WOLLO UNIVERSITY

KIOT
SCHOOL OF ELECTRICAL AND COMPUTER ENG.
DEPT. OF POWER ENGINEERING
ELECTRICAL MACHINE AND DRIVES (MCEG3261)

CHAPTER ONE
MAGNETICS

BY ASMAMAW.S
OUTLINES
 Magnetic circuits
Magnetic Materials and Their Properties
Magnetically Induced Emf and Force
Ac Operation of Magnetic Circuits
Hysteresis and eddy current losses

1-2
 INTRODUCTION
An electrical 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 electrical
power.
Almost all practical motors and generators convert energy from one form to
another through the action of a magnetic field.
Transformers are usually studied together with generators and motors because
they operate on the same principle, the difference is just in the action of a
magnetic field to accomplish the change in voltage level.
PRINCIPLE OF ELECTROMAGNET
 The principles of magnetism play an important role in the operation of an
electric machine.
The basic idea behind an electromagnet is 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.

4
5
MAGNETIC FIELD
magnetic field encircle their current
source.
Field is perpendicular to the wire and
that the field's direction depends on
which direction the current is
flowing in the wire.
A circular magnetic field develops
around the wire follows right-hand
rules.
 6
PROPERTIES OF MAGNETIC LINES OF FORCE
Magnetic lines of force tend to be as
short as possible.
Magnetic lines of force occupy
three-dimensional space extending
Magnetic lines of force are directed from (theoretically) to infinity.
north to south outside a magnet. Magnetic lines of force enter or
leave a magnetic surface at right
Magnetic lines of force are continuous. angles.
Magnetic lines of force in the same Magnetic lines of force cannot
direction tend to repel each other. cross each other.
7 Cont.….

Magnetic fields are the fundamental mechanism by which energy is

converted from one form to another in motors, generators, and
transformers. Four basic principles describe how magnetic fields are used
in these devices:
1. A current-carrying wire produces a magnetic field in the area around it.
2. A time-changing magnetic field induces a voltage in a coil of wire if it
passes through that coil. (This is the basis of transformer action.)
3. A current-carrying wire in the presence of a magnetic field has a force
induced on it. (This is the basis of motor action.)
4. A moving wire in the presence of a magnetic field has a voltage induced
in it.(This is the basis of generator action.)
8
EXAMPLE OF ELECTROMAGNET
 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.
9 Cont.…

 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.
10 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
11
BASICS OF MAGNETIC CIRCUITS
1. Magnetic flux(ϕ):
 The magnetic lines of force produced by a magnet is called magnetic flux.
 It is denoted by ϕ and its unit is Weber.
 1 weber = 108 lines of force
2. Flux density(B)
 The total number of lines of force per square metre of the crosssectional area of the
magnetic core is called flux density.
 Its SI unit is Tesla (weber per metre square).
B= ϕ/A Wb/𝑚2 or Tesla
Where ϕ -total flux in webers A - area of the core in square meters
B - flux density in weber/meter square.
12 Cont.…

3 . Magneto-Motive Force
 The amount of flux density setup in the core is dependent upon five
factors - the current, number of turns, material of the magnetic core,
length of core and the cross-sectional area of the core.
 More current and the more turns of wire we use, the greater will be the
magnetizing effect.
 This ability of a coil to produce magnetic flux is called the magneto
motive force.
mmf = NI ampere - turns
Where mmf is the magneto motive force in ampere turns
N is the number of turns.
13 Cont.…

4. Magnetic field Intensity(H)

 The magnetic field intensity is the mmf per unit length along the path of
the flux.
 Is also known as magnetic flux intensity and is represented by the letter
H. Its unit is ampere turns per meter.
H= mmf/ Length
H = NI/l AT/m
Where H is magnetic field intensity
N is the number of turns
l is average path length of the magnetic flux
14 Cont.…

5. Magnetic Flux Linkage(𝝀):

 The product of magnetic coupling to a conductor, or the flux thru a single
turn times the number of turns in coils.
𝜆 = 𝑛∅
 Which also relates to define inductance as
𝜆 = 𝐿𝑖
𝑑 𝑑
Where 𝑣 = 𝜆 and 𝑣 = 𝐿𝑖, L is inductance
𝑑𝑡 𝑑𝑡
15 Cont.…

