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CHAPTER
`
4
4.0
BASIC PRINCIPLES OF
ELECTROMAGNETISM
INTRODUCTION
This chapter is explaining about the relationship between current flows in conductor,
classify factors that affect electromagnetic strength and understand the characteristics
of magnetic quantities in electromagnet. The learning outcomes for this chapter are
the students should be able to explain clearly the relationship between current flow
and magnetism.
4.1
MAGNET
Magnet can be defined as material that can attract piece of iron or metal. Magnet has
two poles north and south. Material that attracted by the magnet is known as magnetic
substances. The ability to attract the magnetic substances is known as magnetism.
4.1.1 Principles Of Magnet
Magnet has a magnetic field around the magnet itself. Magnetic field is the
force around the magnet which can attract any magnetic material around it.
Flux magnet is the line around the magnet bar which form magnetic field.
Figure 4.1: Magnetic Field
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4.1.2
Basic Magnet Law
Magnetic flux lines have a direction and pole. The direction of movement
outside of the magnetic field lines is from north to south. The strongest
magnetic fields are at the magnetic poles. Different poles attract each other and
same magnetic poles will reject each other. Flux form a complete loop and
never intersect with each other. Flux will try to form a loop as small as
possible.
Figure 4.2: Magnetic Flux
4.1.3 Types Of Magnet
There are two types of magnet known as pure magnet and manufacture
magnet.
i)
Pure Magnet
Pure magnet is a magnet stone. The stone originally have the natural
magnetic. Basically the stone is found in the form of iron ore.
ii)
Manufacture Magnet
There are two types of manufacture which is permanent magnet and
temporary magnet.
a) Permanent Magnet
The ability of the magnet to kept its magnetism. There are five
basic shape of permanent magnet as shown in Figure 4.3. Basically
permanent magnet is used in a small device such as speakers, meter
and compass. Permanent magnet can be obtained by naturally or
magnetic induction and placing a magnet into a coil then supplied
with a high electrical current. The basic types of permanent magnet
are U Shape, Horseshoe, Rod, Cylinder and Bar.
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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 component
such as relay and small devices such as electrical bell.
4.2
ELECTROMAGNET
Electromagnet is a magnetic iron core produced when the current flowing through the
coil. Thus, the magnetic field can be produced when there is a current flow through a
conductor. The direction of the magnetic field produced by the current in the solenoid
can be determined using two methods:
i)
ii)
Right Hand Grip Rule
Maxwell's Screw Law
4.2.1
Right Hand Grip Rule
Right Hand Grip Rule is a physics principle applied to electric current passing
through a solenoid, resulting in a magnetic field. By wrapping the right hand
around the solenoid, thumb is pointing in the direction of the magnetic north
pole and fingers in the direction of the conventional current. This rule can also
be applied to electricity passing through a straight wire. The thumb points in
the direction of the conventional current from positive to negative. Meanwhile
the fingers points of the magnetic lines of flux.
Figure 4.3: Right Hand Grip Rule
4.2.2 Maxwell's Screw Law
Another way to determine the direction of the flux and current in a conductor
is to use Maxwell's screw rule. A right-handed screw is turned so that it moves
forward in the same direction as the current, its direction of rotation will give
the direction of the magnetic field from south to north.
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Figure 4.4: Maxwell’s Screw Law
4.3
ELECTROMAGNETIC EFFECT
A flow of current through a wire produces a magnetic field in a circular path around
the wire. The field patterns of a current flow in a conductor can de determine using
both rules of right hand grip or Maxwell’s Screw. Note that, conventional current
flow towards or inside the conductor is marked by cross (X) and current flow away or
outside the conductor is marked as dot ( · ).
4.3.1
Single Conductor
The direction of the field pattern in going and out going produced by a current
flowing through a single conductor can be determine by applying both rules as
illustrated in Figure 4.5.
Source: Fundamental Electrical & Electronic Principles by Christopher R Robertson
Figure 4.5: Current flow (a) in going (b) out going
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4.3.2
Two Conductors
If the two conductors where the current flow in the same direction, the
magnetic flux pattern will produce around both conductors and combine to
create attraction between them as shown in Figure 4.6 (a). If the current in
conductors flow in opposite direction, the field pattern will repulse each other.
The effect is shown in Figure 4.6(b).
(a)
(b)
Source: Pengajian Kejuruteraan Elektrik dan Elektronik,Cetakan Pertama 2000 by Abd.
Samad Hanif
Figure 4.6: Two closed current-carrying conductors flow
(a) in same direction (b) in opposite direction
4.4
ELECTROMAGNETIC STRENGTH
There are 4 factors that affect electromagnetic strength:
1. Number of turns
The strength of the electromagnet is directly proportional to the number of turn in
the coil. By varying the number of turns in its coil can produce very strong
magnetic fields and its strength.
2. Current strength
The strength of the electromagnet is directly proportional to the current flowing in
the coil. Greater the current flow through the coil, stronger will be the magnetic
fields produced.
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3. Length of coil
The strength of the electromagnet is directly proportional to the length of the coil.
