Magnetic circuits and magnetic materials

EE8301 – ELECTRICAL MACHINES - I
Unit – I – MAGNETIC CIRCUITS AND MAGNETIC
MATERIALS
By
Mr. D. Karthik Prabhu,
Assistant Professor,
Department of Electrical and Electronics Engineering.
Email: karthikprabhu@ritrjpm.ac.in
Cell: 9750588231
1

UNIT - I
MAGNETIC CIRCUITS AND
MAGNETIC MATERIALS

Types of Electrical Machines
• An electrical machine is one which converts
mechanical energy into electrical energy or vice
versa, and changes AC voltage from one level to
another level.
• Electrical machines can be classified into three
types.
1. DC Machines
2. AC Machines
3. Special Machines

1. DC Machines:
DC Machines can be classified into two
types.
i. DC Generator
ii. DC motor

2. AC Machines
These are further classified as
i. Transformers
ii. Synchronous machines
iii. Asynchronous machines (induction machines)

i. Transformers
It is a static machine that converts AC
voltage from one level to another level higher or
lower, or even to the same level without
changing the frequency. It works based on the
principle of mutual induction; so its power
remains approximately constant, where as
frequency also remains the same.

(ii) Asynchronous or Induction Machines:
There are two types of induction motor
1. Three phase induction motor
2. Single phase induction motor
It converts AC electrical energy into
mechanical energy.

(iii) Synchronous Machines:
A synchronous machine is a doubly-excited
machine. There are two types of synchronous
machines.
1. Synchronous generator
2. Synchronous motor (Constant speed motor)

Magnetic Circuits
• Magnet:
It is a piece of solid body which possesses a
property of attracting iron pieces and pieces of
some other metals. This is called a natural magnet.
While as per the discovery of scientist
Oersted we can have an electromagnet. Scientist
Oersted stated that any current carrying conductor
is always surrounded by a magnetic field. This
property of such current is called magnetic effect
of an electric current.

Laws of Magnetism
• Law 1: It states that “Like magnetic poles repel and unlike
poles attract each other”.
• Law 2: Coulomb’s Law:
The force exerted by one pole on the other pole is,
a) Directly proportional to the product of the pole
strengths
b) Inversely proportional to the square of the distance
between them
c) Nature of medium surrounding the poles.

Magnetic Field
• The region around a magnet within which the
influence of the magnet can be experienced is
called magnetic field.
1. Magnetic lines of force
2. Direction of magnetic field
3. Properties of line of force

Definition of Magnetic Quantities
• Magnetic flux:
The magnetic lines of force produced by a
magnet are called magnetic flux. It is denoted by
‘φ’ and its unit is weber.
1 weber = 108 lines of force

• Magnetic flux density:
Magnetic flux density is the flux per unit area at right
angles to the flux. It is denoted by ‘B’ and its unit is
weber/m2 .
wb/m2 (or) Tesla
where φ is the magnetic flux in weber and A is the
area of cross section in m2

• Magneto-motive force (MMF):
MMF is the cause for producing flux in a
magnetic circuit. The amount of flux set up in the
core depends upon current (I) and number of turns
(N). The product NI is called magneto-motive force
(MMF) and determines the amount of flux set up in
magnetic circuit.
MMF = NI Ampere Turns (AT)

• Reluctance:
The opposition that the magnetic circuit
offers to flux is called reluctance. It is defined as
the ratio of MMF to flux. It is denoted by ‘S’ and its
unit is ampere turns/weber.
Reluctance in a magnetic circuit corresponds
to resistance in an electric circuit.
Reluctance = MMF/flux (AT/wb)

• Permeance:
It is reciprocal of reluctance. It is defined as
the property of the magnetic circuit due to which
it allows flow of the magnetic flux through it.
Permeance = 1/Reluctance
Permeance of a magnetic circuit corresponds
to conductance in an electric circuit.

