‫‪Introduction‬‬
‫تم مراجعة المادة العلمٌة واعتمادها لتكون مرجعا للزمالء مدرسً الفٌزٌاء وأبنائنا‬
‫المتدربٌن فى مراكز التدرٌب المهنً الحكومٌة فً المستوي الثانً‪.‬‬
‫ونتقدم بالشكر الجزٌل إلى االستاذ محمد إبراهيم مدرس أول فٌزٌاء‬
‫بمركز التدرٌب المهنً بصور علً الجهد المبذول فً إعداد تلك المادة‪.‬‬
‫غريب زكي‬
‫أخصائً مناهج الرٌاضٌات والفٌزٌاء‬
‫دائرة تطوٌر المناهج‬
‫‪2010/11/30‬م‬
5 - Magnetic Field
Introduction :



Magnets have both a north pole and a south pole.
The magnetic lines of force flow from pole to pole as shown in the sketch.
It is easy to feel the attraction or repulsion when one plays with two magnets.

A magnetic field is produced when an electric current flows through a coil
of wire. This is the basis of the electromagnet.
 We can make an electromagnet stronger by doing these things:
1. wrapping the coil around an iron core
2. adding more turns to the coil
3. increasing the current flowing through the coil.
Definition
A magnetic field is a region in which a body with magnetic properties experiences a
force.
Sources of Magnetic Field
Magnetic fields are produced by electric currents, which can be macroscopic currents
in wires, or microscope currents associated with electrons in atomic orbits.
Magnetic Field Lines
A magnetic field is visualised using magnetic lines of force which are imaginary lines
such that the tangent at any point gives the direction of the magnetic field at that
point.
1
Properties of Magnetic Field Lines
 Magnetic lines of force never intersect.
 By convention, magnetic lines of force point from north to south outside a
magnet (and from south to north inside a magnet).
 Field lines converge where the magnetic force is strong, and spread out where it
is weak. (Number of lines per unit area is proportional to the magnetic field
strength.)
The Earth’s Magnetic Field
The Earth's magnetic field appears to come from a giant bar magnet, but with its
south pole located up near the Earth's north pole
ø
Magnetic Flux
The total number of magnetic lines of force passing through a specified area in a
magnetic field.
Magnetic Flux Pattern
2
Magnetic flux pattern due to current in a straight wire at right angles to a uniform
field
Net flux is greater
on this side of the
wire
Net flux is lesser
on this side of the
wire
I
Fleming’s Left Hand Rule
If you point your left forefinger in the direction of the magnetic field, and your second
finger in the direction of the current flow, then your thumb will point naturally in the
direction of the resulting force
Force on a current-carrying conductor
The direction of magnetic force always perpendicular to the direction of the magnetic
field and the direction of current passing through the conductor.



F  I  B



F  IF IB sin 
3
Magnetic Flux Density
Magnetic flux density is the amount of magnetic flux per unit area of a section,
perpendicular to the direction of flux.
The next Equation is the mathematical representation of magnetic flux density.
B=
ø/A =Wb/m
2
ø
Where B = magnetic flux density in Tesla (T), = magnetic flux in Weber (W b)
A = area in square meters (m2)
The result is that the SI unit for flux density is Weber per square meter.
One Weber per meter square equals one Tesla.
A magnetic field of one Tesla is quite strong. That is why magnetic fields are usually
expressed in microtesla (µT).
Source
4
B-Field (Tesla)
Human Brain
10-12
Interstellar Space
10-10
Near Household Wiring
10-4
Sunlight
3x10-5
Earth's Magnetic Field at Pole
5x10-4
Sunspots
.3
Largest man-made Magnet
5.0
Surface of a Nucleus
106
Magnetic field of a straight wire which carry Electric current
The magnetic field lines around a long wire which carries an electric current
form concentric circles around the wire.
If you point your right thumb in the direction of the current your fingers will curl in
the direction of the magnetic field. When the direction of the current is reversed the
direction of the magnetic field is also reversed.

