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2005 Pearson Education South Asia Pte Ltd
ELECTROMAGNETISM
FE1001 Physics I NTU - College of Engineering
21. Electric Charge and
Electric Field
22. Gausss Law
23. Electric Potential
24. Capacitance and
Dielectrics
25. Current, Resistance, and ElectromotiveForce
26. Direct-Current Circuits
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ELECTROMAGNETISM
FE1001 Physics I NTU - College of Engineering
27. Magnetic Field and
Magnetic Forces
28. Sources of Magnetic Field
29. Electromagnetic Induction
30. Inductance
31. Alternating Current
32. Electromagnetic Waves
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21. Electric Charge and Electric Field
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Chapter Objectives
The nature of electric charge Interactions of electric charges
Coulombs law
The concept of electric field
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21. Electric Charge and Electric Field
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Chapter Outline
1. Electric Charge
2. Conductors, Insulators, and Induced Charges
3. Coulombs Law
4. Electric Field and Electric Forces
5. Electric-Field Calculations6. Electric Field Lines
7. Electric Dipoles
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21. Electric Charge and Electric Field
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21.1 Electric Charge
Electric chargeis a fundamental attribute of
particles.
Electrostatics are defined as the interactions
between electric charges that are at rest (or nearlyso).
The figure shows some experiments used todemonstrate electrostatics.
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21. Electric Charge and Electric Field
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21.1 Electric Charge
Fig. 21.1
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21. Electric Charge and Electric Field
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21.1 Electric Charge
Electrostatics experiments show that there are
exactly two kinds of electric charge, negativeand
positive.
Two positive charges or two negative chargesrepel each other. A positive charge and a
negative charge attract each other.
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21. Electric Charge and Electric Field
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21.1 Electric Charge
CAUTION
Like charges only mean that two charges have
the same algebraic sign(both positive or both
negative).
Opposite charges means that the electriccharges on both objects have different signs
(one positive and the other negative).
A technological application is in a laser printer; the
figure shows a schematic diagram of such a printer
in operation.
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21. Electric Charge and Electric Field
2005 Pearson Education South Asia Pte Ltd Fig. 21.2
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21. Electric Charge and Electric Field
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21.1 Electric Charge
Electric Charge and the Structure of Matter
The atomic structure consists of three particles: the
negatively charged electron, the positively charged
proton, and the uncharged neutron.
Protons and neutrons make up the nucleuswhile
electrons orbit it from a distance.
The figure shows how changes in the atomic
structure of lithium determines its net electric
charge.
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21. Electric Charge and Electric Field
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21.1 Electric Charge
Electric Charge and the Structure of Matter
Fig. 21.4
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21. Electric Charge and Electric Field
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21.1 Electric Charge
Electric Charge and the Structure of Matter
Atomic numberis defined as the number of
protons or electrons in a neutral atom of an
element.
A positive ionis formed by removing one or more
electrons from an atom; a negative ionis one that
has gainedone or more electrons. This process is
called ionization.
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21. Electric Charge and Electric Field
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21.1 Electric Charge
Electric Charge and the Structure of Matter
When the total number of protons equals the total
number of electrons in a macroscopic body, its total
charge is zero and the body as a whole is
electrically neutral.
When we speak of the charge of a body, we always
mean its netcharge.
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21. Electric Charge and Electric Field
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21.1 Electric Charge
Electric Charge and the Structure of Matter
The Principle of Conservation of Charge: The
algebraic sum of all the electric charges in any
closed system is constant.
In any charging process, charge is not created or
destroyed but merely transferredfrom one body to
another.
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21. Electric Charge and Electric Field
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21.1 Electric Charge
Electric Charge and the Structure of Matter
The magnitude of charge of the electron or
proton is a natural unit of charge.
Every observable amount of electric charge on any
macroscopic body is always either zero or an
integer multiple (positive or negative) of this basic
unit, the electron chargequantization of charge.
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21.2 Conductors, Insulators, and Induced Charges
Fig. 21.5
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21.2 Conductors, Insulators, and Induced Charges
Charging by inductionis the process in which a
charged body can give another body a charge of
oppositesign without losing any of its own charge.
The figure shows the charging of a metal sphere byinduction.
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21.2 Conductors, Insulators, and Induced Charges
Fig. 21.6
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21.2 Conductors, Insulators, and Induced Charges
Excess charges that develop in the region of a
body during electrical induction are called induced
charges.
The earth is a conductor, and it is so large that itcan act as an infinite source of extra electrons or
sink of unwanted electrons. The charge it acquires
via induction will be equal and opposite to the
charge remaining on the electrically induced body.
