Magnetism.pptx

Chapter 2
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz

Aim: impart an understanding of
electromagnetic principles
Important as electromagnetism underpins
the operation of many electrical machines
Linkage between electrical and
mechanical worlds
Electromagnetism

Describes the relationship between
electricity and magnetism
Is essentially the foundation for all of
electrical engineering
Use electromagnets to generate electricity,
store memory on our computers, generate
pictures on a television screen, diagnose
illnesses,
Electromagnetism

Electromagnetism works on the principle that an
electric current through a wire generates a
magnetic field
 In a bar magnet, the magnetic field runs from the
north to the south pole.
 In a wire, the magnetic field forms around the wire.
 If we wrap that wire around a metal object, we can
often magnetize that object. In this way, we can
create an electromagnet.
Electromagnetism

 Magnetism is a force field that acts
on magnetic materials but not on
other materials.
 Magnetic field around a bar magnet
 Two “poles” dictated by direction of
the field
 Opposite poles attract (aligned
magnetic field)
 Same poles repel (opposing
magnetic field)
Electromagnetism

Electromagnetism

Field Detector
 Can use a compass to
map out magnetic field
 Field forms closed “flux
lines” around the
magnet
 Magnetic flux measured
in Webers (Wb)
 Symbol
Electromagnetism

Magnetic Flux
 Magnetic flux lines are assumed to have the following
properties:
 Leave the north pole (N) and enter the south pole (S)
of a magnet.
 Like magnetic poles repel each other.
 Unlike magnetic poles create a force of attraction.
 Magnetic lines of force (flux) are assumed to be
continuous loops.
Electromagnetism

Magnetic Field conductor
 A magnetic field also forms
round a conductor along
which a current is flowing
 Field can be described using
“right hand screw rule”
Electromagnetism

Right Hand Rule
 Thumb indicates
direction of
current flow
 Finger curl
indicates the
direction of field
Electromagnetism

Wire Coil
 Notice that a coil
of wire will
produce a
perpendicular
field
Electromagnetism

Magnetic Field: Coil
 A series of coils produces a field
similar to a bar magnet – but weaker!
Electromagnetism

Magnetic Field : Coil
 Placing a ferrous material
inside the coil increases the
magnetic field
 Acts to concentrate the field
also notice field lines are
parallel inside ferrous
element
 ‘flux density’ has increased
Electromagnetism

Flux Density
Electromagnetism

Permeability μ is a measure of the ease by
which a magnetic flux can pass through a
material (Wb/Am)
Permeability of free space μo = 4π x 10-7
(Wb/Am)
Relative permeability:
Electromagnetism- Permeability

Reluctance: “resistance” to
flow of magnetic flux
@
Associated with “magnetic circuit” –
flux equivalent to current
What’s equivalent of voltage?
Electromagnetism- Reluctance
A
l
S
r
0




Magnetomotive Force
 Coil generates magnetic
field in ferrous toroidal
 Driving force F needed to
overcome toroidal
reluctance
 Magnetic equivalent of
ohms law
Electromagnetism

Circuit Analogy
Electromagnetism

Magnetomotive Force (MMF)
 The MMF is generated by the coil
 Strength related to number of turns and
current, measured in Ampere turns (At)
Electromagnetism- Magnetomotive Force

• The longer the magnetic path the greater the
MMF required to drive the flux
• Magnetomotive force per unit length is known as
the “magnetizing force” H
• Magnetizing force and flux density related by:
Electromagnetism- Field Intensity

B(T)
H(A/m)
Magnetization curve (B-H characteristic)
Saturation
H
B r
0


Free space, electrical conductors (aluminium or copper), insulators:
= unity.
Ferromagnetic materials (iron, cobalt and nickel):
= several hundred - several thousand
A large value of : a small current can produce a large flux density
r

r

r

Electromagnetism

Magnetic Field Intensity and Ampère’s
Law
H
B 

Am
Wb
10
4 7
0


 

0


 
r
Ampère’s Law:

 
 i
dl
H
Electromagnetism

Flux Linkages and Faraday’s Law
A
B d
A

 
 
 N

Faraday’s law of magnetic induction:
dt
d
e


Electromagnetism

Ampere’s Law
Electromagnetism

Magnetic Field Around a Long Straight
Wire
r
I
H
B



2


Electromagnetism

• Ampere’s Law
Electromagnetism

Lenz’s Law states that the polarity of the
induced voltage is such that the voltage
would produce a current (through an
external resistance) that opposes the
original change in flux linkages
Electromagnetism

Lenz’s Law
 Voltages Induced in Field-Cutting Conductors
Blu
e 
Electromagnetism

In many engineering applications, we need
to compute the magnetic fields for
structures that lack sufficient symmetry for
straight-forward application of Ampère’s
law. Then, we use an approximate method
known as magnetic-circuit analysis.
Electromagnetism- magnetic circuit

Advantage of the Magnetic-Circuit
Approach is that it can be applied to
unsymmetrical magnetic cores with
multiple coils.
Electromagnetism- magnetic circuit

