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PHY002
Lecture Notes for Pre-Degree Science
Course Contents:
Magnets, Magnetic fields and Electrostatic
By
Odusote Y. A
Department of Physics
Federal University of Technology
P. M.B. 704, Akure, Ondo State.
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MAGNETS AND MAGNETIC FIELDS
Definitions:
A magnet has two poles North (N) and South (S).
A permanent magnet is a piece of ferromagnetic material (such as iron, nickel or cobalt) which has
properties of attracting other pieces of these materials. A permanent magnet will position itself in a
north and south direction when freely suspended. The north-seeking end of the magnet is called the
North pole, N, and the south-seeking end the South pole, S. If a bar magnet is suspended from its
midpoint and can swing freely in a horizontal plane, it will rotate until its north pole points to the
Earth’s geographic North Pole and its south pole points to the Earth’s geographic South Pole. (The same
idea is used in the construction of a simple compass) i.e. when suspended freely N shows north and S
shows south.
The area around a magnet is called the magnet field and it is in this area that the effects of the
magnetic force produced by the magnet can be detected. A magnetic field cannot be seen, felt, smelt or
heard and therefore is difficult to represent. Michael Faraday suggested that the magnetic field could be
represented pictorially, by imaging the field to consist of lines of magnetic flux, which enables
investigation of the distribution and density of the field to be carried out.(see Fig.1)
Fig. 1: Showing lines of magnetic flux
The distribution of a magnetic field can be investigated by using some iron fillings. A bar
magnet is placed on a flat surface covered by, say, cardboard, upon which is sprinkled some iron
fillings. If the cardboard is gently tapped the fillings will assume a pattern similar to that shown in Fig.
2(a, b,c) below. If a number of magnets of different strength are used, it is found that the stronger the
fields the closer are the lines of magnetic flux and vice-versa. Thus a magnet field has the property of
exerting a force, demonstrated in this case by causing the iron fillings to move into the pattern shown.
The strength of the magnetic field decreases as we move away from the magnet.
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Fig.2 (a) Magnetic field pattern surrounding a bar magnet as displayed with iron filings. (b) Magnetic
field pattern between unlike poles of two bar magnets. (c) Magnetic field pattern between like poles of
two bar magnets.
It should be noted that:
-Poles always exist in pairs;
-There is no magnetic monopoles; (All attempts thus far to detect an isolated magnetic pole have been
unsuccessful. No matter how many times a permanent magnet is cut in two, each piece always has a
north and a south pole.)
-Poles of a magnet have the same strength;
-Like poles repels, unlike poles attract each other.
Fig. 3: when a magnet is broken into half
Materials attracted by a magnet is called magnetic e.g. Iron, Nickel, while materials not attracted by a
magnet is called non-magnetic e.g. wood, plastic.
A compass is a navigational instrument for finding directions. It consists of a magnetised pointer free to
align itself accurately with Earth's magnetic field. A compass provides a known reference direction
which is of great assistance in navigation. The cardinal points are north, south, east and west. A compass
can be used in conjunction with a clock and a sextant to provide a very accurate navigation capability.
This device greatly improved maritime trade by making travel safer and more efficient.
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A compass can be any magnetic device using a needle to indicate the direction of the magnetic north of
a planet's magnetosphere. Any instrument with a magnetized bar or needle turning freely upon a pivot
and pointing in a northerly and southerly direction can be considered a compass.
Magnetic Flux and Flux Density
Magnetic flux is the amount of magnetic field (or the number of lines of force) produced by a magnetic
source. The symbol for magnetic flux is ϕ . The unit of 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 the flux.
magneticflux φ
= (unit Tesla,T)
area
A
The SI unit of magnetic field is the newton per coulomb-meter per second, which is called the tesla (T):
where 1T = 1Wb/m2; A(m2) is the area. Also there is Gauss(G): 1T = 104G
Magnetic flux density, B =
Example 1: A magnetic pole face has a rectangular section having dimensions 200mm by 100mm. If
the total flux emerging from the pole is 150µ Wb, calculate the flux density.
Solution:
Area, A = 200mm x100mm = 20,000mm2 =20,000 x 10-6m2.
Magnetic flux, = 150µWb = 150 x 10-6Wb
φ
150 x10 −6
= 0.0075T = 7.5mT
∴B = =
A 20000 x10 −6
Magnetic field of the earth
The earth is a giant magnet itself. The geographical pole and magnetic pole are not at the same place.
Declination angle is between geographical and magnetic north.(See Fig.4)
Inclination angle is between the magnet needle and horizontal. (Inclination angle is zero only at the
magnetic equator). The magnetic field of the earth is about 10-5T.
