1. Electrical Machines and Energy Conversion
Unit 1 Deck 1
Magnetism Basics

2. Summary Magnetic Quantities
Magnetic fields are described by drawing flux lines that represent the magnetic field.
Where lines are close together, the flux density is higher.
Where lines are further apart, the flux density is lower.

3. Summary Magnetic Quantities
The unit of flux is the weber. The unit of flux density is the weber/square meter, which defines the unit tesla, (T), a very large unit.
Flux density is given by the equation
where
B = flux density (T)
j = flux (Wb)
A = area (m2)

4. Summary Magnetic Quantities
Example: What is the flux density in a rectangular core that is 8 mm by 10 mm if the flux is 4 mWb?

5. Summary Magnetic Quantities
Magnetic flux lines surround a current carrying wire.
The field lines are concentric circles.
As in the case of bar magnets, the effects of electrical current can be visualized with iron filings around the wire – the current must be large to see this effect.
Current-carrying wire
Iron filings

6. Summary Magnetic Quantities
Permeability (m) defines the ease with which a magnetic field can be established in a given material. It is measured in units of the weber per ampere-turn meter.
The permeability of a vacuum (m0) is 4p x 10-7 weber per ampere-turn meter, which is used as a reference.
Relative Permeability (mr) is the ratio of the absolute permeability to the permeability of a vacuum.

7. Summary Magnetic Quantities
Reluctance (R) is the opposition to the establishment of a magnetic field in a material.
R= reluctance in A-t/Wb
l = length of the path
m = permeability (Wb/A-t m).
A = area in m2

8. Summary Magnetic Quantities
Recall that magnetic flux lines surround a current-carrying wire. A coil reinforces and intensifies these flux lines.
The cause of magnetic flux is called magnetomotive force (mmf), which is related to the current and number of turns of the coil.
Fm = NI
Fm = magnetomotive force (A-t)
N = number of turns of wire in a coil
I = current (A)

9. Summary Magnetic Quantities Problem:
Ohm’s law for magnetic circuits is
flux (j) is analogous to current
magnetomotive force (Fm) is analogous to voltage
reluctance (R) is analogous to resistance.
Problem:
What flux is in a core that is wrapped with a 300 turn coil with a current of 100 mA if the reluctance of the core is 1.5 x 107 A-t/Wb ?
2.0 mWb

10. Summary Magnetic Quantities
The magnetomotive force (mmf) is not a true force in the physics sense, but can be thought of as a cause of flux in a core or other material.
Current in the coil causes flux in the iron core.
Iron core
What is the mmf if a 250 turn coil has 3 A of current?
750 A-t

11. Summary
Magnetic field intensity is the magnetomotive force per unit length of a magnetic path. or
H= Magnetic field intensity (Wb/A-t m)
Fm = magnetomotive force (A-t)
l = average length of the path (m)
N = number of turns
I = current (A)
Magnetic field intensity represents the effort that a given current must put into establishing a certain flux density in a material.

12. Summary Magnetic Quantities
If a material is permeable, then a greater flux density will occur for a given magnetic field intensity. The relation between B (flux density) and H (the effort to establish the field) is
B = mH
m = permeability (Wb/A-t m).
H= Magnetic field intensity (Wb/A-t m)
This relation between B and H is valid up to saturation, when further increase in H has no affect on B.

13. Summary
As the graph shows, the flux density depends on both the material and the magnetic field intensity.

14. Summary
As H is varied, the magnetic hysteresis curve is developed.

15. Summary Magnetization Curve
A B-H curve is referred to as a magnetization curve for the case where the material is initially unmagnetized. The B-H curve differs for different materials; magnetic materials have in common much larger flux density for a given magnetic field intensity, such as the annealed iron shown here.
Annealed iron

16. Relative motion
When a wire is moved across a magnetic field, there is a relative motion between the wire and the magnetic field.
When a magnetic field is moved past a stationary wire, there is also relative motion.
In either case, the relative motion results in an induced voltage in the wire.

17. Summary Induced voltage
The induced voltage due to the relative motion between the conductor and the magnetic field when the motion is perpendicular to the field is dependent on three factors:
the relative velocity (motion is perpendicular)
the length of the conductor in the magnetic field
the flux density

18. Summary
Faraday’s law
Faraday experimented with generating current by relative motion between a magnet and a coil of wire. The amount of voltage induced across a coil is determined by two factors:
The rate of change of the magnetic flux with respect to the coil.
Voltage is indicated only when magnet is moving.

