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
Dr. Mohd Junaidi Abdul Aziz
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
Dr. Mohd Junaidi Abdul Aziz
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
Dr. Mohd Junaidi Abdul Aziz
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
Dr. Mohd Junaidi Abdul Aziz
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
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
Dr. Mohd Junaidi Abdul Aziz
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
Dr. Mohd Junaidi Abdul Aziz
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
Dr. Mohd Junaidi Abdul Aziz
Right Hand Rule Thumb indicates
direction of current flow
Finger curl indicates the direction of field
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
Wire Coil Notice that a coil
of wire will produce a perpendicular field
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
Magnetic Field: Coil A series of coils produces a field
similar to a bar magnet – but weaker!
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
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
Dr. Mohd Junaidi Abdul Aziz
Flux Density
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
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
Dr. Mohd Junaidi Abdul Aziz
Reluctance: “resistance” to flow of magnetic flux
@
Associated with “magnetic circuit” – flux equivalent to current
What’s equivalent of voltage?
Electromagnetism- Reluctance
Dr. Mohd Junaidi Abdul Aziz
A
lS
r0
Magnetomotive Force Coil generates magnetic
field in ferrous toroidal Driving force F needed to
overcome toroidal reluctance
Magnetic equivalent of ohms law
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
Circuit Analogy
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
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
Dr. Mohd Junaidi Abdul Aziz
• 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
Dr. Mohd Junaidi Abdul Aziz
B(T)
H(A/m)
Magnetization curve (B-H characteristic)
Saturation
HB r0
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
rr
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
Magnetic Field Intensity and Ampère’s LawHB
AmWb104 70
0 r
Ampère’s Law:
idlH
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
Flux Linkages and Faraday’s Law
AB dA
N
Faraday’s law of magnetic induction:
dt
de
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
Ampere’s Law
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
Magnetic Field Around a Long Straight Wire
r
IHB
2
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
• Ampere’s Law
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
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
Dr. Mohd Junaidi Abdul Aziz
Lenz’s Law Voltages Induced in Field-Cutting
Conductors
Blue
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
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
Dr. Mohd Junaidi Abdul Aziz
• Advantage of the Magnetic-Circuit Approach is that it can be applied to unsymmetrical magnetic cores with multiple coils.
Electromagnetism- magnetic circuit
Dr. Mohd Junaidi Abdul Aziz
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
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
lci
N+F-
S
Equivalent circuit
Analogy between magnetic circuit and electric circuit
E R
i
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
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
Reluctance S Resistance R
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
Series Magnetic Circuit
with air gap lc
i
N lg
+F-
Sc
Sg
g
g
g
c
cc
ggcc
gC
g0
g
g
cc
cc
AB;
AB
densityFlux
lHlHNiSS
Ni
A
lS;
A
lS
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
Series composite magnetic circuit with different material
i
N
iron steel
cobalt
+F-
bS
aS
cS
ccbbaacba
cc
cc
bb
bb
aa
aa
lHlHlHNiSSS
Ni
A
lS
A
lS
A
lS
;;
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
Circuit Analogy
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
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
Dr. Mohd Junaidi Abdul Aziz
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
Dr. Mohd Junaidi Abdul Aziz
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
Dr. Mohd Junaidi Abdul Aziz
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
Movablepart
lg
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
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
Dr. Mohd Junaidi Abdul Aziz
Series Parallel Magnetic Circuit
i
N
2
+F-
1 2
1
3S 2S
2233
3311
321
lHlH2loop
lHlHNI1loop
LawsKirchoff
:
:
:
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
Series Parallel Magnetic Circuit i
N
+F-
1 2
1S
3S
2S
2233
133
213
lHlHNI2loop
lHlHNI1loop
LawsKirchoff
:
:
:
`
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
Series Parallel Magnetic Circuit with Air Gap
iN
+F-
1 2
1S 3S2S
g
22ss33
11ss33
213
lHlHlHNI2loop
lHlHlHNI1loop
LawsKirchoff
:
:
:
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
The relationship between B and H is not linear for the types of iron used in motors and transformers.