I
B
r
 o I
B
2 r
The permeability of free space is
μ° = 4π× 10-7 T. m/A
The strength of the magnetic field depends on the current I in the wire and r, the
distance from the wire.
B = μ°I/2πr
The constant μ° is the magnetic permeability. If one remembers the case of the electric
field of a uniformly charged wire, it also fell as 1/r..
Example 1:
Calculate the magnetic field at a distance of 1m from a straight wire if a current of 5A
is flowing through it?
Solution:
The magnetic field due to a straight wire is
B = μ°I/2πr =(4π× 10-7×5) / (2×π×1)
= 2× 10-7 T
Example 2
A magnetic field of magnitude 4× 10-7 T is measured a distance of 2m from a long
straight wire. What is the current in the wire?
Solution:
one can solve for I.
Using
B = μ°I/2πr
I = B×2πr/ μ°
= (4× 10-7×2π × 2) / (4π× 10-7 ) = 4 A
5
Magnetic Field Inside a Solenoid :A solenoid is a long straight coil of wire, often wrapped around a metallic core,
which produces a magnetic field when an electric current is passed through
it. Solenoids are important because they can create controlled magnetic fields and can
be used as electromagnets.
The magnitude of the magnetic field, B, inside a solenoid is given by
B = 0nI
Where n is the number of turns per metre,
If(N) is the number of turns , the length (L)in metre of the solenoid (n = N/L).
Magnetic field = permeability x turn density x current
The magnitude of the field depends on the following factors.
1-The amount of current passing through the solenoid (I)
2-The number of turns of the solenoid. (n)
3-It also depends on the core material. Introduction of soft iron increases the field.
Example1: A long cylindrical solenoid with 200 turns/cm carries a current of 4.0
amps. What is the magnetic field inside the solenoid?
Solution:
The magnetic field only depends on the current (I = 4.0 amps) and the number of
turns per unit length (N/L = 200).
B = 0nI
B = 0.1005T
6
Magnetic Field of Current Loop
Examining the direction of the magnetic field produced by a current-carrying
segment of wire shows that all parts of the loop contribute magnetic field in the same
direction inside the loop.
Electric current in a circular loop creates a magnetic field which is more
concentrated in the center of the loop than outside the loop.
Field at Center of Current Loop
If a current flows through a circular coil the lines of magnetic flux are such that the
field at the centre of the coil is at right angles to the plane of the coil.Inthis special case
the symmetry is such that the contributions due to all the current elements add to the
centre.
1-The direction of magnetic field changes when the direction of flow of
current is reversed.
2-The strength of the magnetic field increases with increase in current (I)
3- The strength of the magnetic field at the centre of a circular coil carrying current
is proportional to the number of turns in the coil (n).
4- The strength of the magnetic field is inversely proportional to the radius of the
circular coil i.e. the field strength reduces as the radius of the coil increases. (r).
As we go away from the wire, the strength of the magnetic field decreases, and the
concentric circles grow larger in size
B =μoI/2πr
(at centre)For a single coil
B =μonI/2πr
(at centre) For a coil of n turns
7
Exercise
1- A magnetic field line is used to find the direction of
a. South- north
b.bar magnet
c. compass needle
d. magnetic field
Answer (d)
2- The magnetic field lines due to a straight wire carrying a current are
a. straight
b. parabolic
c. circular
d. elliptical
Answer (c )
3- The magnetic field lines inside a long, current carrying solenoid are nearly
a. straight
b. circular
c. parabolic
d. none
Answer (a )
4- The direction of the magnetic field due to a straight current carrying conductor
is given by :
a. Flemings left hand rule
b. Flemings right hand rule
c. Lenzs law
d. Right hand thumb rule
Answer ( d)
5- A soft iron bar is introduced inside a current carrying solenoid. The magnetic
field inside the solenoid
a. increases
b, decreases
c, remains same
d. is zero
Answer ( a )
6- A long, thin straight solenoid has 500 turns wound over a length of 50cm.