Magnetic leakage and Fringing
• Magnetic leakage/ leakage flux
• Flux not passing through in the magnetic material or in air
gap
» In air gap – useful fluxs
• Occurs at the magnetic source
– As shown in Figure 2.a
air gap,
(useful fluxs)
magnetic
Source, NI
useful
fluxs, a
leakage
flux, l
Total
flux, T
leakage_ factor,a =
totalflux
usefulflux

33
Magnetic leakage and Fringing
• Fringing
• Occurs at the air gap
• Flux intends to bulge outwards
» Increasing the effective area
» Reduce the flux density
As shown in Figure 2.a
(still useful flux)
Contoh 1.2 page 1.11, Contoh 1.3 page 1.12,
Contoh 1.4 page 1.14 and Contoh 1.5 page 1.15

Magnetic Circuit
lc
i
N
+
F
-
S

Equivalent circuit
Analogy between magnetic
circuit and electric circuit
E R
i
Electromagnetism

Magnetic circuit Electric circuit
Term Symbol Term Symbol
Magnetic flux  Electric current I
Flux density B Current density J
Magnetic field strength H Electric field strength E
Magnetomotive force F Electromotive force E
Permeability  Permittivity e
Reluctance S Resistance R
Electromagnetism

Series Magnetic Circuit
with air gap
lc
i
N lg
+
F
-

Sc
Sg
g
g
g
c
c
c
g
g
c
c
g
C
g
0
g
g
c
c
c
c
A
B
;
A
B
density
Flux
l
H
l
H
Ni
S
S
Ni
A
l
S
;
A
l
S














Electromagnetism

Series composite magnetic circuit
with different material
i
N
iron steel
cobalt
+
F
-

b
S
a
S
c
S
c
c
b
b
a
a
c
b
a
c
c
c
c
b
b
b
b
a
a
a
a
l
H
l
H
l
H
Ni
S
S
S
Ni
A
l
S
A
l
S
A
l
S














;
;
Electromagnetism

Example 3
A coil of 200 turns is wound uniformly over a wooden ring
having a mean circumference of 600mm and a uniform
cross-sectional area of 500mm2. if the current through
the coil is 4A, calculate
(a) the magnetic field strength
(b) the flux density
(c) the total flux
( 1330A/m, 1680µT,0.838µWb)
Electromagnetism

Example 4
Calculate the magnetomotive force required to produce a
flux of 0.015Wb across an air gap 2.5mm long, having
effective area of 200cm2
(1492At)
Electromagnetism

Example 5
A mild-steel ring having a cross- sectional area of 500
mm2 and a mean circumference 0f 400mm has a coil 0f
200 turns wound uniformly around it. The relative
permeability of the mild steel for the respective flux
density is about 380. Calculate
(a) the reluctance of the ring
(b) the current required to produce a flux of 800µWb in
the ring
(1.68 x 106 At/Wb, 6.7A)
Electromagnetism

Example 6
The Figure represents the magnetic
circuit of a relay. The coil has 500
turns and the mean core path is lc =
360 mm. When the air-gap lengths
are 1.5 mm each, a flux density of
0.8 Tesla is required to actuate the
relay. The core is cast steel with the
field intensity 510 At/m. Find the
current in the coil.
(4.19 A)
Compute the values of permeability
and relative permeability of the core.
(1.57 x 10-3 Wb/Am, 1250 Wb/Am)
If the air-gap is zero, find the current
in the coil for the same flux density
(0.8 T) in the core. (0.368 A)
i
N
 Movable
part
lg
Electromagnetism

Example 7
A magnetic circuit comprises three parts in series
each of uniform cross-sectional area (A). They are:
(a) a length of 80 mm and A= 50 mm2
(b) a length of 60 mm and A = 90 mm2
(c) an air gap of length 0.5 mm and A = 150 mm2
A coil of 4000 turns is wound on part (b) and the flux density in the
air gap is 0.3 T. Assuming that all the flux passes through the given
circuit, and the relative permeability is 1300, estimate the coil current
to produce such a flux density
(45.43mA)
Electromagnetism

Series Parallel Magnetic Circuit
i
N
 2

+
F
-

1 2


1

3
S 2
S
2
2
3
3
3
3
1
1
3
2
1
l
H
l
H
2
loop
l
H
l
H
NI
1
loop
Laws
Kirchoff








:
:
:
Electromagnetism

Series Parallel
Magnetic Circuit i
N
 

+
F
-

1 2


1
S
3
S
2
S
2
2
3
3
1
3
3
2
1
3
l
H
l
H
NI
2
loop
l
H
l
H
NI
1
loop
Laws
Kirchoff









:
:
:
`
Electromagnetism

Series Parallel
Magnetic Circuit with Air
Gap
 

i
N
+
F
-

1 2


1
S 3
S
2
S
g

2
2
s
s
3
3
1
1
s
s
3
3
2
1
3
l
H
l
H
l
H
NI
2
loop
l
H
l
H
l
H
NI
1
loop
Laws
Kirchoff