• Magnetic field intensity:
It is defined as the MMF per unit length of
the magnetic flux path. It is denoted by ‘H’ and its
unit is AT/m
H = NI/L (AT/m)

• Permeability:
Permeability of a material means its conductivity
for magnetic flux. The greater the permeability of a
material, the greater is its conductivity for magnetic flux
and vice-versa. The flux density (B) is proportional to the
magnetizing force (H) which produces it.
B α H
B = µ H
µ = B/H
Where µ is the constant of proportionality and is called
permeability.

• Relative Permeability:
Relative permeability of a material is equal to
the ratio of flux density produced in that material
to the flux density produced in air by the same
magnetizing force.
Where µ = absolute permeability of the material
µo = absolute permeability of air or vacuum
µr = relative permeability of the material

Magnetic Circuits
• The closed path followed by magnetic flux is
called a magnetic circuit.
• A magnetic circuit usually consists of materials
having high permeability such as iron, soft steel.

Classification of magnetic Circuits
• Magnetic Circuits can be classified into
1. Simple magnetic circuit
2. Composite magnetic circuit
3. Parallel magnetic circuit

Analysis of Simple Magnetic Circuit
• Consider a circular solenoid or a toroidal iron ring as
shown. A winding of ‘N’ turns is provided in the ring.
• Let I be the current flowing in the winding, ‘a’ is the
area of cross section in m2 and ‘L’ is the mean length in
metre.

Leakage flux
• The flux does not follow the desired path in a
magnetic circuit is called a leakage flux.
• In practical magnetic circuits, a large part of flux
is through a magnetic material and the
remainder part of flux path is through air. The
flux in the air gap is known as useful flux.

Magnetic Circuit Electric Circuit
The closed path for magnetic flux is
called a magnetic circuit
The closed path for electric current is
called an electric circuit
Flux = mmf/reluctance Current = emf/resistance
Reluctance = L/µoµra Resistance = ρl/a
Permeance = 1/Reluctance Conductance = 1/Resistance
Flux density B = φ/a Current density J = I/a
Magnetising force H = NI/L Electric field Intensity E = V/d
The reluctance varies with flux
density in the material
The resistance remains
practically constant, even
though it varies slightly with
temperature

Magnetic Circuit Electric Circuit
Magnetic flux does not
actually flow in a
magnetic circuit
The electric current
actually flows in a
electric circuit
In a magnetic circuit,
energy is required to
create the flux and not
to maintain it.
In an electric circuit,
energy is required so
long as the current has
to flow through it.
There is no magnetic
insulator. Even in air,
flux can be set up.
There are many electric
insulators available.

Electromagnetic Induction
• In 1824, Oersted discovered that a magnetic field
exists around a current carrying conductor. That is,
magnetism can be created by means of an electric
current.
• Later in 1831, Michale Faraday, discovered that a
magnetic field can create an electric current in a
conductor. He demonstrated that when the magnetic
flux linking a conductor changes, an e.m.f is induced
in the conductor. This phenomenon is known as
electromagnetic induction.
• Most of the electrical devices are based on this
principle

Law of electromagnetic induction
• Faraday’s Law:
• Whenever the magnetic flux linking a conductor
changes an e.m.f. is always induced in it. The
magnitude of induced e.m.f. is proportional to the
rate of change of flux linkages.
• e = 𝑁−
𝑑𝑡
𝑑ϕ
Where, e = induced e.m.f in volts
N = number of turns in the coil
dφ/dt = rate of change of flux

Law of electromagnetic induction
• Lenz’s Law:
• The law states that any induced e.m.f. will
circulate in such a direction so as to oppose
the cause producing it.
• e = -N (dφ/dt)

Electromagnetic Induction
• When the magnetic flux linking a conductor
changes, an e.m.f. is induced in the conductor.
If the conductor forms a closed loop or circuit,
a current will flow in it. This phenomenon is
called electromagnetic induction.