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21. Electric Charge and Electric Field
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21.2 Conductors, Insulators, and Induced Charges
In a metallic conductor, the mobile charges are
always negative electrons.
In ionic solutions and ionized gases, both positive
and negative charges are mobile.
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21.2 Conductors, Insulators, and Induced Charges
A charged body can exert forces even on objects
that are notcharged themselvesinduced-charge
effect.
This is due topolarization, in which a chargedobject of eithersign exerts an attractive force on an
uncharged (neutral) insulator.
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Coulombs Lawstates that:
The magnitude of the electric force between
two point charges is directly proportional to the
product of the charges and inverselyproportional to the square of the distance
between them.
The directions of the forces the two charges exert
on each other are always along the line joining
them, as shown in the figure.
21.3 Coulombs Law
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21.3 Coulombs Law
Fig. 21.9
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21.3 Coulombs Law
Coulombs Law is usually written as:
where
229
0
22120
/100.94
1
/10854.8
CmN
mNC
21 C
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21.3 Coulombs Law
The most fundamental unit of charge is the
magnitude of the charge of an electron or proton,
denoted by e, where
e= 1.602176462(63) x 10-19
C
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Example 21.1 Electric force versus gravitational force
An particle (alpha) is the nucleus of a helium
atom. It has a mass of m= 6.66 x 10-27kg and a
charge q= +2e= 3.2 x 10-19C. Compare the force of
the electric repulsion between two particles with the
force of gravitational attraction between them.
21 El t i Ch d El t i Fi ld
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Example 21.1 (SOLN)
Identify and Set Up
The magnitudeFeof the electric force is given by
Eq. (21.2),
The magnitudeFgof the gravitational force is givenby Eq. (12.1),
We compare these two magnitudes by calculating
their ratio.
2
2
04
1
r
qFe
2
2
r
mGFg
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Example 21.1 (SOLN)
Execute
The ratio of the electric force to the gravitational force
is
35
227
219
2211
229
2
2
0
101.3
)1066.6(
)102.3(
/1067.6
/100.9
4
1
kg
C
kgmN
CmN
m
q
GF
F
g
e
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21. Electric Charge and Electric Field
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Example 21.1 (SOLN)
Evaluate
This astonishingly large number shows that the
gravitational force in this situation is completely
negligible in comparison to the electric force. This is
always true for interactions of atomic and subatomicparticles. (Notice that this result doesnt depend on
the distance rbetween the two particles.) But within
objects the size of a person or a planet, the positive
and negative charges are nearly equal in magnitude,and the net electric force is usually much smallerthan
the gravitational force.
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Example 21.2 (SOLN)
Identify and Set Up
We use Coulombs law, Eq. (21.2), to calculate the
magnitude of the force that each particle exerts on
the other. The problem asks us for the force on
each particle due to the other particle, so we useNewtons third law.
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21. Electric Charge and Electric Field
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Example 21.2 (SOLN)
Execute
a) Converting charge to coulombs and distance to
meters, the magnitude of the force that q1exerts on q2 is
N
m
CCCmN
r
qq
F on
019.0
)030.0(
|)1075)(1025(|)/100.9(
||
4
1
2
99229
221
021
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21. Electric Charge and Electric Field
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Example 21.2 (SOLN)
Since the two charges
have opposite signs, the
force is attractive; that is,
the force that acts on q2is
directed toward q1alongthe line joining the two
charges, as shown in Fig.
21.10b.
Fig. 21.10
21 Electric Charge and Electric Field
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Example 21.2 (SOLN)
b) Remember that Newtons third law applies to the
electric force. Even though the charges have
different magnitudes, the magnitude of the force that
q2exerts on q1is the same as the magnitude of the
force that q1exerts on q2:
Newtons third law also states that the direction of the
force that q2exerts on q1is exactly opposite the
direction of the force that q1exerts on q2 ; this is shown
in Fig. 21.10c.
NF on 019.012
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21. Electric Charge and Electric Field
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Example 21.2 (SOLN)
Evaluate
Note that the force on q1is directed toward q2, as it
must be, since charges of opposite sign attract each
other.
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Example 21.3 Vector addition of electric forces on a line
Two point charges are located on the positivex-axis
of a coordinate system (Fig. 21.11a). Charge q1= 1.0
nC is 2.0 cm from the origin, and charge q2= -3.0 nC
is 4.0 cm from the origin. What is the total force
exerted by these two charges on a charge q3= 5.0 nClocated at the origin? Gravitational forces are
negligible.