6. Reluctance [S] or
 It is the opposition of a magnetic circuit to setting up of a magnetic flux in
it. 𝑓𝑙𝑢𝑥 = ∅ = 𝐵𝐴; 𝐹 = 𝑚𝑚𝑓 = 𝐻𝑙; 𝐵 = 𝜇𝐻
∅ BA 𝜇0 𝜇𝑟 𝐴 𝜇0 𝜇𝑟 𝐴
= = ; ℎ𝑒𝑛𝑐𝑒 ∅= ( )F
𝐹 𝐻𝑙 𝑙 𝑙
𝐹 𝐹 𝐹 𝑙
∅= = ; S= 𝑤ℎ𝑒𝑟𝑒 𝑠 =
𝑙 𝑆 ∅ 𝜇0 𝜇 𝑟 𝐴
𝜇0 𝜇𝑟 𝐴
Where, S – reluctance of the magnetic circuit
l - length of the magnetic path in meters
μo- permeability of free space µr - relative permeability
16 Cont.…

7. Permeability [μ]
 A property of a magnetic material which indicates the ability of
magnetic circuit to carry electromagnetic flux.
 Ratio of flux density to the magnetizing force, μ = B / H
 Unit: henry / meter
 Permeability of free space or air or non magnetic material
𝜇𝑜 = 4𝜋 × 10−7 𝐻/Τ𝑚
Relative permeability [𝜇𝑟]
𝜇
𝜇𝑟 =
𝜇0
17 Cont.…

8. Residual Magnetism
 It is the magnetism which remains in a material when the effective
magnetizing force has been reduced to zero.
9. Magnetic Saturation
 The limit beyond which the strength of a magnet cannot be increased is
called magnetic saturation.
18 CONT.…

10. End Rule

 According to this rule the current direction when looked from one end of
the coil is in clock wise direction then that end is South Pole. If the current
direction is in anti clock wise direction then that end is North Pole.
11. Lenz’s Law
 When an emf is induced in a circuit electromagnetically the current set up
always opposes the motion or change in current which produces it.
1
19 Cont.…

12. Electro magnetic induction

 Electromagnetic induction means the electricity induced by the magnetic
field.
Faraday's Laws of Electro Magnetic Induction
 There are two laws of Faraday's laws of electromagnetic induction.
They are,
1) First Law
2) Second Law
20 Cont.…

• First Law
 Whenever a conductor cuts the magnetic flux lines an emf is induced in
the conductor.
Second Law
 The magnitude of the induced emf is equal to the rate of change of flux
linkages
𝑑∅
𝑣 = −𝑁
𝑑𝑡
• Where V is induced voltage N is number of turns in coil
𝑑∅ is change of flux in coil 𝑑𝑡 is time interval
21
MAGNETIC MATERIALS
 Ferro Magnetic Materials: these materials are strongly attracted by a
magnet. example: iron, steel, nickel, cobalt, some metallic alloys. The relative
permeability of these materials is very high.
 Para Magnetic Materials: these materials are attracted by a magnet but
not very strongly. example: aluminum, tin, platinum, magnesium, manganese
etc. The relative permeability of these materials is slightly more than one.
 Dia Magnetic Materials: these materials are not at all attracted by any
magnet. The relative permeability of these materials is less than one.
example: zinc, mercury, lead, sulfur, copper, silver etc.
22
MAGNETIC CIRCUIT
 The complete closed path followed by any group of magnetic lines of flux
is referred to as magnetic circuit.
23
ANALOGY WITH ELECTRIC CIRCUITS
Similarities
Electric circuit Magnetic circuit
o Emf (volt) o m.m.f (AT)
o Current(ampere) o Flux(weber)
o Resistance(ohm) o Reluctance(A/Wb)
o Current density(A/𝑚2) o flux density(T or Wb/𝑚2)
o Conductivity o Permeability
Difference
Current actually flows flux is created, but does not flow
Circuit may be open or closed Circuit is always closed
24 Cont.…
25 Cont.…

The equivalent reluctance of a

number of reluctances in series is
just the sum of the individual
reluctances:

 Similarly, reluctances in parallel

combine according to the equation
26
LEAKAGE FLUX AND FRINGING
 Leakage Flux : the magnetic flux
which does not follow the
particularly intended path in a
magnetic circuit.
 When a current is passed through a
solenoid, magnetic flux is produced
by it.
27 Cont.…

Most of the flux is set up in the core of the solenoid and passes through the
particular path that is through the air gap and is utilised in the magnetic
circuit. This flux is known as Useful flux, ∅𝒖
Practically it is not possible that all the flux in the circuit follows a particularly
intended path and sets up in the magnetic core and thus some of the flux also sets
up around the coil or surrounds the core of the coil, and is not utilised for any
work in the magnetic circuit. This type of flux which is not used for any work is
called Leakage Flux and is denoted by , ∅𝒍.
The total flux Φ produced by the solenoid in the magnetic circuit is the sum of
the leakage flux and the useful flux.
28 Cont.….