By coil up the wire can increasing the length and increase the force of magnetic
field.
4. Types of conductor
Depend on the nature of the core material. The use of soft of core can produces
the strongest magnetism.
4.5
ELECTROMAGNETIC INDUCTION
When a conductor is move across a magnetic field, an electromagnetic force (emf) is
produced in conductor. This effect is known as electromagnetic induction. The effect
of electromagnetic induction will cause induced current. There are two laws of
electromagnetic induction:
i.
ii.
Faraday’s law
Lenz’z Law
4.5.1
Faraday’s law
Faraday’s law is a fundamental relationship which comes from Maxwell’s
equations. It is a relative movement of the magnetic flux and the conductor
then causes an emf and thus the current to be induced in the conductor.
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 cut conductor is when the magnet is move towards the coil as shown in
Figure 4.9, a deflection is noted on the galvanometer showing that a current
has been produced in the coil.
Source: Pengajian Kejuruteraan Elektrik dan Elektronik, Cetakan Pertama 2000 by Mohd. Isa
bin Idris
Figure 4.7: Flux cuts conductor
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b.
Conductor cuts flux
Conductor cut flux is when the conductor is moved through a magnetic field
as shown in Figure 4.8. 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
[4.1]
where
B
l
v
=
=
=
flux density, T
length of the conductor in the magnetic field, m
conductor velocity, m/s
If the conductor moves at the angle θ° to the magnetic field, then
E = Blv sinθ° volts
[4.2]
Source: Pengajian Kejuruteraan Elektrik dan Elektronik, Cetakan Pertama 2000 oleh Mohd.
Isa bin Idris
Figure 4.8: Conductor cuts flux
Example 4.1
A conductor 300mm long moves at a uniform speed of 4m/s at right-angles to
a uniform magnetic field of flux density 1.25T. Determine the current flowing
in the conductor when
(a)
(b)
its ends are open-circuited
its ends are connected to a load of 20 Ω resistance.
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Solution 4.1
When a conductor moves in a magnetic field it will have an emf induced in it
but this emf can only produce a current if there is a closed circuit. Induced emf
E = Blv = (1.25)(300/1000)(4)
(a)
If the ends of the conductor are open circuit, no current will flow even
though 1.5 V has been induced.
(b)
From Ohm’s law
I=
4.5.2
E 1. 5
=
75mA
R 20
Lenz’z Law
The direction of an induced emf is always such that it tends to set up a current
opposing the motion or the change of flux responsible for inducing that emf.
This effect is shown in Figure 4.9.
Source: Pengajian Kejuruteraan Elektrik dan Elektronik, Cetakan Pertama 2000 by Mohd. Isa
bin Idris
Figure 4.9: Bar magnet move in and move out from a solenoid
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4.6
MAGNETIC QUANTITY CHARACTERISTICS
There are many magnetic quantities in the System International (SI) unit. This chapter
is only going to discuss on magnetomotive force, magnetic field strength, magnetic
flux, flux density, permeability and reluctance.
4.6.1
Magnetiomotive Force, Fm
Magnetomotive force is a cause of the existence of magnetic flux in a
magnetic circuit. The total flux produced is depends on the number of turn (N)
made in the circuit. It is also proportional to the current (I) passing through the
coil. Then, the magnetomotive force is the product of current and the number
of turns.
Fm = NI ampere turn
4.6.2
[4.3]
Magnetic Field Strength, H
Magnetic field strength or magnetizing force is defined as magnetomotive
force, Fm per meter length of measurement being ampere-turn per meter.
H=
Fm NI
=
ampere turn / meter
l
l
[4.4]
where
Fm
N
I
l
-
magnetomotive force
number of turns
current
average length of magnetic circuit
Example 4.2
A current of 500mA is passed through a 600 turn coil wound of a toroid of
mean diameter 10cm. Calculate the magnetic field strength.
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Solution 4.2
I
N
d
H=
4.6.3
=
=
=
0.5A
600
π x 10 x 10-2m
NI
600 × 0.5
ampereturn / metre =
= 954.81 AT/m
l
0.3142
Magnetic Flux and Flux Density
Magnetic flux is the amount of magnetic filed produced by a magnetic source.
The symbol for magnetic flux is phi (Φ). The unit for magnetic flux 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:
Magnetic flux density =
B=
magnetic flux
area
Φ
Tesla
A
[4.5]
The symbol for magnetic flux density is B. The unit of magnetic flux density
is the tesla, T, and the unit for area A is m2 where 1 T = 1 Wb/m.
Example 4.3
A magnetic pole face has rectangular section having dimensions 200mm by
100mm. If the total flux emerging from the the pole is 150µWb, calculate the
flux density.
Solution 4.3
Magnetic flux, Φ = 150 µWb = 150 x 10-6 Wb
Cross sectional area, A = 200mm x 100mm = 20 000 x 10-6 m2
Flux density, B =
Φ
150 × 10 −6
=
A 20000 × 10 −6
= 7.5 mT
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4.6.4
Permeability
Permeability is the measure of the ability of the material to allow the magnetic
field to exist in it. Absolute permeability, µ of a material is the ratio of the flux
density to magnetic field strength.