It carries a current of 0.5A.
What is the magnetic field inside this solenoid?
solution
N = 500
L = 50 cm = 0.5m
I = 0.5A
B = μ0NI/L
B= 4 x 10-7 x 5 x 102 x 0.5 / 5 x 10-1= 6.284 x 10-4 T
7- A long straight wire carries a current of 4A. What is the magnetic field at a point
distant 10cm from the wire?
Answer ( 8x10-6 ) T
8
8- 1. If we were to trace the magnetic lines of flux extending from this bar magnet,
what would they appear like?
Answer
9- What happens when a current carrying conductor is placed in a magnetic field?
Answer
A current carrying conductor placed in a magnetic field experiences a force whose
direction is given by Fleming's left hand rule.
10- When does a current carrying conductor experience a maximum force in the
magnetic field?
Answer
When it is placed perpendicular to the magnetic field.
11- Find the magnetic flux density in the center of a 4.0 cm long air-core solenoid
made with 4900 turns of wire and carrying a 2.5A current.
Answer
B = μ0NI/L
B = (4πx10-7)(4900)(2.5)/0.040) = 0.385 T
9
6 - Electromagnetic induction
Introduction :
In electronics, the production of an electromotive force (emf)
in a circuit by a change of magnetic flux through the circuit or by relative motion of
the circuit and the magnetic flux. As a magnet is moved in and out of a coil of wire in
a closed circuit an induced current will be produced. All dynamos and generators
produce electricity using this effect. When magnetic tape is driven past the playback
head (a small coil) of a tape recorder, the moving magnetic field induces an emf in the
head, which is then amplified to reproduce the recorded sounds.
Electromagnetic induction takes place when the magnetic field around a conductor
changes. If the magnetic field is made to change quickly, the size of the current
induced is larger. A galvanometer can be used to measure the direction of the current.
As a magnet is pushed into a coil, the needle on the galvanometer moves in one
direction. As the magnet is removed from the coil, the needle moves in the opposite
direction.
If the change of magnetic flux is due to a variation in the current flowing in the same
circuit, the phenomenon is known as self-induction; if it is due to a change of current
flowing in another circuit it is known as mutual induction.
(electromagnetism) The production of an electromotive force either by motion of a
conductor through a magnetic field so as to cut across the magnetic flux or by a
change in the magnetic flux that threads a conductor. Also known as induction.
Fleming's right hand rule
(for generators) shows the direction of induced
current flow when a conductor moves in a magnetic
field.
The right hand is held with the thumb, first finger
and second finger mutually perpendicular to each
other {at right angles}, as shown in the diagram .
-The Thumb represents the direction of Motion of
the conductor.
-The First finger represents the direction of the
Field. (north to south)
-The Second finger represents the direction of the induced or generated Current (the
direction of the induced current will be the direction of conventional current; from
positive to negative).
One particular way of remembering the rule is the "FBI" acronym for Force(or
otherwise motion), B as the magnetic field sign and I as the current. The subsequent
letters correspond to subsequent fingers, counting from the top. Thumb -> F; First
finger -> B; Second finger -> I
10
Ways to generated induced currents :
1) move quickly conductor V perpendicular to the field lines to cut these lines field
index G as proof of the existence of electric current and therefore e.m.f.
Depends on the direction of flow: the direction of conductor and the direction of field
lines.
possible to obtain electric power from kinetic energy in the magnetic field, an idea
underlying the electric generator (dynamo)
2 ) The entrance of a magnet within a file spiral
N
S
N
S
The direction of flow depends on the direction of movement of the magnet
3) Two coils primary and secondary
Magnetic Field lines from primary coil penetrate the secondary coil arises when a
change in flux thereby creating an induced current in the secondary coil
Lenz's law
The direction of an electromagnetically-induced current (generated by moving a
magnet near a wire or by moving a wire in a magnetic field) will be such as to oppose
the motion producing it. This law is named after the German physicist Heinrich
Friedrich Lenz (1804–1865), who announced it in 1833.