Fleming’s left hand rule
• Stretch out the fore finger, middle finger and thumb of
the left hand so that they are at right angles to one
another. If the fore finger points in the direction of
magnetic field, the middle finger points towards the
direction of current, then the thumb will point in the
direction of motion of the conductor.

Fleming’s right hand rule
• The direction of the induced emf can be found out by
applying Fleming’s right hand rule. Hold the thumb, the
fore finger and the middle finger of the right hand at
right angles to one another. If the fore finger points in
the direction of magnetic field, thumb in the direction of
motion of the conductor, then the middle finger will
point in the direction of induced emf.

Induced EMF
• When the magnetic flux linking a conductor
changes, an emf is induced in it. This change in
flux linkage can be brought by two ways
1. The conductor is moved in a stationary magnetic
field in such a way that the flux linking it
changes. The emf induced in this way is called
dynamically induced emf. It is so called because
emf is induced in the conductor which is in
motion. Eg. DC generator, AC generator.

Induced EMF
2. The conductor is stationary and the magnetic
field is moving or changing. This kind of induced
emf is known as statically induced emf. It is so
called because the emf is induced in the
stationary conductor. Eg. Transformer

Dynamically Induced EMF
• Consider a stationary magnetic field of flux
density B wb/m2 with direction as shown.

• A circular conductor is placed in this field. Let ‘L’
be the effective length of the conductor in meters.
The conductor is moved in the direction at right
angles to the field. In a time ‘dt’ seconds, the
distance moved is ‘dx’ metres.

• By faraday’s law of electromagnetic induction, emf
induced in the conductor is given by
e = N (dφ/dt)
• If the conductor has one turn N=1
• e = (dφ/dt) = (B L dx/dt) = B Lv
• V = dx/dt = Linear velocity
• If the conductor moves at angle θ to the magnetic
field, then the velocity at which the conductor
moves across the field is vsin θ
• e = B L v sin θ
• The direction of induced emf can be determined by
Fleming’s right hand rule.

Statically Induced EMF
• In this case, the conductor is held stationary and
the magnetic field is moving or changing. The emf
induced in the conductor is called statically
induced emf. It can be further subdivided into
1. Self induced emf
2. Mutually induced emf

Self Induced emf
• Self induced emf is the emf induced in a
circuit due to change of its own flux linking
with it.

Self Inductance (L)
• The property of a coil that opposes any change in
the amount of current flowing through it is called
its self-inductance.
• The self-inductance of a coil depends upon
1. Shape and number of turns
2. Relative permeability of the material
surrounding the coil
3. The speed with which the magnetic field
changes.

Co-Efficient of Coupling (K) or Magnetic Coupling

Force on a current carrying conductor in a magnetic field

Magnitude of force experienced by the conductor
• The magnitude of the force experienced by the
conductor depends on the following factors
1. Flux density (B) of the magnetic field in which
the conductor is placed measured in Wb/m2 or
tesla.
2. Magnitude of the current I passing through the
conductor in Amperes.
3. Active length ‘L’ of the conductor in meters.

Magnitude of force experienced by the conductor
• If the conductor is at right angles to the magnetic
field, then force F is given by,
• F = B I L Newtons
• But if the conductor is not exactly at right angles,
but inclined to axis of magnetic field, then force F
is given by,
• F = B I L sinθ Newtons

B-H Curve or Magnetization Curve

B-H Curve and Permeability
• B/H is nothing but slope of B-H curve
• Slope of B-H curve at various points decide the value of relative
permeability at that point

Practical use of B-H Curve
• While designing the magnetic circuits,
magnetization curves are useful to design the
values of B corresponding to H. From this,
proper material with required relative
permeability can be selected.
• The various materials like iron, steel are
generally represented by B-H curves and µr-H
curves

Classification of Magnetic Materials
• The magnetic materials are classified based on
the presence of magnetic dipole moments in the
materials.
• Ferromagnetic material
• Ferrimagnetic material

Ferro Magnetic Materials
• The materials in which the atoms have large
magnetic dipole moments which are lined up in
parallel fashion are called ferromagnetic material
• Most of electrical components and devices use
ferromagnetic material. Iron, nickel, cobalt and
various alloys are example for ferromagnetic
material
• The chrome steel, alnicos certain copper-nickel
alloys are hard ferromagnetic materials.
• The non-linear B-H relationship, high
permeability, saturation, hysteresis are the
important properties of ferromagnetic materials.