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Fig. 4: The Earth’s magnetic field lines. Note that a south magnetic pole is near the north
geographic pole, and a north magnetic pole is near the south geographic pole.
What is Electrostatic?
Electrostatics is the study of electric charge which is not moving i.e. is static.
Charge
All objects surrounding us (including people!) contain large amounts of electric charge. Charge can be
negative or positive and is measured in units called coulombs (C). Usually, objects contain the same
amount of positive and negative charge so its effect is not noticeable and the object is called electrically
neutral. However, if a small imbalance is created (i.e. there is a little bit more of one type of charge than
the other on the object) then the object is said to be electrically charged.
Some rather amusing examples of what happens when a person becomes charged are for example when
you charge your hair by combing it with a plastic comb and it stands right up on end! Another example
is when you walk fast over a nylon carpet and then touch a metal doorknob and give yourself a small
shock (alternatively you can touch your friend and shock them!)
Electric Charges: Production, types and storage of charges
In so many cases when two objects are rubbed against each other, they become charged and they are
said to posses ELECTRIC CHARGES. Examples are rubbing a piece of hard rubber, a glass rod or a
plastic with a cloth.
The amount of charge transferred depends on the type of materials and the intensity of the rubbing.
There is attraction when two balls suspended close to each other, one touch by the glass rod and the
other by the cloth (this is observed if the glass rod and the cloth have been rubbed together before).
When the two balls are touched by the same objects (glass rod or cloth) there is repulsion (Fig. 5).
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Fig. 5: Attraction and Repulsion Phenomenon.
What actually happens is that when you rub the glass with silk, tiny amounts of negative charge are
transferred from the glass onto the silk, which causes the glass to have less negative charge than positive
charge, making it positively charged. When you rub the plastic rod with the fur, you transfer tiny
amounts of negative charge onto the rod and so it has more negative charge than positive charge on it,
making it negatively charged.
From this evidence, Charles du Fay in 1733 concluded there are two kinds of charge, which he
called “Electric fluid”. As we can see from above like charges repel, and unlike charges attract. The
“electric fluid” on glass was named vitreous, while that on cloth was named resinous. He believed that
these fluids were separated by the friction involved in rubbing. However, around 1750, Benjamin
Franklin proposed the flow of a single fluid from one body to the other during the process of rubbing.
Positive charges was associated with the body that gains fluid and negative to the body that loses fluid
(this convention still stands till today).
PROPERTIES OF ELECTRIC CHARGE
Electric charge and electric forces play a major role in determining the behaviour of the universe. The
basis building blocks of matter, electrons and protons, have a property called electric charge. Electric
charge is observed to have the following characteristics:
(i)
An electric charge has a polarity; that is, it is either positive or negative.
Like charges repel each other, and opposite (unlike) charges attract.
(ii)
The force between charges is proportional to their magnitudes and varies as the
inverse square of their separation.
(iii) An electric charge is conserved. It cannot be created or destroyed. We obtain charges by
separating neutral objects into a negative piece and a positive piece.
(iv)
An electric charge is quantized. Not until 19th century electrical charge was considered to
be continuous. Experiments have shown that electrical charge is quantized (i.e. appears only
in discrete amounts). It is always observed to occur as an integer multiple of e, the
fundamental quantity of charge. We choose the unit of electric unit of electric charge as the
Coulomb, where e = 1.602 x 10-19 Coulomb (C). The charge on the electron is –e, and on a
proton +e.
Conductors are materials in which charge can move relatively freely and in which there are some
free charges. Examples of good conductors are metals, plasmas (ionized gases), liquids containing
ions (for examples, sulfuric acid, blood, salt water), and some semiconductors.
Insulators are materials that do not readily transport charge. Examples are a vacuum, glass, distilled
water, paper and rubber. There is not a sharp demarcation between conductors and insulators. Some
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materials (for example, Semiconductors like Silicon or Germanium) have properties intermediate
between a good conductor and a good insulator.
ELECTRIC CHARGE: WHERE DOES IT ORIGINATE?
The electric charge has it origin within the atom itself. Atoms are the building blocks of matter. They
are the basis of all the structures and organisms in the universe. The planets, the sun, grass and trees, the
air we breathe, and people are all made up of atoms.
Atoms are very small and cannot be seen with the naked eye. They consist of two main parts: the
positively charged nucleus at the centre and the negatively charged elementary particles called electrons
which surround the nucleus in their orbitals. (Elementary particle means that the electron cannot be
broken down to anything smaller and can be thought of as a point particle.) The nucleus of an atom is
made up of a collection of positively charged protons and neutral particles called neutrons.
