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Chapter 21
Electric Charge and
Electric Field
PowerPoint® Lectures for
University Physics, Thirteenth Edition
– Hugh D. Young and Roger A. Freedman
Lectures by Wayne Anderson
Copyright © 2012 Pearson Education Inc.
Goals for Chapter 21
• To study electric charge and charge conservation
• To see how objects become charged
• To calculate the electric force between objects
using Coulomb’s law
• To learn the distinction between electric force and
electric field
• To calculate the electric field due to many charges
• To visualize and interpret electric fields
• To calculate the properties of electric dipoles
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Electric charge
• Two positive or two negative charges repel each other. A positive
charge and a negative charge attract each other.
• Figure 21.1 below shows some experiments in electrostatics.
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Figure 21.4a
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Figure 21.4b
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Conservation of charge
• The proton and electron have the same magnitude
charge.
• The magnitude of charge of the electron or proton is a
natural unit of charge. All observable charge is
quantized in this unit.
• The universal principle of charge conservation states
that the algebraic sum of all the electric charges in any
closed system is constant.
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Conductors and insulators
• A conductor permits the
easy movement of charge
through it. An insulator
does not.
• Most metals are good
conductors, while most
nonmetals are insulators.
(See Figure 21.6 at the
right.)
• Semiconductors are
intermediate in their
properties between good
conductors and good
insulators.
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Charging by induction
• In Figure 21.7 below, the negative rod is able to charge the metal
ball without losing any of its own charge. This process is called
charging by induction.
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Figure 21.7a
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Figure 21.7b
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Figure 21.7c
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Figure 21.7d
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Figure 21.7e
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Electrostatic painting
• Induced positive charge on the metal object attracts the
negatively charged paint droplets.
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Coulomb’s law
• Coulomb’s Law: The
magnitude of the electric
force between two point
charges is directly
proportional to the
product of their charges
and inversely proportional
to the square of the
distance between them.
(See the figure at the
right.)
• Mathematically:
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F k
q1q2
r
2

1
q1q2
4 0 r 2
Measuring the electric force between point charges
• The figure at the upper
right illustrates how
Coulomb used a torsion
balance to measure the
electric force between
point charges.
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Example 21.1
An alpha particle (an He nucleus
or He2+) has a mass of 6.64 x 1027 kg and a charge of 3.2 x 10-19
C. Compare the magnitude of the
electric repulsive force with the
gravitational attraction, for any
separation, r.
q2
Fe  k 2
r
q2
k 2
2
Fe
kq
35
 r2 

3.1

10
m
Fg
Gm2
G 2
r
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m2
Fg  G 2
r
Example 21.3 Force between charges along a line
• Two point charges are located on the x-axis of a coordinate
system: q1=1.0 nC is at x = +2.0 cm, and q2 = -3.0 nC is at x=
+4.0 cm. What is the total electric force exerted by q1 and q2 on
charge q3?
The force on q3 (F3) is the combination of the force
applied by q1 (F13) and the force applied by q2 (F23).
F13  112  Niˆ
F23  84 Niˆ
F3  112  Niˆ  84  Niˆ  28 Niˆ
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Example 21.4 Vector addition of electric forces
• Two equal charges q1=q2= 2.0 µC are located at x=0, y=0.30 m
and x=0, y=-0.30 m, respectively. What are the magnitude and
direction of the total electric force that q1 and q2 exert on a third
charge Q=4.0 µC at x=0.40 m and y=0?
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Ftotal
Ftotal
q1Q
 2 F1onQ  2k 2 cos  iˆ
r
6
6
9
2
2 (4  10 C )(2.0  10 C )  4  ˆ
 2(9 10 Nm / C )
  i  0.23Niˆ
2
(0.50m)
5
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Electric field
• A charged body produces an electric field in the space around it
(see Figure 21.15 at the lower left).
• We use a small test positive charge q0 to find out if an electric field
is present (see Figure 21.16 at the lower right).
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Definition of the electric field
• Follow the definition in the text of the electric field
using Figure 21.17 below.
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Electric field of a point charge
• Follow the discussion in the text of the
electric field of a point charge, using
Figure 21.18 at the right.
• Follow Example 21.5 to calculate the
magnitude of the electric field of a
single point charge.
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Example 21.6 Electric-field vector of a point charge
• Find the electric field at
the indicated point.
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Example 21.7 Electron in a uniform field
When the terminals of a battery are connected to two
parallel plates with a small gap between them, the resulting
charges on the plates produce a nearly uniform electric field
E. If the plates are 1.0 cm apart and are connected to a 100volt battery the field is vertically upward and has a
magnitude E=1.00 x 104 N/C (a) If an electron (charge –e =
-1.60 x 10-19 C and mass = 9.11 x 10-31 kg is released from
rest at the upper plate, what is its acceleration? (b) What
speed and kinetic energy does it acquire while travelling 1.0
cm to the lower plate? (c) How long does it take to travel
this distance?
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Example 21.7
ay 
Fy
m

