1E6 Electrical Engineering
Electricity and Magnetism
Lecture 17: Electromagnetism
17.1 Magnetism
A small number of materials in nature exhibit the
property known as magnetism. The effect of
magnetism first being discovered is generally
attributed to the Chinese in the 3rd century BC. A
naturally occurring magnetic material known as
Lodestone, a particular crystallised form of the
mineral Magnetite as seen in Fig.1, was later
discovered by the ancient Greeks. Another naturally
occurring magnetic material is Pyrrhotite, which is
an Iron Sulphide mineral. In fact, the Earth itself
also possesses a magnetic field and magnetised
materials readily interact with this, as for example
the needle of a compass.
Fig. 1 A Piece of
Magnetised Lodestone
It is generally also well known that other materials are easily magnetised
when subjected to the influence of a strong magnetic field and that when the
field is removed they retain a large degree of magnetism on the long-term. Such
materials are elements like Iron, Nickel and Cobalt, and man-made materials
such as Ferrite which is an Iron-Ceramic compound. Man-made permanent
magnets are usually made from Iron or Steel. In Electronic Engineering, Ferrite
is commonly used as a core for inductors and transformers.
In the structure of an atom the numbers of protons and electrons are the
same and hence the associated charges cancel so that elements are electrically
neutral. Electrons rotate in orbits at specific energy levels around the nucleus
and at the same time spin on their own axes, rather like the Earth’s orbiting
around the sun and yet spinning itself. A charged particle in motion, such as an
orbiting electron, has a miniscule magnetic moment associated with it. Each
energy level can have two electrons and when they occur in pairs they orbit and
spin in opposite directions and so the magnetic moments cancel out.
Materials which become easily magnetised have an odd number of
electrons. This means that there is one electron, in the outermost orbit of the
atom, with a direction of orbit and spin which is not counterbalanced by a
second electron. This gives rise to a net magnetic moment. In magnetic materials
several thousands of molecules of the material combine into a domain where the
miniscule magnetic fields of individual molecules align to give a stronger field.
1
Under the right conditions the domains then align within the material so that the
magnetic fields add cumulatively to give an overall magnetic field associated
with the piece of material. If a piece of magnetised material is suspended in free
space it will align with the Earth’s magnetic field. The North-seeking end of the
material is called the North Pole (N) of the magnet while the South-seeking end
is called the South Pole (S).
17.2 Magnetic Flux
Consider a permanent bar magnet with North and South poles aligned as
shown in Fig. 2. Magnetisation of the material produces an Energy or Force
Field in the vicinity of the magnet. That is, any material subject to magnetism
which is placed within this field will experience a force. The field can be
represented by lines of flux which show the intensity and direction of the force
as indicated in Fig. 2. It is important to note that these lines are imaginary or
illustrative but nonetheless do represent a definite experienced effect. The lines
are referred to as lines of Magnetic Flux. The intensity of the field is usually
represented by the density of the lines and arrows are used to show the
direction. This is admirably illustrated by the classic Iron Filings Experiment,
where iron filings are sprinkled on to a page placed over a bar magnet as shown
in Fig. 3. The stronger the magnet, the greater the intensity of the field and the
greater the density of the lines of flux within a given space.
N
S
permanent
magnet
lines of flux
indicating the
strength and
direction of
the magnetic
field
Fig. 2 Lines of Magnetic Flux
Fig. 3 Iron Filings Experiment
2
There are a number of fundamental axioms or rules associated with lines of
magnetic flux as follows:
1.
Lines of magnetic flux form closed loops.
2.
Lines of flux never intersect.
3.
Lines of magnetic flux flow from south to north within the magnetic
material and from north to south outside of it.
4.
They generally flow in straight lines within the (homogeneous) material
and in curved ellipsoids outside of it.
5.
Parallel lines of flux running in the same direction repel each other
while those running in opposite directions attract each other.
The nature of the magnetic field associated with a magnetised source can also be
altered by adding one or more additional sources. The fields of all sources
interact to create a modified resulting field which depends on the directions and
strengths of the individual fields. The rule between magnetic sources is that: like
poles repel each other while unlike poles attract.
Definitions:
Magnetic Flux is defined as the lines of force illustrating the intensity and
direction of a magnetic field.
Magnetic Flux is given the symbol Ф and has units of Webers (Wb). This unit is
named after Wilhelm Eduard Weber (1804 – 1891), a German physicist.
Magnetic Flux Density is a measure of the intensity of a magnetic field. It is
defined as the quantity of magnetic flux passing through a unit area
perpendicular to the direction of the field.