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21. Electric Charge and Electric Field
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Example 21.3 (SOLN)
Identify
Here there are twoelectric forces acting on the
charge q3, and we must add these forces to find the
total force.
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21. Electric Charge and Electric Field
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Example 21.3 (SOLN)
Set Up
Figure 21.11a shows the
coordinate system. Our
target variable is the net
electric force exerted oncharge q3by the other
two charges. This is the
vector sum if the forces
due to q1and q2individually. Fig. 21.11
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Example 21.3 (SOLN)
Execute
Figure 21.11b is a free-body diagram for charge q3.
Note that q3is repelled by q1(which has the same
sign) and attracted to q2(which has the opposite
sign).
21 Electric Charge and Electric Field
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21. Electric Charge and Electric Field
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Example 21.3 (SOLN)
Execute
Converting charge to coulombs and distance to
meters, we use Eq. (21.2) to find the magnitudeF1 on 3
of the force of q1on q3:
This force has a negativex-component because q3is
repelled (that is, pushed in the negativex-direction)
by q1.
NN
m
CCCmN
rqqF on
1121012.1
)020.0(
|)100.5)(100.1(|)/100.9(
||4
1
4
2
99229
231
031
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21. Electric Charge and Electric Field
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Example 21.3 (SOLN)
Execute
The magnitudeF2 on 3of the force of q2on q3is
This force has a positivex-component because q3isattracted (that is, pulled in the positivex-direction) by
q2.
NN
m
CCCmN
r
qqF on
84104.8
)040.0(
|)100.5)(100.3(|)/100.9(
||
4
1
5
2
99229
232
032
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21. Electric Charge and Electric Field
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Example 21.3 (SOLN)
Execute
The sum of thex-components is
There are noy-orz-components. Thus the total
force on q3 is directed to the left, with magnitude 28N = 2.8 x 10-5N.
NNNFx 2884112
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Example 21.3 (SOLN)
Evaluate
To check the magnitudes of the individual forces,
note that q2 has three times as much charge (in
magnitude) as q1but is twice as far from q3. From
Eq. (21.2) this means that F2 on 3must be 3/22= aslarge as F1 on 3. Indeed, our results show that this ratio
is (84 N)/(112 N) = 0.75. The direction of the net
force also makes sense: is opposite to and has a
larger magnitude than , so the net force is in the
direction of .
4
3
31onF
32onF
31onF
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21. Electric Charge and Electric Field
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Example 21.4 Vector addition of electric forces in a plane
In Fig. 21.12, two equal
positive point charges q1
= q2= 2.0 C interact with
a third point charge Q=
4.0 C. Find themagnitude and direction
of the total (net) force on
Q.
Fig. 21.12
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21. Electric Charge and Electric Field
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Example 21.4 (SOLN)
Identify and Set Up
As in Example 21.3, we have to compute the force
each charge exerts on Q and then find the vector sum
of the forces. The easiest way to do this is to use
components.
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21. Electric Charge and Electric Field
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Example 21.4 (SOLN)
Execute
Figure 21.12 shows the force on Qdue to the upper
charge q1. From Coulombs law the magnitudeFof
this force is
N
mCCCmNF Qon
29.0
50.0)100.2)(100.4()/100.9(
2
66
2291
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Example 21.4 (SOLN)
Execute
The angle is below thex-axis, so the components
of this force are given by
Nm
mNFF
N
m
mNFF
QonyQon
QonxQon
17.050.0
30.0)29.0(sin)()(
23.0
50.0
40.0)29.0(cos)()(
11
11
21. Electric Charge and Electric Field
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21. Electric Charge and Electric Field
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Example 21.4 (SOLN)
Execute
The lower charge q2exerts a force with the same
magnitude but at an angle abovethex-axis. From
symmetry we see that itsxcomponent is the same as
that due to the upper charge, but itsycomponent hasthe opposite sign. So the components of the total
force on Qare
The total force on Qis in the +x-direction, with
magnitude 0.46 N.
F
017.017.0
46.023.023.0
NNF
NNNF
y
x
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21. Electric Charge and Electric Field
Example 21.4 (SOLN)
Evaluate
The total force on Qis in a direction that points
neither directly away from q1nor directly away from
q2. Rather, this direction is a compromise that points
away from the systemof charges q1 and q2. Can yousee that the total force would notbe in the +x-
direction if q1 and q2were not equal or if the
geometrical arrangement of the charges were not so
symmetrical?