eE
 1.76 1015 m / s 2
m
Is it OK to ignore
g=-9.81m/s2 in this
problem?
KE  qV  (1.6 1019 C)(100V )  1.6 1017 J
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Example 21.7
1
KE  mv 2f
2
2 KE
2(1.6 1017 J )
6
vf 


5.9

10
m / s  0.02c
31
m
9.1110 kg
2s
2(0.01m)
9
t


3.4

10
s
6
v f 5.9 10 m / s
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Charge Densities
Charge can be distributed in various shapes.
We’ll look at three possibilities: a wire, a sheet
and a block. If we assume the charge is evenly
distributed throughout the shape, we can define
a linear charge density, lambda (C/m), a
surface charge density, sigma (C/m2) and a
volume charge density, rho (C/m3)
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Example 21.8 Electric field of a dipole
Point charges q1=+12 nC and q2=-12 nC are 0.100m apart. Calculate the
field caused by q1, the field caused by q2 and the total field at points a, b
and c.
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Example 21.8
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Example 21.9 Field of a ring of charge
• Change Q is uniformly distributed around a conducting
ring of radius a. Find the electric field at a point P on
the ring axis at a distance x from its center.
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Example 21.9 alternate approach
Figure 21.3 can be reconfigured to the situation shown below.
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Paradigm for Example 21.9
1. Identify given values
2. Identify salient equations
dE 
1
dQ
4 0 x 2  a 2
3. Express equations in differential form, i.e.
4. Determine correct limits for integral
5. Perform integral
6. Evaluate result. What happens at the
extremes, i.e. 0 and infinity? Does it conform
to what we already know?
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Example 21.10
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Example 21.11
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Electric field lines
•
An electric field line is an imaginary line or curve
whose tangent at any point is the direction of the electric
field vector at that point. (See Figure 21.27 below.)
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Electric field lines of point charges
•
Figure 21.28 below shows the electric field lines of a single point
charge and for two charges of opposite sign and of equal sign.
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Michael Faraday
1791-1867
The Farad
Explained much of what
we know about
magnetic forces
Source: St. Andrews College
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Made some of the first
electric motors and
generators
Michael Faraday
When asked by a
politician what good
they were, he replied
“At present I do not
know, but one day you
will be able to tax them.”
Source: St. Andrews College
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Electric dipoles
• An electric dipole is a pair
of point charges having
equal but opposite sign and
separated by a distance.
• Figure 21.30 at the right
illustrates the water
molecule, which forms an
electric dipole.
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Force and torque on a dipole
The forces on a dipole in a constant electric field, E. Figure 21.31
These forces cause a torque because they are not co-linear.
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Example 21.13 Force and torque on an electric dipole
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Goals for Chapter 21
• To study electric charge and charge conservation
• To see how objects become charged
• To calculate the electric force between objects
using Coulomb’s law
• To learn the distinction between electric force and
electric field
• To calculate the electric field due to many charges
• To visualize and interpret electric fields
• To calculate the properties of electric dipoles
Copyright © 2012 Pearson Education Inc.
Question 21.7 The figure
shows some of the
electric field lines due to
three point charges
arranged along the
vertical axis. All three
charges have the same
magnitude. (a) what are
the signs of the three
charges? (b) At what
point(s) is the magnitude
of the electric field the
smallest? Explain how
the electric fields
combine to yield this
small value of E?
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