∅ = ∅𝑢 + ∅𝑖 Fringing
Leakage coefficient The useful flux when sets up in the air
The ratio of the total flux produced to the gap, it tends to bulge outward at (b and
useful flux set up in the air gap of the
b’) as shown in figure, because of this
magnetic circuit is called leakage
coefficient or leakage factor. It is denoted bulging the effective area of the air gap
by (λ). increases and the flux density of the air
𝑇𝑜𝑡𝑎𝑙 𝑓𝑙𝑢𝑥(𝑓𝑙𝑢𝑥 𝑖𝑛 𝑡ℎ𝑒 𝑖𝑟𝑜𝑛 𝑝𝑎𝑡ℎ) gap decreases. This effect is known as
λ=
𝑢𝑠𝑒𝑓𝑢𝑙 𝑓𝑙𝑢𝑥(𝑓𝑙𝑢𝑥 𝑖𝑛 𝑡ℎ𝑒 𝑎𝑖𝑟𝑔𝑎𝑝)
∅ Fringing and the longer the air gap the
λ=
∅𝑢 greater is the fringing.
29 MAGNETIC BEHAVIOR OF FERROMAGNETIC
MATERIALS
To illustrate the behavior of magnetic permeability in a ferromagnetic material,
apply a direct current to the core, starting with 0 A and slowly working up to the
maximum permissible current.
At first, a small increase in the magnetomotive force produces a huge
increase in the resulting flux. After a certain point, though, further increases in the
magnetomotive force produce relatively smaller increases in the flux. Finally, an
increase in the magnetomotive force produces almost no change at all.
The graph between the flux density(B) and the magnetic field intensity(H)
for the magnetic material is called its magnetization curve or B-H curve.
It is also called a saturation curve.
30 Cont.…
31 Cont.…

 Magnetic Saturation is The limit beyond which magnetic flux density in

a magnetic area does not increase sharply further with increase of mmf.
 Residual magnetism is the amount of magnetization left behind after
removing the external magnetic field from the circuit. In another word the
value of the flux density retained by the magnetic material is called Residual
Magnetism and the power of retaining this magnetism is called retentivity
of the material. or
 Residual flux density is the certain value of magnetic flux per unit area
that remains in the magnetic material without presence of magnetizing
force (i.e. H = 0).
32 Cont.…
33 Cont.…

The region of this figure in which the curve flattens out is called the
saturation region, and the core is said to be saturated.
In contrast, the region where the flux changes very rapidly is called the unsaturated region
of the curve, and the core is said to be unsaturated.
The transition region between the unsaturated region and the saturated region is
sometimes called the knee of the curve.
The value of relative permeability mainly depends on the value of flux density. But for the
non-magnetic materials like plastic, rubber, etc. and for the magnetic circuit having an air
gap, its value is constant, denoted by (µ0). Its value is 4πx10-7H/m and commonly known
as absolute permeability or permeability of free space.
34
MAGNETIC HYSTERESIS
 1: When supply current I = 0, so no existence of flux density (B) and
magnetizing force (H). The corresponding point is ‘O’ in the graph below.
 2: When current is increased from zero value to a certain value,
magnetizing force (H) and flux density (B) both are set up and increased
following the path o – a.
 3: For a certain value of current, flux density (B) becomes maximum
(Bmax). The point indicates the magnetic saturation or maximum flux density
of this core material. All element of core material get aligned perfectly. Hence
H_max is marked on H axis. So no change of value of B with further
increment of H occurs beyond point ‘a’.
35 Cont.…
36 Cont.…

 4: When the value of current is decreased from its value of magnetic flux
saturation, H is decreased along with decrement of B not following the
previous path rather following the curve a – b.
 5: The point ‘b’ indicates H = 0 for I = 0 with a certain value of B. This
lagging of B behind H is called hysteresis. The point ‘b’ explains that after
removing of magnetizing force (H), magnetism property with little value
remains in this magnetic material and it is known as residual magnetism (Br).
Here o – b is the value of residual flux density due to retentivity of the
material.
37 Cont.…

 6: If the direction of the current I is reversed, the direction of H also gets

reversed. The increment of H in reverse direction following path b – c
decreases the value of residual magnetism (Br) that gets zero at point ‘c’
with certain negative value of H. This negative value of H is called coercive
force (Hc).
 7: H is increased more in negative direction further; B gets reverses
following path c – d. At point ‘d’, again magnetic saturation takes place but
in opposite direction with respect to previous case. At point ‘d’, B and H
get maximum values in reverse direction, i.e. (-Bm and -Hm)
38 Cont.…

