CHAPTER ONE

MAGNETICS
1.1 Magnetic Field Properties & Magnetic Materials
• Magnetics- is a field of study that deals with magnetism.
• Magnetism –is the property of a material to be attracted to or repelled by a
magnetic field. These effects arise mainly from motion of electrons.
Magnetism is also the ability of a material to attract/repel magnetic
substances.
• Magnet can be defined as a material that can attract piece of iron or metal.
Magnet has two poles: north and south. Materials that can be attracted by a
magnet are known as magnetic substances. Magnet has a magnetic field
around the magnet itself.
• Magnetic field is the force around a magnet which can attract/repel any
magnetic material around it.
• Flux is the line around a magnetic bar which forms magnetic field.

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• Magnetic flux lines have a direction and pole.
• The direction of movement outside of the magnetic field lines is from north
to south.
• Inside the magnetic bar, field lines are directed from south to north. The
strongest magnetic fields are at the magnetic poles.
• Different poles attract each other and same magnetic poles will repel each
other.
• Flux lines form a complete loop and never intersect with each other. Flux
will try to form a loop as small as possible.

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Properties of Magnet
1. Magnets attract objects of iron, cobalt and nickel.
2. The force of attraction of a magnet is greater at its poles than in the middle.
3. Like poles of two magnets repel each other.
4. Opposite poles of two magnets attracts each other.
5. If a bar magnet is suspended by a thread and if it is free to rotate, its South
Pole will move towards the North Pole of the earth and vice versa.
• There are two types of magnet known as pure magnet and manufactured
magnet.
i) Pure Magnet
• Pure magnet is a magnet stone. The stone originally has a natural magnetic
behavior. Basically the stone is found in the form of iron ore.

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ii) Manufactured Magnet
There are two types of manufactured magnet;
a) Permanent Magnet
The ability of the magnet keeps its magnetism. Basically permanent magnet is
used in small devices such as speakers, meter and compass. Permanent magnet
can be obtained naturally or by magnetic induction and placing a magnet into a
coil then supplied with a high electric current.

b) Temporary magnet
An electric current can be used for making temporary magnets known as
electromagnet. It has magnetic properties when subjected to magnetic force and
it will be lost when power is removed.
Typically the temporary magnet is used in electrical devices such as relays and
small devices such as electrical bell.

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 Characteristics magnetic field lines :
1. Magnetic field lines always go from the north pole to the south pole
(outside a magnet).

2. Magnetic field lines are closed loops and never cross or intersect.

3. Where the magnetic field lines are closer the magnetic field is stronger.
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Magnetic materials:
diamagnetic material: weakly magnetized
Those materials which when placed in a magnetic field become weakly
magnetized in a direction opposite to that of the applied field, are called as
diamagnetic materials. Diamagnetic materials are those which are repelled
by magnets and when placed in magnetic field.
Diamagnetic materials do not exhibit permanent magnetism, Ex.: hydrogen,
copper, gold, silicon, germanium, graphite, bismuth, helium, sulfur.

paramagnetic material, weakly magnetized

it refers to a property of materials that are weakly attracted to a magnetic
field When exposed to an external magnetic field. Once the applied field
is removed, the material loses its magnetism.
Ex.: Aluminum, Platinum, air, potassium, tungsten, liquid oxygen.

ferromagnetic material. Strongly magnetized

In these materials strong interactions between atomic magnetic moments
cause them to line up parallel to each other in regions called magnetic
domains.
Ex: cobalt, nickel, iron are usually used to fabricate permanent magnets
due to the ability to retain their magnetism properties for long time. 7
 Magnetic Quantity Characteristics
There are many magnetic quantities in the System International (SI) unit.
magnetomotive force, magnetic field strength, magnetic flux, flux
density, permeability and reluctance.

