This document provides an overview of magnetic circuits and induction in electrical machines. It begins by outlining the learning outcomes, which are to understand the principles behind electromagnets and their relationship to voltage and magnetic materials. It then defines electric machines as devices that convert between electrical and mechanical power. The rest of the document discusses key concepts related to magnetism and induction that are important for understanding electric machines, including electromagnets, magnetic fields, flux, flux linkage, Faraday's law, Lenz's law, and induced voltages. Worked examples are provided to illustrate how to apply these concepts.

1. © MRM
FKEE, UMP 1
Magnetic Circuits
and Induction
Mohd Rusllim Bin Mohamed
Ext: 2080
A1-E10-C09
BEE2123
ELECTRICAL MACHINES

2. MRM
FKEE, UMP 2
Learning Outcomes
 At the end of the lecture, student should :
 Understand the principle and the nature
behind an electromagnet and its
relationship to voltage and magnetic
materials.
 Understand the fundamental laws in the
dynamic magnetic systems and their
relation to the electrical machines.

3. MRM
FKEE, UMP 3
Introduction to Electrical Machine
 An electric machine
 is a device which converts electrical power
(voltages and currents) into mechanical power
(torque and rotational speed), and/or vice
versa.
 A motor describes a machine which converts
electrical power to mechanical power; a
generator (or alternator) converts mechanical
power to electric power.

4. MRM
FKEE, UMP 4
Introduction to Electrical Machine
 Many electric machines are capable of
performing both as motors and
generators;
 The capability of a machine performing
as one or the other is often through the
action of a magnetic field, to perform
such conversions.

5. MRM
FKEE, UMP 5
Electromagnets and Motors
 The principles of magnetism play an
important role in the operation of an
electric machine.
 To understand how an electric motor
works, the key is to understand how
the electromagnet works.

6. MRM
FKEE, UMP 6
Principle of Electromagnetic
 The basic idea behind an electromagnet is
extremely simple: a magnetic field around
the conductor can be produced when
current flows through a conductor.
 In other word, the magnetic field only exists
when electric current is flowing
 By using this simple principle, you can
create all sorts of things, including motors,
solenoids, read/write heads for hard disks
and tape drives, speakers, and so on

7. MRM
FKEE, UMP 7
Electromagnet (Cont)
 If a wire is attached directly between the positive
and negative terminals of a battery-cell, three things
will happen:
 Electrons will flow from the negative side of
the battery to the positive side as fast as they
can.
 The battery will drain fairly quickly (in a
matter of several minutes). For that reason, it is generally
not a good idea to connect the two terminals of a battery to one another
directly. Normally, you connect some kind of load in the middle of the wire so
the electrons can do useful work. The load might be a motor, a light bulb, a
radio or whatever.
 A small magnetic field is generated in the
wire. It is this small magnetic field that is the
basis of an electromagnet.

8. MRM
FKEE, UMP 8
Magnetic Field
 Unlike electric fields (which start on +q and end on
–q), magnetic field encircle their current source.
 The field weakens as you move away from the wire
A circular magnetic field
develops around the wire
follows right-hand rules
field is perpendicular to
the wire and that the
field's direction depends
on which direction the
current is flowing in the
wire

9. MRM
FKEE, UMP 9
Electromagnet (Cont)
 When SW is ON, hence current flows thru a current-carrying
wire (otherwise conductor) then create magnetic field.
 Being small, it is sensitive to small magnetic fields.
Therefore, the compass is affected by the magnetic field
created in the wire by the flow of electrons.
Right Hand Rule for
magnetic field from
flowing current

10. MRM
FKEE, UMP 10
Principle of Electromagnetic
 The magnetic field is made up of lines of
flux.
 The size and strength of the magnetic field
will increase and decrease as the current
flow strength increases and decreases.

11. MRM
FKEE, UMP 11
A Regular Magnet
 All magnets have two characteristics:
 magnets attract and hold metal objects like
steel and iron.
 If free to move, like the compass needle, the
magnet will assume roughly a north-south
position.

12. MRM
FKEE, UMP 12
Magnetic lines of flux
 magnet attracts an iron or steel object by an invisible
force. The magnet’s invisible force is called lines of flux.
These lines of flux make up an invisible magnetic field.
 Invisible magnetic lines of flux leave the north pole and
enter the south pole. While the lines of flux are invisible,
the effects of magnetic fields can be made visible.
 When a sheet of paper is placed on a magnet and iron
filings loosely scattered over it, the filings will arrange
themselves along the invisible lines of flux.

13. MRM
FKEE, UMP 13
Magnet Repels and Attracts
 the fundamental law of all magnets: Opposites attract
and likes repel.
• The magnetic lines of flux always form closed loops,
leaving the north pole and entering the south pole.
• the north end of one magnet will attract the south
end of the other. On the other hand, the north end of
one magnet will repel the north end of the other (and
similarly to south will repel south).