µ = µ0 µr
[4.6]
If the magnetic fields exist in the vacuum, the ratio of the flux density to the
magnetic field strength is a constant called the permeability of free space. For
air or any other non-magnetic medium, the ratio of magnetic flux density to
B
magnetic field strength is constant ,
= a constant. The equation for
H
permeability of free space in non-magnetic medium is as shown in equation
4.7 below.
B
= µ0
H
[4.7]
The permeability of free space, µ 0 is equal to 4π x 10-7 H/m. In the air or any
non-magnetic material µr = 1, this is the same magnetic properties as a
vacuum as shown in equation 4.7. µr is relative permeability and it is
considered when the different type of material is used. µr is defined as the
ratio of the flux density produced in the material that produced in the air or as
define in equation 4.8.
µr =
flux density in material
flux density in vacuum
[4.8]
µr varies with the type of magnetic material. The approximate ranges of
relative permeability for some common magnetic materials are as follows:
Cast iron: µr = 100 – 250
Mild steel: µr = 200 – 800
Cast steel: µr = 300 – 900
Therefore the permeability for all media other than free space in a magnetic
medium or material is as shown in equation in 4.9 below.
B
= µ0 µr
H
[4.9]
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Example 4.4
A flux density of 1.2 T is produced in a piece of cast steel by a magnetizing
force of 1250 A/m. Find the relative permeability of the steel under these
conditions.
Solution 4.4
B = µ0 µr H
µr =
4.6.5
B
1.2
=
µ 0 H (4π × 10 − 2 )(1250)
= 764
Reluctance
Reluctance, S is the magnetic resistance of a magnetic circuit to presence of
magnetic flux. The equation for reluctance is as equation 4.10 below
S=
Fm Hl
l
1
=
=
=
Φ BA ( B / H ) A µ 0 µ r A
[4.10]
The unit for reluctance is 1/H or H-1 or A/Wb. The ferromagnetic materials
have low reluctance and can be used as magnetic screens to prevent magnetic
fields affecting materials within the screen.
Example 4.5
Determine the reluctance of a piece of metal with length 150mm, when the
relative permeability is 4 000. Find the absolute permeability of the metal.
Solution 4.5
Reluctance,
S=
=
1
µ0 µr A
150 × 10 −3
(4π × 10 − 7 )(4000)(1800 × 10 −6 )
= 16 580 H-1
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Absolute permeability, µ = µ 0 µ r
= (4π × 10 −7 )(4000)
= 5.027 x 10-3 H/m
REFERENCE
Robertson, C.R (2008) “Fundamental Electrical and Electronic Principles 3rd
Newnes, New York
Edition”,
PROBLEMS
1.
Find the magnetic field strength applied to a magnetic circuit of mean length 50 cm
when a coil of 400 turns is applied to it carrying a current of 1.2 A.
(960AT/m)
2.
A current of 2.5A when flowing through a coil produces an mmf of 675 At. Calculate
the number of turns on the coil
(270 turns)
3.
A magnetizing force 8000 A/m is applied to a circular magnetic circuit of mean
diameter 30 cm by passing a current through a coil wound on the circuit. If the coil is
uniformly wound around the circuit and has 750 turns, find the current in the coil.
(10.05 A)
4.
The maximum working flux density of a lifting electromagnet is 1.8 T and the effective
area of a pole face is circular in cross-section. If the total magnetic flux produced is 353
mWb, determine the radius of the pole.
(0.196m)
A coil of 300 turns is wound uniformly on a ring of non-magnetic material. The ring
has a mean circumference of 40 cm and a uniform cross-sectional area of 4cm2. If the
current in the coil is 5 A, calculate (a) the magnetic field strength, (b) the flux density
and (c) the total magnetic flux in the ring.
(3750AT/m, 4.712mT, 1.885µWb)
5.
6.
At what velocity must a conductor 75mm long cut a magnetic flux of density 0.6T if an
e.mf. of 9V is to be included in it? Assume the conductor, the field and the direction of
motion are mutually perpendicular.
(200m/s)
7.
A conductor of length 15cm is moved at 750mm/s at right-angles to a uniform flux
density of 1.2 T. Determine the emf induced in the conductor.
(0.135V)
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8.
Find the speed that a conductor of length 120mm must be moved at right angles to a
magnetic field of flux density 0.6 T to induce in it an emf of 1.8 V.
(25m/s)
9.
A 25 cm long conductor moves at a uniform speed of 8 m/s through a uniform magnetic
field of flux density 1.2T. Determine the current flowing in the conductor when (i) its
ends are open-circuited (ii) its ends are connected to a load of 15 ohms resistance.
(0, 0.16A)
10.
A conductor of length 0.5 m situated in and at right angles to a uniform magnetic field
of flux density 1 wb/m2 moves with a velocity of 40 m/s. Calculate the emf induced in
the conductor. What will be the emf induced if the conductor moves at an angle 60º to
the field.
(20V, 17.32V)
Basic Principles of Electromagnetism