 Magnetomotive Force (F )
• Magnetomotive force is a cause for the existence of magnetic flux in a
magnetic circuit. The “driving force” that causes a magnetic field
F = NI Ampere-turns, (A-t)
N is number of turns, I is current passing through the coil
 Magnetic Field Strength (Intensity), H
• Magnetic field strength or magnetizing force is defined as magnetomotive
force per meter length of measurement being ampere-turn per meter.
– Symbol, H
H = F/l = NI/l (A-t/m)
Where F is magnetomotive force , N - number of turns ,I – current,
l - average length of magnetic circuit (path length followed by field) 8
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 Magnetic Flux and Flux Density

• Magnetic flux is the amount of magnetic field produced by a magnetic
source. The symbol for magnetic flux is phi (Φ) and its SI unit is the weber,
Wb.
• Magnetic flux density is the amount of flux passing through a defined area
that is perpendicular to the direction of flux. The symbol for magnetic flux
density is B.

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 Permeability
• Permeability is a measure of the ability of a material to allow magnetic field to
exist in it. Absolute permeability, μ of a material is the ratio of the flux density
to magnetic field strength.

• If the magnetic fields exist in vacuum, the ratio of flux density to magnetic field
strength is a constant called permeability of free space. For air or any other
nonmagnetic medium, the ratio of magnetic flux density to magnetic field
strength is constant,

• The permeability of free space, μ0 = 4πx10-7 Wb/A-t-m or H/m

• μr =1, in the air or any non-magnetic material. μr is relative permeability
• Example A flux density of 1.2 T is produced in a piece of cast steel by a
magnetizing force of 1250 AT/m. Find the relative permeability of the steel
under these conditions. solution

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 Reluctance
– The measure of “opposition” the magnetic circuit offers to the flux
– The analog of Resistance in an electrical circuit
– Symbol, R
– R = F/Φ
– Units, (A-t/Wb) or

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 1.2 Magnetic Circuits
Magnetic circuit may be defined as the route or path which is followed by magnetic
flux. Consider a solenoid or a toroidal iron ring having a magnetic path of l, area of
cross section and a coil of N turns carrying I amperes wound anywhere on it as
shown in fig below.

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• Reluctances in a magnetic circuit obey the same rules as resistances in an

electric circuit. 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:

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Series magnetic circuit Example 1
• Figure (a) below shows a simplified rotor and stator for a dc motor. The
mean path length of the stator is 50 cm, and its cross-sectional area is 12
cm2. The mean path length of the rotor is 5 cm, and its cross-sectional area
may be assumed to be 12 cm2. Each air gap between the rotor and the
stator is 0.05 cm wide, and the cross-sectional area of each air gap is 14
cm2. The iron of the core has a relative permeability of 2000, and there are
200 turns of wire on the core. If the current in the wire is adjusted to be 1
A, what will the resulting flux density in the air gaps be?

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• Solution
• To determine the flux density in the air gap, it is necessary to first calculate
the magnetomotive force applied to the core and the total reluctance of the
flux path. With this information, the total flux in the core can be found.
Finally, knowing the cross-sectional area of the air gaps enables the flux
density to be calculated.

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• Example. A ferromagnetic core is shown in Figure a. Three sides of this core
are of uniform width. while the fourth side is somewhat thinner. The depth of
the core (into the page) is 10 cm. and the other dimensions are shown in the
figure. There is a 200-turn coil wrapped around the left side of the core.
Assuming relative permeability of 2500. how much flux will be produced
by a 1-A input current?
Solution
• Three sides of the core have the same cross-sectional areas. while the fourth
side has a different area. Thus. the core can be divided into two regions: (1)
the single thinner side and (2) the other three sides taken together. The
magnetic circuit corresponding to this core is shown in Figure b.

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 Fringing and Leakage Flux
• In a series magnetic circuit containing an air gap, there is a tendency for the air gap
flux to spread out (i.e., to create a bulge) as shown in Figure below. This spreading
effect is called fringing and it reduces the net flux density in the air gap.

Fig fringing flux

• Leakage flux is that flux in a magnetic circuit which is not useful or effective.
Since a large amount of leakage flux requires a greater magnetomotive force,
the designer of electromagnetic devices must minimize this ineffective flux.