Faraday's laws
English scientist Michael Faraday proposed three laws of electromagnetic induction:
(1) a changing magnetic field induces an electromagnetic force in a conductor;
(2) the electromagnetic force is proportional to the rate of change of the field;
(3) the direction of the induced electromagnetic force depends on the orientation of
the field.
Induced Electromotive force (e.m.f.)
A voltage is induced when a conductor cuts magnetic field lines or when the magnetic
field through a coil changes. This is called induced e.m.f. (electromotive force).
11
Electric generator
 converts mechanical energy to electrical energy
 Opposite system to dc motor
 In this system the coil is turned mechanically in the magnetic field
• As the coil turns an emf is produced across the coil, and a current flows.
• Each ½ cycle the direction of the induced current changes direction, thus
generating A.C.
• If d.c. is required a split ring commutator is used to change the direction every
½ cycle
• Generators are found in power stations, alternators in cars, dynamo of a bike
How An Electric Generator Works
An electric generator is a device used to convert
mechanical energy into electrical energy.
The generator is based on the principle of
"electromagnetic induction" discovered in 1831 by
Michael Faraday, a British scientist. Faraday
discovered that if an electric conductor, like a
copper wire, is moved through a magnetic field, electric current will flow (be
induced) in the conductor. So the mechanical energy of the moving wire is
converted into the electric energy of the current that flows in the wire.
12
The motor
An electric motor uses electrical energy to produce
mechanical energy, very typically through the
interaction of magnetic fields and current-carrying
conductors. The reverse process, producing
electrical energy from mechanical energy, is
accomplished by a generator or dynamo. Traction
motors used on vehicles often perform both tasks.
Many types of electric motors can be run as
generators, and vice versa.
Electric motors are found in applications as diverse as industrial fans, blowers and
pumps, machine tools, household appliances, power tools, and disk drives. They
may be powered by direct current (for example a battery powered portable device
or motor vehicle), or by alternating current from a central electrical distribution
grid. The smallest motors may be found in electric wristwatches. Medium-size
motors of highly standardized dimensions and characteristics provide convenient
mechanical power for industrial uses. The very largest electric motors are used for
propulsion of large ships, and for such purposes as pipeline compressors, with
ratings in the millions of watts. Electric motors may be classified by the source of
electric power, by their internal construction, by their application, or by the type of
motion they give.
The physical principle of production of mechanical
force by the interactions of an electric current and
a magnetic field was known as early as 1821.
Electric motors of increasing efficiency were
constructed throughout the 19th century, but
commercial exploitation of electric motors on a
large scale required efficient electrical generators
and electrical distribution networks.
13
Electrical motor efficiency:
is the ratio between the shaft output power - and the electrical input power.
Electrical Motor Efficiency when Shaft Output is measured in Watt
If power output is measured in Watt (W), efficiency can be expressed as:
ηm = Pout / Pin
(1)
where
ηm = motor efficiency
Pout = shaft power out (Watt, W)
Pin = electric power in to the motor (Watt, W)
Electrical Motor Efficiency when Shaft Output is measured in Horsepower
If power output is measured in horsepower (hp), efficiency can be
expressed as:
ηm = Pout 746 / Pin
(2)
where
Pout = shaft power out (horsepower, hp)
Pin = electric power in to the motor (Watt, W)
14
Self induction
• When ac flows through a coil, a magnetic field is created around the coil. Thus
the coil itself is now sitting in a changing magnetic field, so an emf is induced in
the coil.
• This induced emf opposes the driving emf, according to Lenz’s law.
The property of self-inductance is a particular form of electromagnetic induction. Self
inductance is defined as the induction of a voltage in a current-carrying wire when the
current in the wire itself is changing. In the case of self-inductance, the magnetic field
created by a changing current in the circuit itself induces a voltage in the same circuit.
Therefore, the voltage is self-induced.
