Topic 3

Magnetic Circuits

Dr. Zulkarnain Ahmad Noorden

P06-210, 07-5535451

School of Electrical Engineering

Universiti Teknologi Malaysia
 Course Topics

1 – AC Power (2 weeks)

2 – 3-Phase System (2 weeks)

3 – Magnetic Circuits (2 weeks)

4 – Transformers (2 weeks)

5 – Generation, Transmission & Distribution (4 weeks)

6 – DC Machines (1 week)

7 – AC Machines (1 weeks)

TOTAL – 14 weeks
 Announcement

Test 1 – 15% (Week 7)

Date: 29 November 2021 (Monday)
Venue: Online Webex
Time: 9:00 – 10:00 pm

Topic 1 – AC Power
Topic 3 – Magnetic Circuits
 Topics for today!

§ Basic Concepts of Magnet

§ Magnetic Parameters
§ Magnetic Circuit
§ Self Inductance
§ Mutual Inductance
Basic Concepts
of Magnet
 Applications

Near-Field Communication
Traffic light
(NFC)
 Magnetism and Magnets
What is magnetism?

§ Magnetism is a force field that acts on some

materials but not on other materials.
§ Physical devices that possess this force are
called magnets.
 The magnet we used
today are all
manufactured.

Lodestone is a
natural magnet. Magnet

These magnets are much, much

Made from various alloys stronger than natural lodestone
→ copper, nickel, aluminium,
magnet.
iron, and cobalt.
 Magnetic Field
Magnetic field Two “poles” dictated by
→ the force of magnetism. field direction.

Flux lines
Field forms closed “flux Can use a compass to
lines” around the map out magnetic field.
magnet
 Magnetic Field Characteristics

Opposite poles attract Same poles repel

(aligned magnetic field) (opposing magnetic field)
 Electromagnetism
§ Electricity and magnetism cannot be separated.
§ Wherever an electric current exists, a magnetic field also
exists.
§ Magnetism, also created by an electric current,
operates many devices, such as transformers, motors,
and speakers.
 Magnetic Field for Conductor
§ A magnetic field also forms round a conductor along
which a current is flowing.

Magnetic field
direction

Current direction

§ Field can be described using “right hand rule”.

o Thumb → direction of current flow.
o Finger curl → the direction of field.
 Magnetic Field for Coil

N S

Flux ϕ
I out I in

§ Direction of magnetic flux is based of “right hand rule”.

 Effect of Core

• 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!
 Magnetic
Parameters
 Magnetic Flux ϕ
Lines of magnetic flux that are
Magnetic flux → the total parallel and in the same
number of force lines in the direction, repel one another.
magnetic field.

N S
Never intersect
Symbol: ϕ each other.
Unit: Wb
Flux ϕ
I out I in

They form Always starts from N and end in the S and

closed loops. are then continuous through the body of
the magnet.
 Flux Density B
Area A

Magnetic flux density is defined as

the magnetic flux per unit area of a N S
surface at right angles to the
magnetic field.

Flux ϕ
I out I in
Symbol: B
Unit: Tesla or Wb/m2
 Permeability μ
Permeability → the measure of the degree to
which lines of force of the magnetizing field can Air μo
penetrate the medium.

Symbol: μ
Unit: H/m
Material μ
Express in terms of relative
permeability μr.
Permeability of all non-magnetic
materials including air μo = 4π x 10-
7 (H/m)
 Magnetomotive Force F
Magnetomotive force F can be Symbol: F
produced when current flows in a coil
of one or more turns. Unit: At

Related to number of turns

N and current I.

Driving force F needed to

overcome toroid reluctance.
 Magnetic Field Strength H
Magnetomotive force per unit length
is known as the “magnetizing force”
H.

Symbol: H
Unit: At/m

The longer the magnetic path l the

greater the magnetomotive force F
required to drive the flux.
 Reluctance Ʀ
Reluctance → “Resistance” to flow of
magnetic flux.

Symbol: Ʀ
Unit: At/Wb Associated with “magnetic circuit” –
flux equivalent to current.
Flux ϕ

Flux ϕ

Reluctance Ʀ

Area A
 B-H Curve
B(T)
B = µ0 µ r H

Saturation

H(A/m)

Magnetization curve (B-H characteristic)

Fringing Effect
Summary of Magnetic Parameters
 Electric & Magnetic Parameters
Magnetic parameters Symbol Electric parameters Symbol

Magnetic flux ϕ (Wb) Electric current I

Flux density B (T) Current density J

Magnetic field
H (At/m) Electric field strength E
strength
Magnetomotive force F (At) Electromotive force Emf

Permeability μ (H/m) Permittivity

Ʀ
Reluctance Resistance R
(At/Wb)
Magnetic
Circuits
 Magnetic Circuit
§ Analogy between magnetic circuit and electric circuit.

F i

i
lc
+
N E R
F Â
-

Magnetic circuit with only single core material.