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 1.3 Saturation and Iron Losses
• Saturation is the effect of little change in flux density when the field
intensity increases.
• Hysteresis refers to a situation where the magnetic flux lags the increases
or decreases in magnetizing force.
• Hysteresis loss is energy wasted in the form of heat when alternating
current reverses rapidly and molecular dipoles lag the magnetizing force
• Eddy current, It is caused when a moving (or changing) magnetic field
intersects a conductor, or vice-versa.
• The relative motion causes a circulating flow of electrons, or current,
within the conductor.
• The flowing of eddy current will dissipate energy and the lost energy goes
into heating the iron core. This loss is the eddy current loss.
• To reduce the eddy current losses, the resistivity of the material is increased by
adding silicon in the metal or ferromagnetic materials.
• Another effective way to achieve low eddy current loss is by using laminations of
electrical metal sheets. These metal sheets are coated with electric insulation which
break the eddy currents path.
• Iron loss = hysteresis loss + eddy current loss
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• Both hysteresis and eddy current losses cause heating in the core material,
and both losses must be considered in the design of any machine or
transformer. Since both losses occur within the metal of the core, they are
usually lumped together and called core losses or iron losses.
• The atoms of iron and similar metals (cobalt, nickel, and some of their
alloys) tend to have their magnetic fields closely aligned with each other.
Within the metal, there are many small regions called domains, in each
domain, all the atoms are aligned with their magnetic fields pointing in the
same direction, so each domain within the material acts as a small
permanent magnet.
• It is known that magnetic permeability was defined by the equation:

• the permeability of ferromagnetic materials is very high when compared to

permeability of free space.
• The core is initially unmagnetized and the current I = 0. If the current I is
increased to some value above zero, the magnetizing force H will increase
to a value determined by

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 1.4 Production of EMF & EM force-torque
ELECTROMAGNETIC INDUCTION
• When a conductor moves across a magnetic field, an electromagnetic force
(emf) is produced in the conductor. This effect is known as electromagnetic
induction. The effect of electromagnetic induction will cause induced
current. There are two laws of elctromagnetic induction:
• i. Faraday‟s law ii. Lenz‟s Law
• i. Faraday’s law
• Faraday's law 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.

• the voltage induced across the whole coil is given by:

N = number of turns of wire in coil

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• The minus sign in the equations is an expression of Lenz„s slaw. 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 sign is included in Equation above.
• There is one major difficulty involved in using the above equation in practical
problems. That equation assumes that exactly the same flux is present in each
turn of the coil. Unfortunately, the flux leaking out of the core into the
surrounding air prevents this from being true.
• Therefore, the magnitude of the voltage in the ith turn of the coil is always given
by

• If there are N turns in the coil of wire, the total voltage on the coil is

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• The term in parentheses is called the flux linkage of the coil, and Faraday‟s
law can be rewritten in terms of flux linkage as:

The units of flux linkage are weber-turns.

• The change of flux as discussed in the Faraday's laws can be produced in two
different ways: (i) by the motion of the conductor or the coil in a magnetic
field, i.e. the magnetic field is stationary and the moving conductors cut
across it. The emf generated in this way is normally called dynamically
induced emf; (ii) by changing the current (either increasing or decreasing) in
a circuit. thereby changing the flux linked with stationary conductors, i.e. the
conductors or coils remain stationary and the flux linking these conductors is
changed. The emf is termed statically induced emf.
• The concept of dynamically induced emf gave rise to the development of
generators, whereas statically induced emf was helpful in developing
transformers.
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Induced emf on the conductor could be produced by two methods i.e. flux cuts
conductor or conductor cuts flux.
a. Flux cuts conductor
• Flux cuts conductor when the magnet moves towards the coil as shown in
Figure below, a deflection is noted on the galvanometer showing that a
current has been produced in the coil.