Ferri Magnetic Materials
• The materials in which the magnetic dipole
moments are lined up in antiparallel fashion are
called ferrimagnetic materials.
• Ferrites are the special ferrimagnetic material
having very low electrical conductivity and used
as a.c. inductors and core of the transformers.
• The nickel ferrite, nickel-zinc ferrite and various
mixed oxides of iron are the examples of ferrites.

Classification of magnetic materials
based on the value of coercive force
• Soft magnetic material
• Hard magnetic material

Soft Magnetic Materials
• These Materials are easy to magnetise and easy
to demagnetise. Hence to obtain quick response,
such materials are used in the devices like
transformers where they are subjected to
alternating electric fields.
• To minimize the hysteresis loss in a cycle, the area
of hysteresis loop should be as small as possible.
• The materials with very small hysteresis loop are
classified as soft magnetic materials.

• The different types of soft magnetic materials are,
1. Alloys based on iron
2. Nickel-iron alloys
3. Ferrites
• The coercivity and retentivity of soft magnetic
materials are low hence are not used to
manufacture permanent magnets.

• Characteristics :
1. High saturation magnetisation
2. Low coercivity
3. High permeability
4. Low core loss
5. High resistivity
6. High susceptibility

Applications:
• These materials are used in many electrical
machines such as transformers, generators,
motors etc. and also used in inductor cores
and recording heads.

Hard Magnetic Materials
• These are difficult to magnetise and demagnetise.
• These materials have high value of coercive force,
and high retentivity hence are used as excellent
permanent magnets.
• The hysteresis loop area of hard magnetic
materials is large.

Applications:
• Measuring instruments – tranducers
• Motors
• Television tubes
• Due to high retentivity are used in recording
media.

Characteristics:
• High coercive force
• Appreciable residual magnetism
• High curie temperature
• Low susceptibility
• High saturation magnetisation
• Maximum BH product

Materials:
• Alloys of iron
• Nickel
• cobalt

Magnetic Loss (core loss or iron loss)
• Hysteresis loss
• Eddy current loss
• The magnetic loss occurs in core hence they are
known as core losses.
• Since core material is generally iron or its alloy,
this loss is also referred as iron loss.
• The magnetic loss will result in following effects
1. It reduces the efficiency of the electrical
equipment
2. It increases the temperature because of heating
of the core.

Hysteresis loss
• When a magnetic material is subjected to
repeated cycles of magnetisation and
demanetisation, it results into disturbance in the
alignment of the various domain.
• Now energy get stored when magnetic field is
established and energy is returned when field
collapses. But due to hysteresis, all the energy is
never returned though field completely collapses.
This loss of energy appears as heat in the
magnetic material. This is called as hysteresis loss.

Hysteresis loss
Hysteresis loss depends on the following factors:
• Loss is directly proportional to the area under the
hysteresis curve i.e. area of the hysteresis loop
• It is directly proportional to frequency i.e. number
of cycles magnetisation per second
• It is directly proportional to volume of the
material. It can be shown that quantitatively the
hysteresis loss in joules per unit volume of the
material in one cycle is equal to the area of the
hysteresis loop.

Hysteresis loss
Hysteresis loss = Kh (Bm)1.6 f × volume watts
• Where Kh = characteristics constant of the
material
• Bm = maximum flux density
• F= frequency in cycles per second

Hysteresis loss
• Hysteresis loss can be reduced by selecting
good quality magnetic material.
• The area of hysteresis loop should be narrow.
Silicon steel is employed for the core material
so that hysteresis loss can be minimized.