Atoms are electrically neutral which means that they have the same number of negative electrons as
positive protons. The number of protons in an atom is called the atomic number which is sometimes also
called Z. The atomic number is what distinguishes the different chemical elements in the Periodic table
from each other. In fact, the elements are listed on the Periodic table in order of their atomic numbers.
For example, the first element, hydrogen (H), has one proton whereas the sixth element, carbon (C) has
6 protons. Atoms with the same number of protons (atomic number) share physical properties and show
similar chemical behaviour. The number of neutrons plus protons in the nucleus is called the atomic
mass of the atom. An atoms which has lost an electron is called an ion, i.e. +vely charged and is thus
able to attract an electron to itself from another atom. Electrons that move from one atom to another are
called free electrons and such random motion can continue indefinitely.
PRODUCTION OF CHARGES
Charges can be produced by the following two methods
•
Charging by Induction
•
Charging by Contact
Induction is a method through which an object can be charged. This process of charging is based on the
discovery of John Canton in 1753 that an insulated metal object can be charged even without connecting
it to a charged body. The process of charging without contact is termed INDUCTION.
When a negatively charged rod is brought near a square object, it leaves a negative charge at the
opposite end of the square object as shown below (Fig. 6). A charge is said to have been induced at the
two ends of the square object. No charge has been created; it has merely separated; the net charge on the
square object is still zero. However, if the metal were now cut in half, we would have two charged
objects, one positive and one negative.
There are two ways of creating a charged object, with net charge not equal to zero, by induction:
•
By charging two objects which are initially in contact with each other (Method 1)
•
By charging a single object, then earth it for charge neutralization (Method 2).
Method 1
Consider two square objects (1 and 2) on an insulating stands and initially in contact (Fig. 6). When a
negatively charged rod is brought close to 1, the free electrons in the object are repelled away from the
rod. This repulsion leaves unbalanced positive charge on the left side of object 1, and negative charge on
the right surface of object 2. The rod has induced a charge separation. The next step is to separate the
two objects with the rod still present. If the rod is removed before separating the objects, the charge
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separation will be lost and the objects will become neutral. The last step is the removal of the charged
rod. The charges carried by the two square objects are always equal and opposite.
(a)
(b)
(c)
Fig. 6: Two square objects given equal and opposite charges by the process of induction.
Method 2
This involves only one square object. The object is stand on an insulator (Fig. 7). When a negatively
charged rod is brought near, it induces a charge separation. The step that follows this is to connect the
object to the ground using for example a water pipe, while the rod is still present. (The earth is so large,
it can easily accept or give up electrons; hence it acts like a reservoir). Through this connection electron
will leave the object to the ground leaving the object positively charged.
The ground connection is then removed with the rod still present; because if the rod is moved away
before the connection is removed, the electrons would all have moved back into the object and it would
be neutral.
(a)
(b)
(c)
(d)
Fig. 7: A single square object charged by induction.
The Electroscope
The electroscope is a device for detecting small amount of charge. An electroscope consists of a
transparent container inside of which are two movable leaves often made of gold. The leaves are
attached by a conductor to a metal ball on the outside of the container, but are insulated from the
container itself. If a positively charged glass rod is brought near an uncharged electroscope, the
electrons in the knob are attracted to the glass rod. The motion of these electrons brings about an
unbalanced positive charge on the leaves, which causes them to repel each other (Fig. 8a). The leaves
will fall back to the vertical position if the rod is moved away.
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The knob can also be charged by conduction, in this case the whole apparatus becomes charged with the
same kind of charge (Fig. 8b). In both the induction and conduction methods of charging an
electroscope, the greater the amount of charge the stronger the repulsion between the leaves. Even, if
roughly, it is therefore clear that an electroscope can be used to measure the amount of charge.
(a)
(b)
Fig. 8: Electroscope charged by (a) Induction, (b) Conduction
The sign of the charge on an object can also be determined using an electroscope. This can be done by
first charging the electroscope (positively or negatively) by conduction. Suppose the electroscope is
charged negatively and a negative object is brought close, electrons are induced to move farther down
into the leaves and they separate further. On the other hand, if a positive object is brought close, the
electrons are induced to flow upward, leaving the leaves less negative and their separation is reduced
(Fig. 9).
Fig. 9: Determination of sign of a given charge
Coulomb's Law
The behaviour of the electrostatic force was studied in detail by Charles Coulomb around 1784.