19. Summary
Faraday’s law
Faraday also experimented generating current by relative motion between a magnet and a coil of wire. The amount of voltage induced across a coil is determined by two factors:
The rate of change of the magnetic flux with respect to the coil.
The number of turns of wire in the coil.
Voltage is indicated only when magnet is moving.

20. Summary Magnetic field around a coil
Just as a moving magnetic field induces a voltage, current in a coil causes a magnetic field. The coil acts as an electromagnet, with a north and south pole as in the case of a permanent magnet.

21. Summary DC Generator A dc generator includes a rotating coil,
Mechanical drive turns the shaft
A dc generator includes a rotating coil,
which is driven by an external mechanical force (the coil is shown as a loop in this simplified view). As the coil rotates in a magnetic field, a pulsating voltage is generated.
Brushes
Commutator
To external circuit

22. Magnetic units
It is useful to review the key magnetic units from this chapter:
Quantity SI Unit Symbol
Magnetic flux density
Tesla
Weber
Weber/ampere-turn-meter
Ampere-turn/Weber
Ampere-turn
Ampere-turn/meter B f m R Fm H
Flux
Permeability
Reluctance
Magnetomotive force
Magnetizing force

23. Selected Key Terms Magnetic field
Magnetic flux
Weber (Wb)
Permeability
Reluctance
A force field radiating from the north pole to the south pole of a magnet.
The lines of force between the north pole and south pole of a permanent magnet or an electromagnet.
The SI unit of magnetic flux, which represents 108 lines.
The measure of ease with which a magnetic field can be established in a material.
The opposition to the establishment of a magnetic field in a material.

24. Selected Key Terms Magnetomotive force (mmf)
Solenoid
Hysteresis
Retentivity
The cause of a magnetic field, measured in ampere-turns.
An electromagnetically controlled device in which the mechanical movement of a shaft or plunger is activated by a magnetizing current.
A characteristic of a magnetic material whereby a change in magnetism lags the application of the magnetic field intensity.
The ability of a material, once magnetized, to maintain a magnetized state without the presence of a magnetizing current.

25. Selected Key Terms Induced voltage (vind)
Faraday’s law
Lenz’s law
Voltage produced as a result of a changing magnetic field.
A law stating that the voltage induced across a coil of wire equals the number of turns in the coil times the rate of change of the magnetic flux.
A law stating that when the current through a coil changes, the polarity of the induced voltage created by the changing magnetic field is such that it always opposes the change in the current that caused it. The current cannot change instantaneously.

26. Quiz 1. A unit of flux density that is the same as a Wb/m2 is the
a. ampere-turn
b. ampere-turn/weber
c. ampere-turn/meter
d. tesla

27. Quiz
2. If one magnetic circuit has a larger flux than a second magnetic circuit, then the first circuit has
a. a higher flux density
b. the same flux density
c. a lower flux density
d. answer depends on the particular circuit.

28. Quiz 3. The cause of magnetic flux is a. magnetomotive force
b. induced voltage
c. induced current
d. hysteresis

29. Quiz 4. The measurement unit for permeability is a. weber/ampere-turn
b. ampere-turn/weber
c. weber/ampere-turn-meter
d. dimensionless

30. Quiz 5. The measurement unit for relative permeability is
a. weber/ampere-turn
b. ampere-turn/weber
c. weber/ampere-turn meter
d. dimensionless

31. Quiz
6. The property of a magnetic material to behave as if it had a memory is called
a. remembrance
b. hysteresis
c. reluctance
d. permittivity

32. Quiz
7. Ohm’s law for a magnetic circuit is a. b. c. d.
Fm = NI
B = mH

33. Quiz 8. The control voltage for a relay is applied to the
a. normally-open contacts
b. normally-closed contacts
c. coil
d. armature

34. Quiz
9. A partial hysteresis curve is shown. At the point indicated, magnetic flux
a. is zero
b. exists with no magnetizing force
c. is maximum
d. is proportional to the current

35. Quiz
10. When the current through a coil changes, the induced voltage across the coil will
a. oppose the change in the current that caused it
b. add to the change in the current that caused it
c. be zero
d. be equal to the source voltage

36. Quiz
Answers:
1. d
2. d
3. a
4. c
5. d
6. b
7. c
8. c
9. b
10. a

37. Electrical Machines and Energy Conversion
Unit 1 Deck 1
Magnetism Basics

38. Electrical Machines and Energy Conversion
End of Presentation
Electrical Machines and Energy Conversion