Magnetic Flux Density is given the symbol B and has units of Webers per square
metre (Wb/m2) or more correctly Teslas (T) named after Nicola Tesla (1856 1943), a Serbian-American inventor and electrical/mechanical engineer.
Magnetic Flux Density =
Magnetic Flux
Area
B=
Magnetic Flux = Magnetic Flux Density x Area
3
Φ
A
Wb/m 2 (T)
Φ = BA Wb
17.3 Illustrative Examples
Example 1
A bar magnet has dimensions of 8cm x 2cm x 1cm and possesses a total magnetic
flux of 25Wb. Determine the density of the magnetic field experienced close to a
pole face of the magnet.
Solution:
8 cm
2 cm
pole
face
1 cm
Area of pole face A = 2cm x 1 cm = 2 x 10-2 x 1 x 10-2 = 2 x 10-4 m2
The density of the magnetic field is the Magnetic Flux Density B:
B=
Φ
25
=
= 12.5x104 Wb/m 2 (T)
−4
A 2x10
Example 2:
The magnetic rod used in the aerial of an AM radio is formed of magnetised
ferrite material having a total volume of 10cc. The ferrite is uniformly
magnetised to have a flux of 1.25 mWb/cc of material. The aerial must possess
an internal magnetic field intensity of 120T in total. Determine the dimensions of
the rod required.
4
Solution:
The total flux possessed by the ferrite aerial is the flux per unit volume of
material times the total volume of ferrite used so that:
Φ = 1.25 x 10−3 x 10 = 1.25 x 10−2 Wb
The overall intensity of the magnetic field generated within the aerial is the
magnetic field intensity B so that:
Φ
Φ 1.25 x 10−2
B=
∴A = =
=1.04 x 10− 4 m 2
A
B
120
The area of the rod is given as πr2 where r is the radius of the rod.
A 1.04 x 10−4
πr = A ∴ r = =
= 3.31x 10− 5 m 2
π
3.14
2
2
so that:
r = 3.31 x 10−5 = 5.76 x 10 −3 m = 5.76 mm
The length of the aerial needed, l, can be found from the radius and the volume:
V
10 x 10 −6
V = πr l ∴ l = 2 =
= 0. 096 m = 9.6 cm
−4
πr
1.04 x 10
2
The dimensions of the required ferrite rod are therefore:
length l = 9.6 cm
diameter d = 2r = 1.15 cm
5
17.4 Electromagnetism
When electric current flows in a conductor (metal), free charge carrying
electrons are in motion. This results in a magnetic field being generated around
the conductor as was discovered by Hans Christian Oersted (1777 – 1851), a
Danish physicist and chemist in the 19th century.
There is a convention for showing the direction of current in the
conductor when viewed end-on as illustrated in Fig. 4. A dot is used,
corresponding to the tip of an arrow, to indicate current flowing towards the
observer, while a cross is used, corresponding to the end feathers at the back of
an arrow, to indicate current flowing away from the observer. It can be seen
that the direction of the magnetic field around the conductor is clockwise if
viewed with current flowing away from the observer and anticlockwise if viewed
with the current flowing towards the observer.
current
flowing
towards
observer
conductor
current
carrying
conductor
magnetic field
direction of
current flow
current
flowing
away from
observer
Fig. 4 Current Flow Conventions and Associated Magnetic Fields
6
The Right Hand Screw Rule is a means of determining the direction of the
magnetic field surrounding a current carrying conductor as shown in Fig. 5. It is
stated as follows: If the conductor is grasped in the right hand with the thumb
facing in the direction of current flow then the fingers indicate the direction of the
surrounding magnetic field.
Fig. 5 The Right Hand Screw Rule
If the current carrying conductor is formed into a loop then the magnetic
field around the conductor can be seen to orientate so as to pass through the
loop as shown in Fig. 6. As can be expected, the intensity of the field will depend
on the area of the loop and the magnitude of the current flowing in the
conductor. It will be directly proportional to the current and inversely
proportional to the area of the loop.
direction of
current flow
direction of
current flow
direction of
magnetic field
Fig. 6 The Magnetic Field Formed through a Current Carrying Loop
7
This principle can be extended by winding a conductor, often on an
insulated former, so that several conducting loops are formed side-by-side to
create a coil as shown in Fig. 7.
Fig. 7 Conducting Coils
In this case the magnetic fields associated with the individual loops
combine so that a strong longitudinal magnetic field can be generated acting
through the coil as shown in Fig. 8. This is essentially the principle of an
electromagnet where an electrical source is used to provide current through the
coil and this current then creates a magnetic field. When the current ceases to
flow the magnetic field disappears. This principle can be exploited in a wide
range of electromagnetic devices and applications.
Fig. 8 A Wound Coil Generating an Internal Magnetic Field
8