The term inductor is used to describe a circuit element possessing the property of
inductance and a coil of wire is a very common inductor. In circuit diagrams, a coil or
wire is usually used to indicate an inductive component. Taking a closer look at a coil
will help understand the reason that a voltage is induced in a wire carrying a changing
current. The alternating current running through the coil creates a magnetic field in
and around the coil that is increasing and decreasing as the current changes. The
magnetic field forms concentric loops that surround the wire and join to form larger
loops that surround the coil as shown in the image below. When the current increases
in one loop the expanding magnetic field will cut across some or all of the neighboring
loops of wire, inducing a voltage in these loops. This causes a voltage to be induced in
the coil when the current is changing.
By studying this image of a coil, it can be seen that the number of turns in the coil will
have an effect on the amount of voltage that is induced into the circuit. Increasing the
number of turns or the rate of change of magnetic flux increases the amount of
induced voltage. Therefore, Faraday's Law must be modified for a coil of wire and
becomes the following.
Where:
VL = induced voltage in volts
N = number of turns in the coil
dø/dt = rate of change of magnetic flux in webers/second
The equation simply states that the amount of induced voltage (VL) is proportional to
the number of turns in the coil and the rate of change of the magnetic flux (dø/dt). In
other words, when the frequency of the flux is increased or the number of turns in the
coil is increased, the amount of induced voltage will also increase.
15
In a circuit, it is much easier to measure current than it is to measure magnetic flux,
so the following equation can be used to determine the induced voltage if the
inductance and frequency of the current are known. This equation can also be
reorganized to allow the inductance to be calculated when the amount of inducted
voltage can be determined and the current frequency is known.
Where:
VL = the induced voltage in volts
L = the value of inductance in henries
di/dt = the rate of change of current in amperes per second
16
Mutual induction
• If you place 2 coils near each other, a changing magnetic field in one will induce
an emf, and hence current in the other.
• This induced current is a.c. and so induces a changing magnetic field in the
second coil.
• Thus the first coil is now in the changing magnetic field due to the second coil,
so an emf is induced in the first coil
When an emf is produced in a coil because of the change in current in a coupled coil ,
the effect is called mutual inductance. The emf is described by Faraday's law and it's
direction is always opposed the change in the magnetic field produced in it by the
coupled coil (Lenz's law ). The induced emf in coil 1 is due to self inductance L.
The induced emf in coil #2 caused by the change in current I1 can be expressed as
The mutual inductance M can be defined as the proportionality between the emf
generated in coil 2 to the change in current in coil 1 which produced it.
The most common application of mutual inductance is the transformer
17
Transformers
A "transformer" changes one voltage to another.
This attribute is useful in many ways.
A transformer doesn't change power levels. If you
put 100 Watts into a transformer, 100 Watts come
out the other end. [Actually, there are minor losses
in the transformer because nothing in the real
world is 100% perfect. But transformers come
pretty darn close; perhaps 95% efficient.]
A transformer is made from two coils of wire close
to each other (sometimes wrapped around an iron or ferrite "core"). Power is fed into
one coil (the "primary"), which creates a magnetic field. The magnetic field causes
current to flow in the other coil (the "secondary"). Note that this doesn't work for
direct current (DC): the incoming voltage needs to change over time - alternating
current (AC) or pulsed DC.
• a device to change the value of an alternating voltage.
• Consists of 2 coils of wire wound around a soft iron core (to increase the
magnetic effect)
• An alternating voltage (Vp) and current is applied to the primary coil. This
generates a changing magnetic field around this coil.
• The nearby secondary coil is now in a changing magnetic field → an induced
emf (Vs) and current is generated across the secondary coil.
• The relative sizes of the input and output voltages depend on the no. of turns of
wire in primary and secondary coils.