Eddy current loss
• Consider a coil wound on a core. If this coil carries
an alternating current, according to the faraday’s
law of electromagnetic induction, e.m.f gets
induced in the core.
• Now if core is solid, then such induced e.m.f.
circulates currents through the core. Such current
in the core which are due to induced e.m.f. in the
core are called as eddy currents.
• Due to such current there is power loss (I2R) in the
core. Such loss is called as eddy current loss

Eddy current loss
• Eddy current loss depends on the various
factors which are
1. Nature of the material
2. Maximum flux density
3. Thickness of laminations used to construct to
core
4. Volume of magnetic material

Eddy current loss
• It has been found that loss can be minimized by
selecting high resistivity magnetic material like
silicon.
• Most popular method used to reduce eddy
current loss is to use laminated construction to
construct the core. Core is constructed by
stacking thin pieces known as laminations.
• The laminations are insulated from each other by
thin layers of insulating material like varnish,
paper, mica. This restricts the path of eddy
current, to respective laminations only

Eddy current loss
Eddy current loss = Ke (B m)2 f2 t2 × Volume watts
• Where Ke = a characteristics constant of material
• Bm= maximum flux density
• F = frequency
• t = thickness of the lamination

Deltamax Cores
• A core made from an alloy consisting of 50% iron
and 50% nickel has almost square B-H loop are
known as deltamax cores.

Deltamax Cores
• A coil wound on a deltamax core can be used as a
switch.
• When the flux density is less than residual flux
density (B<Br) the magnetic intensity (and hence
the current) is quite low.
• As the flux density exceeds the residual flux
density (B>Br), the magnetic intensity (hence
current) increases sharply.
• This property can be exploited to make a coil
wound on a deltamax core behave as a switch
(very low current when the core is unsaturated
and very high current when the core is saturated).

Stacking factor:
Stacking factor : Net cross sectional area occupied by magnetic material
Gross cross sectional area
As gross cross sectional area is higher, the stacking factor is always less than
unity.

Permanent Magnet
• Permanent magnet materials are characterized by
large value of remanent magnetization and
coercivity. These materials produce significant
magnetic flux even in magnetic circuits with air
gaps.
• Permanent magnet find application in loud
speakers, AC and DC motors, Micro phones and
analog electric meters, meters, transducers, data
storage devices.

Permanent Magnet
• The most commonly available permanent
magnetic materials are
1. Alnico
2. Ceramics (ferrites)
3. Rare –earth materials
(i) Samarium-Cobalt
(ii) Neodymium-iron boron

Alnico Magnets
• These are used in motors up to 200 kW.
• For very high temperature applications Alnico
magnets can be used.
• Alnico 5 is a widely used alloy of iron, nickel,
aluminium and cobalt.
• It has relatively large residual flux density.
• Alnico 8 has a lower residual flux density and a
higher coercivity than Alnico 5.
• Disadvantages of the Alnico materials are their
low coercivity and their mechanical brittleness.

Ceramics (Ferrites)
• Ceramic magnets are most economical in
fractional kW motors.
• Ceramic permanent magnet materials also
known as ferrite magnets are made from iron-
oxide and barium-or strontium-carbonate
powders and have lower residual flux densities
than Alnico materials but significantly higher
coercivities.
• Ceramic magnets have good mechanical
characteristics and are inexpensive to
manufacture.

Rare earth materials
• The rare earth materials are very costly and
suitable for very small motors. For high
temperature applications rare-earth cobalt
magnets can be used.
• Samarium-cobalt has a high residual flux density
such as is found with the Alnico materials, while at
the same time having a much higher coercivity and
maximum energy product.
• The latest of the rare-earth magnetic materials is
the neodymium-iron-boron. It has larger residual
flux density, coercivity and maximum energy
product than samarium cobalt

Magnetization curves for common
permanent magnet materials

Magnetic circuit including both a
permanent magnet and an exciting current

Demagnetization curve with recoil line

Magnetic circuits and magnetic materials

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