 8: If we decrease the value of H in this direction, again B decreases following the

path de. At point ‘e’, H gets zero valued but B is with finite value. The point ‘e’ stands
for residual magnetism (-Br) of the magnetic core material in opposite direction with
respect to previous case.
 9: If the direction of H again reversed by reversing the current I, then residual
magnetism or residual flux density (-Br) again decreases and gets zero at point ‘f ’
following the path e – f. Again further increment of H, the value of B increases from
zero to its maximum value or saturation level at point a following path f – a.
 The path a – b – c – d – e – f – a forms hysteresis loop.
[NB: The shape and the size of the hysteresis loop depend on the nature of
the material chosen]
39 Cont.…

 Hysteresis: The phenomenon of flux density(B) lagging behind the

magnetizing force (H) in a magnetic material is known as Magnetic Hysteresis.
 Coercive force is defined as the negative value of magnetizing force (-H) that
reduces residual flux density of a material to zero.
 Retentivity:It is defined as the degree to which a magnetic material gains its
magnetism after magnetizing force (H) is reduced to zero.
 The hysteresis loss in an iron core is the energy required to accomplish the
reorientation of domains during each cycle of the alternating current applied to
the core.
 The area enclosed in the hysteresis loop formed by applying an alternating
current to the core is directly proportional to the energy lost in a given ac cycle.
40
HYSTERESIS LOSS
The work done by the magnetizing force against the internal friction of the
molecules of the magnet, produces heat. This energy which is wasted in the
form of heat due to hysteresis is called hysteresis loss.
𝑃ℎ = Ƞ𝐵𝑚𝑎𝑥 1.6 𝑓𝑣 𝑤𝑎𝑡𝑡𝑠
Where, Ph – hysteresis loss in watts
Ƞ – hysteresis or Steinmetz’s constant in J/m3,
Bmax – maximum value of the flux density in the magnetic material in wb/m2
𝑓 – number of cycles of magnetization made per second
𝑣- volume of the magnetic material (part in which magnetic reversal occur) in
m3
41
Cont.…

Soft magnetic material

 The soft magnetic material has a narrow magnetic
hysteresis loop which has a small amount of
dissipated energy. They are made up of material
like iron, silicon steel, etc.
 It is used in the devices that require alternating
magnetic field.
 It has low coercivity
 Low magnetization
 Low retentivity
42 Cont.…

Hard magnetic material

 The Hard magnetic material has a
wider hysteresis loop and results in a
large amount of energy dissipation
and the demagnetization process is
more difficult to achieve.
 It has high retentivity
 High coercivity
 High saturation
43
IMPORTANCE OF HYSTERESIS LOOP
 Smaller hysteresis loop area symbolizes less hysteresis loss.
 Hysteresis loop provides the value of retentivity and coercivity of a material. Thus
the way to choose perfect material to make permanent magnet, core of
machines becomes easier.
 From B-H graph, residual magnetism can be determined and thus choosing
of material for electromagnets is easy.
 Magnetic material having a wider hysteresis loop is used in the devices like
magnetic tape, hard disk, credit cards, audio recordings as its memory isn’t
easily erased.
 Magnetic materials having a narrow hysteresis loop are used as electromagnets,
solenoid, transformers and relays which require minimum energy dissipation.
44
EDDY CURRENT LOSS
 When an alternating magnetic field is applied to a magnetic material an
emf is induced in the material itself.
 Since the magnetic material is a conducting material, these EMFs circulates
currents within the body of the material. These circulating currents are
called Eddy Currents. They will occur when the conductor experiences a
changing magnetic field.
 As these currents are not responsible for doing any useful work, and it
produces a loss (𝐼 2 𝑅 loss) in the magnetic material known as an Eddy
Current Loss. Similar to hysteresis loss, eddy current loss also increases the
temperature of the magnetic material.
45 Cont.…

 The hysteresis and the eddy

current losses in a magnetic
material are also known by the
name iron losses or core losses or
magnetic losses.
 When the changing flux links with
the core itself, it induces emf in
the core which in turns sets up the
circulating current called Eddy
Current and these current in return
produces a loss called eddy current
loss or (𝐼2𝑅) loss. where I is the value of the current and
R is the resistance of the eddy current path.
46 Cont.…

 If the core is made up of solid iron of larger cross-sectional area, the

magnitude of I will be very large and hence losses will be high. To reduce the
eddy current loss mainly there are two methods.
 By reducing the magnitude of the eddy current.
 The magnitude of the current can be reduced by splitting the solid core
into thin sheets called laminations, in the plane parallel to the magnetic field.
Each lamination is insulated from each other by a thin layer of coating of
varnish or oxide film. By laminating the core, the area of each section is
reduced and hence the induced emf also reduces. As the area through which
the current is passed is smaller, the resistance of eddy current path increases.
 The eddy current loss is also reduced by using a magnetic material having
the higher value of resistivity like silicon steel.
47 Cont.…