Vp / Vs = Np / Ns
• If there are no energy losses in the transformer then power stays the same
Pin = Pout
But P = V I
Vp Ip = Vs Is
Vp / Vs = Is / Is
18
Finally, and again assuming that the transformer is ideal, let's ask what the resistor in
the secondary circuit 'looks like' to the primary circuit. In the primary circuit:
Vp = Vs/r
and
Ip = Is.r
so
Vp/Ip = Vs/r2Is = R/r2.
R/r2 is called the reflected resistance. Provided that the frequency is not too high, and
provided that there is a load resistance (conditions usually met in practical
transformers), the inductive reactance of the primary is much smaller than this
reflected resistance, so the primary circuit behaves as though the source were driving
a resistor of value R/r2. This allows transformers to be used as impedance matchers. A
load with low input impedance can be matched to circuit with high output impedance
using a step down transformer.
- The number of times the wires are wrapped around the core ("turns") is very
important and determines how the
transformer changes the voltage.
- If the primary has fewer turns
than the secondary, you have a
step-up transformer that
increases the voltage.
- If the primary has more turns
than the secondary, you have a
step-down transformer that reduces the voltage.
- If the primary has the same number of turns as the secondary, the outgoing
voltage will be the same as what comes in. This is the case for an isolation
transformer.
In certain exceptional cases, one large coil of wire can serve as both primary and
secondary. This is the case with variable auto-transformers and xenon strobe trigger
transformers.
Uses of transformers
• Used by power stations to minimise heat losses in cables by
transforming voltages to very high values.
• Used in many everyday household electrical items to supply the
necessary voltages to various parts
19
Types of transformers
In general, transformers are used for two purposes: signal matching and power
supplies.
Power Transformers
Power transformers are used to convert from one voltage to another, at significant
power levels.
1- Step-up transformers
A "step-up transformer" allows a device that requires a high voltage power supply to
operate from a lower voltage source. The transformer takes in the low voltage at a
high current and puts out the high voltage at a low current.
Examples:


Your are a Swiss visiting the U.S.A., and want to operate your 220VAC shaver
off of the available 110 VAC.
The CRT display tube of your computer monitor requires thousands of volts,
but must run off of 110 VAC from the wall.
2- Step-down transformers
A "step-down transformer" allows a device that requires a low voltage power supply
to operate from a higher voltage. The transformer takes in the high voltage at a low
current and puts out a low voltage at a high current.


20
Your Mailbu-brand landscape lights run on 12VAC, but you plug them into the
110 VAC line.
Your doorbell doesn't need batteries. It runs on 110 VAC, converted to 12VAC.
Efficiency of transformers
In practice, real transformers are less than 100% efficient.




First, there are resistive losses in the coils (losing power I2.r). For a given
material, the resistance of the coils can be reduced by making their cross section
large. The resistivity can also be made low by using high purity copper
Second, there are some eddy current losses in the core. These can be reduced by
laminating the core. Laminations reduce the area of circuits in the core, and so
reduce the Faraday emf, and so the current flowing in the core, and so the
energy thus lost.
Third, there are hysteresis losses in the core. The magentisation and
demagnetisation curves for magnetic materials are often a little different
(hysteresis or history depedence) and this means that the energy required to
magnetise the core (while the current is increasing) is not entirely recovered
during demagnetisation. The difference in energy is lost as heat in the core.
Finally, the geometric design as well as the material of the core may be
optimised to ensure that the magnetic flux in each coil of the secondary is nearly
the same as that in each coil of the primary.
Exercise
1- A transformer has an input of 110 DC volts, with 100 turns on the primary and 10
turns on the secondary. What is the output voltage ?
The correct answer: 0 volts (Magnetic fields are created by changing electric fields )
2- 120 volt house current is to be transformed down to 12 volts.
a) What is the ratio of the primary to secondary turns? The correct answer: 10-1
b ) In the preceding question, if the input current (RMS) is 1.5 amps What is the
output current ?
The correct answer: 15 amps
3- A transformer has 150 turns on the primary and 20 on the secondary. 100 volts and
10 amps will be changed to
The correct answer: 13.3 volts and 75 amps
21