:
:
:
Electromagnetism

The relationship between B and H is not linear for the
types of iron used in motors and transformers.
Electromagnetism- magnetic core loss

dB
H
Al
W
W
B
v 


0
Electromagnetism

The relationship between B and H is complicated
by non-linearity and “hysteresis”
 Can be used to calculate µ
Electromagnetism- Hysteresis

Hysterisis
Electromagnetism- Hysteresis

Hysteresis loop
Uniform distribution
From Faraday's law
Where A is the cross section area
Electromagnetism- Hysteresis Loss

Field energy
Input power :
Input energy from t1 to t2
where Vcore is the volume of
the core

• One cycle energy loss
where is the closed area of B-H
hysteresis loop
• Hysteresis power loss
where f is the operating frequency and T
is the period

Empirical equation
Summary : Hysteresis loss is proportional to f and
ABH

Eddy current
Along the closed path, apply Faraday's law
where A is the closed area
Changes in B → = BA changes
→induce e.m.f along the closed path
→produce circulating circuit (eddy current) in the core
Eddy current loss
where R is the equivalent resistance along the
closed path
Electromagnetism- Eddy Current Loss

How to reduce Eddy current loss
– Use high resistively core material
e.g. silicon steel, ferrite core (semiconductor)
– Use laminated core
To decrease the area closed
by closed path
Lamination thickness
0.5~5mm for machines, transformers at line frequency
0.01~0.5mm for high frequency devices

Calculation of eddy current loss
– Finite element analysis
Use software: Ansys®, Maxwell®, Femlab®, etc
– Empirical equation

Core Loss
 Hysterisis loss
• the loss of power in the core due to the hysterisis effect
• Proportional to frequency
 Eddy current loss
• power loss occurs when the flux density changes rapidly in
the core
• Proportional to the square of the frequency
loss
current
eddy
P
loss
hysteresis
P
where
P
P
P
e
h
e
h
c




Electromagnetism- Core Loss

Electromagnetism- Core Loss

Electromagnetic
Induction
 Faraday has made the great
discovery of electromagnet
induction, namely a method of
obtaining an electric current with
the aid of magnetic flux.
 When a conductor cuts or is cut
by a magnetic flux, an e.m.f is
generated in the conductor.
S
A B G
G
S N
C
Electromagnetism

Direction of e.m.f
 Fleming’s right-hand rule
 Lenz’s law
• The direction of an induced
e.m.f is always such that it
tends to set up a current
opposing the motion or the
change of flux responsible for
inducing that e.m.f
Thumb
Motion of conductor
First finger
Flux
Second finger
e.m.f
Electromagnetism

If a conductor cuts or is cut
by a flux of dΦ webers in dt
seconds, e.m.f generated in
conductor
The average e.m.f induced
in one turn is
e.m.f induced in a coil:
S N
C
X
Motion
Electromagnetism

The emf induced in electric circuit
Equating expressions of e.m.f induced in magnetic circuit and
electric circuit:
L is the self-inductance in Henry, or simply the inductance.
For and
dt
d
N
dt
di
L




dt
di
L
e 

current
of
change
linkages
flux
of
change
di
d
N
L 


A
l
S
r
0



S
F


Electromagnetism

Mutual Inductances
S
A B G


Self-inductances of A and B are
S
N
N
I
N
I
N
L A
A
A
A
A
A
A
A
A
2
2





S
N
I
N
L B
B
B
B
B
2



Electromagnetism- Mutual Inductances

B
B
B
A
A
A N
I
N
I
S




S
N
N
M
N
I
N
N
I
N
M
B
A
A
A
A
B
A
A
A
B





2
2
2
2
M
S
N
N
L
L B
A
B
A 

Mutual Inductance:
B
AL
L
M 

Mutual Inductance:
B
AL
L
M 
When there is flux leakage occurs
where k = is coupling coefficient = 0 – 1
k = 1 when the magnetic leakage is zero
B
AL
L
k
M 

Example 8
A ferromagnetic ring of cross-sectional 800mm2 and of
mean radius 170mm has two windings connected in
series, one of 500 turns and one of 700 turns. If the
relative permeability is 1200, calculate the self-
inductance of each coil and the mutual inductance of
each assuming that there is no flux leakage.
( 0.283H, 0.552H, 0.395H)

Energy Stored in the Magnetic Field
 Consider a current increasing at uniform
rate in a coil having a constant inductance
L henrys.
l
i
N
A
Cross-sectional
area
Electromagnetism

 If the current increases by di amperes in
dt seconds, the induced e.m.f
 And if i is the value of the current at that
instant, energy absorbed by the magnetic
field during time dt seconds
dt
di
L
e 

joules
di
Li
dt
dt
di
iL .
.
. 
Electromagnetism

 Hence total energy absorbed by the
magnetic field when the current increases
from 0 to I amperes is
 
joule
LI
E
i
L
di
i
L
E
I
I
2
2
1
0
2
0
2
1
.



 
Electromagnetism

 Since inductance
 Hence
Henry
l
N
A
L
2


l
A
H
I
l
N
A
E
2
2
1
2
2
2
1










?
Electromagnetism

Magnetism.pptx

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