It is difficult to determine the eddy current loss from the resistance and
current values, but by the experiments, the eddy current power loss in a
magnetic material is given by the equation
𝑃𝑒 = 𝐾𝑒 𝐵𝑚 2 𝑡 2 𝑓 2 𝑣 𝑤𝑎𝑡𝑡𝑠
Where, Pe=eddy current loss in watts, Ke=coefficient of eddy current.
Bm= maximum value of flux density in Wb/m2
𝑡 =thickness of lamination in meters
𝑓 =frequency of reversal of magnetic field in Hz
𝑣 =volume of magnetic material in 𝑚3.
48 FARADAY'S LAW- INDUCED VOLTAGE FROM A
TIME-CHANGING MAGNETIC FIELD
From the various ways in which an existing magnetic field can affect its
surroundings, the first major effect is Faraday's law.
 It states that if a flux passes through a turn of a coil of wire, a voltage will be
induced in the turn of wire that is directly proportional to the rate of
change in the flux with respect to time.
𝑑∅
𝑒𝑖𝑛𝑑 = −
𝑑𝑡
Where 𝑒𝑖𝑛𝑑 is the voltage induced in the turn of the coil and
∅ is the flux passing through the turn.
 If a coil has N turns and if the same flux passes through all of them, then the
voltage induced across the whole coil is given by
49 Cont.…

𝑑∅
𝑒𝑖𝑛𝑑 = −𝑁
𝑑𝑡
Where 𝑒𝑖𝑛𝑑 = voltage induced in the coil
N = number of turns of wire in coil
∅ =flux passing through coil
 The minus sign in the equations is an expression of Lenz's law.
 Lenz's law states that the direction of the voltage buildup in the coil is
such that if the coil ends were short circuited, it would produce current that
would cause a flux opposing the original flux change. Since the induced voltage
opposes the change that causes it, a minus sig
50 Cont.…

The above equation assumes that If there are N turns in the coil of
exactly the same flux is present in wire, the total voltage on the coil is
each turn of the coil. Unfortunately, 𝑁 𝑁
𝑑(∅𝑖 ) 𝑑
the flux leaking out of the core into 𝑒𝑖𝑛𝑑 = ෍ 𝑒𝑖 = ෍ = (∅𝑖 )
𝑑𝑡 𝑑𝑡
the surrounding air prevents this 𝑖=1 𝑖=1
from being true. 𝑑𝝀
𝑒𝑖𝑛𝑑 =
𝑑𝑡
The magnitude of the voltage in the
𝑖𝑡ℎ turn of the coil is always given Where 𝝀= σ𝑁 𝑖=1 ∅𝑖
𝑑(∅𝑖 ) 𝜆 =Flux linkage
by 𝑒𝑖 = 𝑑𝑡
51
PRODUCTION OF INDUCED FORCE ON A WIRE
 A second major effect of a magnetic field
on its surroundings is that it induces a force
on a current-carrying wire within the field.
 The force induced on the conductor is
given by 𝐹 = 𝑖(𝐿 × 𝐵)
Where i = magnitude of current in wire
𝐿 = length of wire, with direction of I
defined to be in the direction
of current flow
B = magnetic flux density vector
52 Cont.…

 The direction of the force is given

 where 𝜃 is the angle
by the right-hand rule: If the index
between the wire and the flux
finger of the right hand points in the
density vector.
direction of the vector I and the middle
finger points in the direction of the
flux density vector B, then the thumb
points in the direction of the resultant
force on the wire.
 The magnitude of the force is
given by 𝐹 = 𝑖𝑙𝐵 sin 𝜃
53 INDUCED VOLTAGE ON A CONDUCTOR MOVING
IN A MAGNETIC FIELD
 If a wire with the proper orientation moves through a magnetic field, a
voltage is induced in it. The voltage induced in the wire is given by
𝑒𝑖𝑛𝑑 = 𝑣 × 𝐵 . 𝑙
Where 𝑣= velocity of the wire
B = magnetic flux density vectorType equation here.
𝑙 = length of conductor in the magnetic field
54 Cont.…

Vector 𝑙 points along the direction

of the wire toward the end making
the smallest angle with respect to
the vector 𝑣 × 𝐵.
 The voltage in the wire will be built
up so that the positive end is in the
direction of the vector 𝑣 × 𝐵.