Electromagnetism- magnetic core loss
Dr. Mohd Junaidi Abdul Aziz
dBHAl
WW
B
v 0
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
The relationship between B and H is complicated by non-linearity and “hysteresis” Can be used to calculate µ
Electromagnetism- Hysteresis
Dr. Mohd Junaidi Abdul Aziz
Hysterisis
Electromagnetism- Hysteresis
Dr. Mohd Junaidi Abdul Aziz
Hysteresis loopUniform distribution
From Faraday's law
Where A is the cross section area
Electromagnetism- Hysteresis Loss
Dr. Mohd Junaidi Abdul Aziz
Field energyInput power :
Input energy from t1 to t2
where Vcore is the volume of the core
Electromagnetism- Hysteresis Loss
Dr. Mohd Junaidi Abdul Aziz
• 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
Electromagnetism- Hysteresis Loss
Dr. Mohd Junaidi Abdul Aziz
Empirical equation
Summary : Hysteresis loss is proportional to f and ABH
Electromagnetism- Hysteresis Loss
Dr. Mohd Junaidi Abdul Aziz
Eddy currentAlong the closed path, apply Faraday's law
where A is the closed areaChanges 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
Dr. Mohd Junaidi Abdul Aziz
How to reduce Eddy current loss– Use high resistively core materiale.g. silicon steel, ferrite core (semiconductor)– Use laminated coreTo decrease the area closedby closed path
Lamination thickness0.5~5mm for machines, transformers at line frequency0.01~0.5mm for high frequency devices
Electromagnetism- Eddy Current Loss
Dr. Mohd Junaidi Abdul Aziz
Calculation of eddy current loss– Finite element analysis
Use software: Ansys®, Maxwell®, Femlab®, etc
– Empirical equation
Electromagnetism- Eddy Current Loss
Dr. Mohd Junaidi Abdul Aziz
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
losscurrenteddyP
losshysteresisPwhere
PPP
e
h
ehc
Electromagnetism- Core Loss
Dr. Mohd Junaidi Abdul Aziz
Electromagnetism- Core Loss
Dr. Mohd Junaidi Abdul Aziz
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
GS N
C
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
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
ThumbMotion of conductor
First fingerFlux
Second fingere.m.f
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
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
Dr. Mohd Junaidi Abdul Aziz
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
dN
dt
diL
dt
diLe
currentofchange
linkagesfluxofchange
di
dNL
A
lS
r0
S
F
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
Mutual Inductances
S
A B G
Self-inductances of A and B are
S
N
NI
N
I
NL A
AA
AA
A
AAA
22
S
N
I
NL B
B
BBB
2
Electromagnetism- Mutual Inductances
Dr. Mohd Junaidi Abdul Aziz
B
BB
A
AA NINIS
S
NNM
NI
NN
I
NM
BA
AA
ABA
A
AB
22
22
MS
NNLL BA
BA
Mutual Inductance:
BA LLM
Electromagnetism- Mutual Inductances
Dr. Mohd Junaidi Abdul Aziz
Mutual Inductance:
BA LLM When there is flux leakage occurs
where k = is coupling coefficient = 0 – 1
k = 1 when the magnetic leakage is zero
BALLkM
Electromagnetism- Mutual Inductances
Dr. Mohd Junaidi Abdul Aziz
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)
Electromagnetism- Mutual Inductances
Dr. Mohd Junaidi Abdul Aziz
Energy Stored in the Magnetic Field Consider a current increasing at
uniform rate in a coil having a constant inductance L henrys.
li
N
A
Cross-sectionalarea
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
Energy Stored in the Magnetic Field 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
diLe
joulesdiLidtdt
diiL ...
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
Energy Stored in the Magnetic Field Hence total energy absorbed by the
magnetic field when the current increases from 0 to I amperes is
jouleLIE
iLdiiLEI
I
221
02
0 2
1.
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz
Energy Stored in the Magnetic Field Since inductance
Hence
Henryl
NAL
2
lAH
Il
NAE
221
22
21
?
Electromagnetism
Dr. Mohd Junaidi Abdul Aziz