14. MRM
FKEE, UMP 14
Example of Electromagnetic
 An electromagnet can be made by winding the
conductor into a coil and applying a DC voltage.
 The lines of flux, formed by current flow through the
conductor, combine to produce a larger and stronger
magnetic field.
 The center of the coil is known as the core. In this
simple electromagnet the core is air.

15. MRM
FKEE, UMP 15
Adding an Iron Core
 Iron is a better conductor of flux than air. The air core
of an electromagnet can be replaced by a piece of soft
iron.
 When a piece of iron is placed in the center of the coil
more lines of flux can flow and the magnetic field is
strengthened.

16. MRM
FKEE, UMP 16
Strength of Magnetic Field (Cont)
 Because the magnetic field around a wire is
circular and perpendicular to the wire, an easy
way to amplify the wire's magnetic field is to coil
the wire
 The strength of the magnetic field in the DC
electromagnet can be increased by increasing the
number of turns in the coil. The greater the
number of turns the stronger the magnetic
field will be.

17. MRM
FKEE, UMP 17
Strength of Magnetic Field in AC

18. MRM
FKEE, UMP 18
Magnetic saturation & hysteresis in
ac magnetic field
unmagnetized Material
Iron becomes
magnetically
saturated
Magnetism increase as
magnetic field magnetized
unmagnetized iron
a
b
c
d
Applied field is reduced; the magnetism
reduced thru diff. curve since iron tends to
retains magnetized state - hence produced
permanent magnet, Residual Flux, res
AC increased in negative direction,
magnetic field reversed , the iron
reversely magnetized until saturated
again
If continue apply ac current, curve
continue to follow S-shaped curve
(hysteresis curve)
The area enclosed by hysteresis curve is energy loss per unit volume per cycle – heats the iron and is one
reason why electric machines become hot
Therefore, it is required to select magnetic materials that have a narrow hysteresis loop
Hm
Magnetic field density
Bm

19. MRM
FKEE, UMP 19
Magnetic Flux & Magnetic Flux
Linkage
 Magnetic Flux : magnetic flux lines encircle the
currents that generate them. Thus, it only exist in
closed loops.
 This is given by
 Example : A circular coil has a diameter of 2 cm and
average flux density in a coil of 1.59x10-4 tesla
(webers/m2). Find a flux passing thru it?
  = Bave A
= B* [ j2]
= [1.59x10-4][(0.01)2] = 5x10-8 Wb
A
Baverage


B =flux density (T)
= flux in component (Wb)
A = cross section (m2)

20. MRM
FKEE, UMP 20
Magnetic Flux & Magnetic Flux
Linkage (Cont)
 Magnetic Flux Linkage,  : the product of
magnetic coupling to a conductor, or the flux
thru a single turn times the number of turns in
coils.
 Which also relates to define inductance as
Where; , L = inductance
 n
iL
Li
dt
d
vand
dt
d
v  

21. MRM
FKEE, UMP 21
Magnetic Flux & Magnetic Flux
Linkage (Cont)
 Example :
An inductor has 120Vrms, 60Hz voltage applied.
Calculate the peak flux linkage
Solution
Vrms => v(t) = Vp cos (2f)
v(t) = 1202 cos(120t)V; ac peak line voltage 0
 =
Where the constant, C, represent possible dc flux. The magnitude
of the ac flux linkage is thus 2/ Weber-turn.
Ctdtt  )120sin(
2
)120cos(2120 



dt
d
v 

22. MRM
FKEE, UMP 22
Magnetic Flux & Magnetic Flux
Linkage (Cont)
 Example :
In previous example, say the current in inductor is 200mA
(rms). Calculate the inductance.
Solution
The peak current =2002mA
The peak flux linkage = 2/
H
i
L
peak
peak
59.1
22.0
/2



23. MRM
FKEE, UMP 23
Faraday’s Law and Lenz’s Law
(E due to N)
 Faraday’s Law : If a magnetic flux, , in a coil is changing in
time (n turns), hence a voltage, Vab is induced
 Lenz’s Law : if the loop is closed, a connected to b, the
current would flow in the direction to produce the flux inside
the coil opposing the original flux change. (in other words,
Lenz’s Law will determine the polarity of the induced voltage)

a
b
t
NV



V = induced voltage
N = no of turns in coil
 = change of flux in coil
t = time interval

24. MRM
FKEE, UMP 24
Induced Voltage (Cont)
 Example
A coil of 2000 turns
surrounds a flux of 5mWb
produced by a permanent
magnet as shown in figure.
The magnet is suddenly
withdrawn causing the flux
inside the coil to drop
uniformly to 2mWb in 1/10
of a second. What is the
voltage induced?
Solution
 = (5 – 2)mWb = 3mWb
 V =   V
t
N 60
10
1
103
2000
3








