1. CHAPTER 2 MAGNETIC MATERIALS AND CIRCUITS
Describe, Explain and Calculate fundamental of electricity, magnetism and 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.

3. Magnetic Fields
Flux distribution for a permanent magnet

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

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

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

7. 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.

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

9. 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.

10. 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.

11. 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.)

12. 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).

13. 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 .

14. 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

15. 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:

16. 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.

17. 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.

18. 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.

19. 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:

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

21. 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

22. 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 .

23. 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

24. 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.

25. 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.

26. Magnetizing Force
Substituting:

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

28. 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.

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

30. 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

31. Hysteresis
Hysteresis curve.

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

33. Hysteresis
Normal magnetization curve for three ferromagnetic materials.

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

35. Hysteresis
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

36. Ampere’s Circuital Law
As an example:

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

38. Flux  or

39. 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

40. 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

41. Series Magnetic Circuits : Determining NI
Example 1
Determine the current I to establish the indicated flux in the core.

42. Series Magnetic Circuits : Determining NI
Example 1 solution
Convert all dimensions into metric;

43. Series Magnetic Circuits : Determining NI
Example 1 solution

44. Series Magnetic Circuits : Determining NI
Example 1 solution
Calculate the flux density B;

45. Series Magnetic Circuits : Determining NI
Example 1 solution
Determine H from the B–H curves;

48. Series Magnetic Circuits : Determining NI
Example 1 solution
Calculate Hl for each section;

49. Series Magnetic Circuits : Determining NI
Example 1 solution
The magnetic circuit equivalent
The electric circuit analogy

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

51. 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;

52. Air Gaps
Example 2
Find the value of I to establish  = 0.75 x 10-4 Wb

53. Air Gaps
Example 2
Calculate B;
Use B–H curves to determine H;

54. Air Gaps
Example 2
Calculate H for the air gap;

55. Air Gaps
Example 2
Calculate the mmf drops;

56. Air Gaps
Example 2
Applying Ampere’s circuital law;