27
Magnetic circuit with a core and an air gap.
 Magnetic circuit with different core materials.
Âa

iron steel F
i
+ Âb
N F
-
cobalt Âc

29
 Example 1
l
c
F

i Âc
+
N lg F
-
Âg

For the magnetic circuit, N = 400 turns. Mean core length

= 50 cm. Air gap length = 1.0 mm. Cross-sectional area (Ac
= Ag) = 15 cm2. Relative permeability of core = 3000 and i
= 1.0 A.
Find (a) Flux density in the air gap, and (b) Inductance of
the coil.

(0.43 T, 258.52 x 10-3 H)

 Example 2

A toroid of 200 turns is wound uniformly over a wooden

ring having a mean circumference of 600 mm and a uniform
cross-sectional area of 500 mm2. If the current through the
toroid is 4 A, calculate; (a) the magnetic field strength, (b)
the flux density, and (c) the total flux.

(1333.3 At/m, 1676x10-6 T, 0.8375 uWb)

31
 Example 3
l
c

N lg

Calculate the magnetomotive force required to

produce a flux of 0.015 Wb across air gap 2.5 mm
long, having an effective area of 200 cm2.

(1492 At)
 Example 4
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.

33
 Example 5

34
 (b) F = f = 0.02 ´ 50399 = 1008 At
F 1008
I= = = 2.02 A
N 500
35
Hysteresis Curve
Hysteresis curve
Defining the normal magnetization curve
Normal magnetization curve for
three ferromagnetic materials
Self Inductance
 Coil Inductance
§ A coil wound on a magnetic core is frequently used in
electric circuits.
§ This coil may be represented by an ideal circuit element,
called inductor, which is defined as the flux linkage of
the coil per ampere of its current.

Coil wound Inductor

 Self Inductance
Faraday has made the great discovery of electromagnet
induction, namely a method of obtaining an electric current
with the aid of magnetic flux.

S
S N G
A B G

When a conductor cuts or is cut by a magnetic flux, an

e.m.f. is generated in the conductor.
 X
If a conductor cuts or is cut by a flux
of dϕ (Webers) in dt (seconds), e.m.f
generated in conductor S N
Motion
df
e= C
dt
The average e.m.f induced in one turn is

F
volt
t
df
e.m.f induced in a coil: e = -N
dt
The e.m.f induced in electric circuit

di
e = -L
dt
Equating expressions of e.m.f induced in magnetic circuit
and electric circuit:

di df df change of flux linkages

-L =N L=N =
dt dt di change of current
L is the self-inductance, or simply the inductance (H).

l µ AN2
Φ=F/R R= L= Henry
µ0 µ r A l
 Energy in Magnetic Field

Energy Stored in the Magnetic Field

§ Consider a current increasing at uniform rate in a
coil having a constant inductance L henrys.

i
l Cross-sectional
N area

A
 Energy in Magnetic Field

Energy Stored in the Magnetic Field

§ If the current increases by di amperes in dt
seconds, the induced e.m.f
di
e = -L
dt
§ And if i is the value of the current at that
instant, energy absorbed by the magnetic
field during time dt seconds

di
iL. .dt = Li.di joules
dt
 Energy in Magnetic Field

Energy Stored in the Magnetic Field

§ Hence total energy absorbed by the magnetic
field when the current increases from 0 to I
amperes is

[ ]
I
1 2 I
E = L ò i. di = L ´ i 0
0
2
E= 1
2 LI 2 joule
 Energy in Magnetic Field

Energy Stored in the Magnetic Field

§ Since inductance

µ AN2
L= Henry
l
§ Hence
éµ AN2 ù 2
E= 1
ê úI
2
ë l û ?
= 1
2 µ H 2 Al
Mutual Inductance
 Mutual Inductance

fA fB
S
A B G

N AF A N F A N
2 2 N B F B N B2
LA = = A
= A LB = =
IA I ANA S IB S
 Same material, same reluctant:
I AN A IB NB
S= =
FA FB

N BF A N A N BF A
M = =
IA IANA
NANB
M =
S
2 2
N N
L A LB = A
2
=M
B 2

S
Mutual inductance: M = L A LB
 Example 6
In the magnetic circuit, the relative permeability of the
ferromagnetic materials is 1200. The material length is 50
cm and its cross-sectional area is 4 cm2. Determine the
material flux, flux density and the magnetic field intensity.

N = 500 turns
I = 10 A

F = 5000 At, R = 0.83 x 106 At/Wb, ϕ = 6 x 10-3 Wb,

B = 15.1 Tesla, H = 10 x 103 At/m
 Example 7
In the magnetic circuit, the relative permeability of the
ferromagnetic materials is 900. The material cross-sectional
area is 4 cm2. Determine the material flux, flux density and
the magnetic field intensity.

N = 300 turns
I=8A 20 cm

20 cm

F = 2400 At, R = 1.77 x 106 At/Wb, ϕ = 1.36 x 10-3 Wb,

B = 3.4 Tesla, H = 3 x 103 At/m