 


 

25. MRM
FKEE, UMP 25
Voltage Induced in a conductor
(E reference to conductor)
 In many motors and generators, the coils relatively move with
respect to a flux that is fixed in space. The relative motion
produces a change in the flux linking the coils and, consequently,
a voltage is induced according to Faraday's law. (as describe in
page before)
 However, in this special (although common) case, it is easier to
calculate the induced voltage with reference to the conductors,
rather than with reference to the coil itself. In effect, whenever a
conductor cuts a magnetic field, a voltage is induced across
its terminals. The value of the induced voltage is given by
E = Blv
where
E = induced voltage (V)
B = flux density (T)
l = active length of the conductor in the magnetic field (m)
v = relative speed of the conductor (m/s)

26. MRM
FKEE, UMP 26
Voltage Induced in a conductor

27. MRM
FKEE, UMP 27
Voltage Induced in a conductor
(Cont)
 Example
The stationary conductors
of a large generator have
an active length of 2 m and
are cut by a field of 0.6T,
moving at a speed of
100m/s. Calculate the
voltage induced in each
conductor?
Solution
E = Blv
= 0.6 T x 2 m x 100 m/s
=120V

28. MRM
FKEE, UMP 28
Faraday’s Law (Cont)
 Faraday’s Law for moving conductors : For
coils in which wire (conductor) is moving thru
the magnetic flux, an alternate approach is to
separate the voltage induced by time-varying
flux from the voltage induced in a moving
conductor.
 This situation is indicates the presence of an
electromagnetic field in a wire (conductor). This
voltage described by Faraday’s Law is called
as the flux cutting or Electromotive force, or emf.

29. MRM
FKEE, UMP 29
Faraday’s Law (Cont)
 Example:
 The electrical circuit consists of battery, resistor, two stationary rails, and
movable bar that can roll or slide along the rails with electrical contact.
 When switch is closed:
 Current will not start immediately as inductance of the circuit.
(However time constant L/R is very small). Hence, current quickly
reach V/R.
 Force is exerted on the bar due to interaction between current and
magnetic flux to the right and made the bar move with certain velocity.
The mechanical power out of the bar.
V-E = iR
KVL:

30. MRM
FKEE, UMP 30
Faraday’s Law (Cont)
 The motion of the bar produces an
electromagnetic force. The polarity of
the emf is +ve where the current enters
the moving bars. The moving bar
generates a ‘back’ emf that opposes the
current.
 The instantaneous electrical power into the bar =
mechanical output power

31. MRM
FKEE, UMP 31
Check your understanding
1. What is the different between electric field and electromagnetic
field?
2. A doorbell ringer has 200 turns and operates on 6V in 1/10 of a
second. Find the flux in the magnetic structure.

32. MRM
FKEE, UMP 32
Check your understanding
3. For the circuit and coil,
find the following:
a. draw the magnetic
flux pattern, including
flux direction
b. If the inductance of
the coil were
L=0.05H, find its
magnetic flux linkage.
Note that the wire in
the circuit has a
resistance 1 and
lumped resistance 2
.

33. MRM
FKEE, UMP 33
Check your understanding
4. An auto battery as
shown in figure is
being charged with
a current of 20A.
a. Draw the
magnetic flux
pattern, including
flux direction

34. MRM
FKEE, UMP 34
Check your understanding
5. A toroid is used in an experiment of
magnetism theory with a cross-
section area of 3cm2. The toroid is
wound with a coil of 600 turns and
direct current of 1.5A is passed
through the coil. The flux density
obtained from the experiment is
1.08T. Determine
a. The flux
b. Magnetic flux linkage
c. Inductance in coil
d. Voltage induced if a flux is
reduced 40% of original flux at
1/10 of a second.
e. Voltage induced in the conductor
if a conductor with a length of
2.5cm is inserted inside toroid at
2cm/s
f. Magnetic flux pattern including
flux direction and state what rules
did you applied?

35. MRM
FKEE, UMP 35
Check your understanding
6. The electrical circuit consists of battery,
resistor, two stationary rails, and
movable bar that can roll or slide
along the rails with electrical contact.
Data from the experiment indicates
that the original flux and flux density
were recorded as 1.5 Weber and
1.05T respectively with 40V applied to
the circuit. Assume N=10 Turns.
Determine:-
a) Voltage induced if a flux is
reduced to 25% of original flux at
1/4 of a second.
b) Voltage induced in the conductor
if a conductor with a length of
2.05cm is inserted inside core at
15mm/s.
c) Resistance used in the
experiment if condition (b) is
applied if current is 10A.