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b. Conductor cuts flux (dynamically induced emf)
• Conductor cuts flux when the conductor moves through a magnetic field as
shown in Figure below. An emf is induced in the conductor and thus a source of
emf is created between the ends of the conductor. This is the simple concept of
AC generator. This induced electromagnetic field is given by;
E = Blv volts where
B = flux density, T l = length of the conductor in the magnetic field, m
v = conductor velocity, m/s

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 Dynamically Induced emf
• Dynamically induced emf is produced by the movement of the conductor in
a magnetic field.
• The voltage induced in the conductor is given by

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Statically Induced emf
• When the conductor or coil remains stationary and the flux linking with these
conductors or coil undergo a change, an emf is induced in the conductors. Such
an induced emf is termed as statically induced emf. Statically induced emf can
be further classified as (i) self-induced emf and (ii) mutual induced emf.
Self-induced emf
• Any electrical circuit in which the change of current is accompanied by the
change of flux, and therefore by an induced emf, is said to be inductive or it
possesses self-inductance. Thus the property of the coil which enables to induce
an emf in it whenever the current changes is called self-induction.

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 Cont..
• The phenomenon of self-induction is felt only when the current is changing,
either increasing or decreasing.
• As per Faraday's laws of electromagnetic induction, this induced emf is given
by,

• since coil in question is wound on an iron core, whose permeability is constant,

flux is proportional to the current through the coil, i.e.

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Mutually Induced emf Cont..
• The phenomenon of generation of induced emf in a circuit by changing the
current in a neighboring circuit is called mutual induction. Two coils possessing
this property are said to have mutual inductance.

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 PRODUCTION OF INDUCED FORCE ONAWIRE
• The figure shows a conductor present in a uniform magnetic field of flux density
B, pointing into the page. The conductor it self is l meters long and contains a
current of i amperes. The force induced on the conductor is given by
where
i = magnitude of current in wire
l = length of wire, with direction of l defined to be in the direction of current flow
B = magnetic flux density vector

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• The direction of the force is given by the right-hand rule: If the index finger of
the right hand points in the 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 the equation

• Example. Above Figure shows a wire carrying a current in the presence of a

magnetic field. The magnetic flux density is 0.25 T. directed into the page. If the
wire is 1.0 m long and carries 0.5 A of current in the direction from the top of
the page to the bottom of the page. what are the magnitude and direction of the
force induced on the wire?
• Solution
• The direction of the force is given by the right-hand rule as being to the right.
The magnitude is given by

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 Force on a current-carrying conductor lying in a magnetic field
• It is found that whenever a current-carrying conductor is placed in magnetic field, it experiences a force
which acts in a direction perpendicular both to the direction of current and field. In the fig below is
shown a conductor XY lying at right angles to the uniform horizontal field of flux density B Wb/m2
produced by two solenoids A and B. if l is the length of the conductor lying within this field and I
ampere the current carried by it, magnitude of force experienced by it is:

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 Inductance
• Inductance is, in some sense, a mirror image of capacitance. While capacitors
store energy in an electric field, inductors store energy in a magnetic field.
While capacitors prevent voltage from changing instantaneously, inductors, as
we shall see, prevent current from changing instantaneously.
• Consider a coil of wire carrying some current creating a magnetic field within
the coil. As shown in Figure. Assume that all of the flux stays within the low-
reluctance pathway provided by the core, and apply

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• Flux can be increased and leakage reduced by wrapping the coils around a
ferromagnetic material that provides a lower reluctance path. The flux will
be much higher using the core (a) rather than the rod (b).

• From Faraday‟s law , changes in magnetic flux create a voltage e, called

the electromotive force (emf), across the coil equal to

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 Energy Stored In Magnetic Field
• Consider a coil having a constant inductance of L Henry, in which the
current increases by di in dt seconds, then induced emf in the coil , e
becomes

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 Cont..
• Thus energy absorbed by the magnetic field during the time dt second
= joules
• Hence total energy absorbed by the magnetic field when the current
increases from zero to I amperes

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