Through his observations he was able to show that the electrostatic force between two point-like charges
is inversely proportional to the square of the distance between the objects. He also discovered that the
force is proportional to the product of the charges on the two objects.
Fα
Q 1Q 2
r2
where Q1 is the charge on the one point-like object, Q2 is the charge on the second, and r is the
distance between the two.
The magnitude of the electrostatic force between two point-like charges is given by Coulomb's
Law:
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F = k
Q 1Q 2
r2
and the proportionality constant k is called the electrostatic constant. We will use the value
k = 8:99 x 109N. m2/C2.
The value of the electrostatic constant is known to a very high precision (9 decimal places). Not
many physical constants are known to as high a degree of accuracy as k.
Aside: Notice how similar Coulomb's Law is to the form of Newton's Universal Law of Gravitation
between two point-like particles:
FG = G
m1m 2
r2
where m1 and m2 are the masses of the two particles, r is the distance between them, and G is the
gravitational constant. It is very interesting that Coulomb's Law has been shown to be correct no matter
how small the distance, nor how large the charge: for example it still applies inside the atom (over
distances smaller than 10-10m).
Let's run through a simple example of electrostatic forces.
Question 1: Two point-like charges carrying charges of +3 x10-9C and -5 x 10-9C are 2m apart.
Determine the magnitude of the force between them and state whether it is attractive or repulsive.
Solution:
Determine the magnitude of the force: Using Coulomb's Law we have
Q Q
( + 3 x 10 − 9 C )( − 5 x 10 − 9 C )
F = k 1 2 2 = ( 8 . 99 x 10 − 9 N ⋅ m 2 / C 2 )
r
(2 m )2
= − 3 . 37 x 10
−8
N
Thus the magnitude of the force is 3:37 x 10-8N. The minus sign is a result of the two point charges
having opposite signs. Is the force attractive or repulsive? Well, since the two charges are oppositely
charged, the force is attractive. We can also conclude this from the fact that Coulomb's Law
gives a negative value for the force.
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Question 2: Determine the electrostatic force and gravitational force between two electrons 1Åapart
(i.e. the forces felt inside an atom)
Solution: Get everything into S.I. units: The charge on an electron is -1.60 x 10-19C, the mass
of an electron is 9.11 x 10-31kg, and 1Å =1 x 10-10m.
Step 1: Calculate the electrostatic force using Coulomb's Law:
F =k
− 19
Q1Q2
e.e
C )( − 1 .60 x10 −19 C
2
2 ( − 1 .60 x10
=
=
−
⋅
k
(
8
.
99
x
10
9
N
m
/
C
)
r2
r2
(1x10 −10 m ) 2
= 2 .30 x10 − 8 N
Hence the magnitude of the electrostatic force between the electrons is 2.30 x10-8N. (Note that the
electrons carry like charge and from this we know the force must be repulsive. Another way to see this
is that the force is positive and thus repulsive.)
Step 2: Calculate the gravitational force:
−31
me ⋅ me
m1m2
kg )(9.11x10 −31 kg )
−11
2
2 (9.11x10
FG = G 2 = G
= (6.67 x10 N ⋅ m / kg )
r
r2
(1x10 −10 m) 2
= 5.54 x10 −51 N
The magnitude of the gravitational force between the electrons is 5:54 x 10-51N.
Note that the gravitational force between the electrons is much smaller than the electrostatic force. For
this reason, the gravitational force is usually neglected when determining the force between two charged
objects.
We mentioned above that charge placed on a spherical conductor spreads evenly along the surface. As a
result, if we are far enough from the charged sphere, electrostatically, it behaves as a point-like charge.
Thus we can treat spherical conductors (e.g. metallic balls) as point-like charges, with all the charge
acting at the centre.
Exercises:
1. Find the electric force that a proton exerts on an electron in a hydrogen atom. Compare the result
with the gravitational force between the two.
Hints:
m = 9.11 x10-31kg; m = 1.67x10-27kg; G=6.67x10−11N⋅m2/kg2
1
2
q = -1.6x10-19C; q = +1.6x10-19C; r = 0.052nm
1
2
2. What is meant by “charge is quantized”?
3. Which of the following items will be attracted to the north pole of a permanent magnet by a
magnetic force? (A) The north pole of another permanent magnet (B) A piece of iron that is not
a permanent magnet (C) A positively charged glass rod (D) A negatively charged rubber rod.
Suggested references:
1. University Physics W. Sears
2. Fundamentals of Physics by Halliday-Resnick-Walker
3. Advance level Physics by Nelkon and Parker
4. College Physics by Frederick, J Beuche and Eugene Hecht
5. College Physics 6edition by Faughn & Serway
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