ampere circuital law : 48

49. Series Magnetic Circuits : Determining NI for difference types of core material Example 2 – solution Question : Calculate for current, I 1 Inch=0.0254m 1 Inch 2 =6.451x10 -4 m 2 Determining H efab for sheet steel Determining H bcde for Cast Iron 49

50. Series Magnetic Circuits : Determining NI for difference types of core material Example 2 – solution Calculate Hl for each section and find current, I 1 Inch=0.0254m 1 Inch 2 =6.451x10 -4 m 2 Determining Hl for sheet steel Determining Hl for Cast Iron 50

51. Example 2 – solution (cont’d) 51

52. AIR GAPS The spreading of the flux lines outside the common area of the core for the air gap in Fig. is known as fringing. FIG. Air gaps: (a) with fringing; (b) ideal. 52

53. FIG. 11.15 Some areas of application of magnetic effects. 53

54. AIR GAPS Effects of air gaps on a magnetic circuit The flux density of the air gap is given by; where; and; 54

55. 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; 55

56. Example 1: Relay Find the value of I required to establish a magnetic flux, ϕ of =0.79x10 -4 in this series magnetic circuit. 56

57. AIR GAPS:example solution 57

58. Air Gaps Example A flux 0f 0.2 x 10 -4 Wb will establish sufficient attractive force for the armature of the relay. a. Determine the required current to established this flux level. b. The force exert on the armature is determined by the equation Where B g is the flux density within the ais gap and A is the common area of the air gap. Find the force in newton to establish the flux. 58

59. Air Gaps Example – solution 59

60. Ans. a. I = 29.18 A 60