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PHYSICS 2415
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Copyright © 2009 Pearson Education, Inc.
Chapter 21
Electric Charge and
Electric Field
Copyright © 2009 Pearson Education, Inc.
Units of Chapter 21
• Static Electricity; Electric Charge and Its
Conservation
• Electric Charge in the Atom
• Insulators and Conductors
• Induced Charge; the Electroscope
• Coulomb’s Law
• The Electric Field
• Electric Field Calculations for Continuous
Charge Distributions
Copyright © 2009 Pearson Education, Inc.
Units of Chapter 21
• Field Lines
• Electric Fields and Conductors
• Motion of a Charged Particle in an Electric
Field
• Electric Dipoles
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21-1 Static Electricity; Electric
Charge and Its Conservation
Objects can be charged by rubbing
Copyright © 2009 Pearson Education, Inc.
21-1 Static
Electricity; Electric
Charge and Its
Conservation
Charge comes in two
types, positive and
negative; like charges
repel and opposite
charges attract.
Copyright © 2009 Pearson Education, Inc.
ConcepTest 21.1a Electric Charge I
Two charged balls are
repelling each other as
they hang from the ceiling.
What can you say about
their charges?
1) one is positive, the other
is negative
2) both are positive
3) both are negative
4) both are positive or both
are negative
ConcepTest 21.1a Electric Charge I
Two charged balls are
repelling each other as
they hang from the ceiling.
What can you say about
their charges?
1) one is positive, the other
is negative
2) both are positive
3) both are negative
4) both are positive or both
are negative
The fact that the balls repel each
other can tell you only that they
have the same charge, but you do
not know the sign. So they can
be either both positive or both
negative.
Follow-up: What does the picture look like if the two balls are oppositely
charged? What about if both balls are neutral?
21-1 Static Electricity; Electric
Charge and Its Conservation
Electric charge is conserved – the
arithmetic sum of the total charge cannot
change in any interaction.
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21-2 Electric Charge in the Atom
Atom:
Nucleus (small,
massive, positive
charge)
Electron cloud (large,
very low density,
negative charge)
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Elementary charge
Charge on the electron:
e = 1.602 x 10-19 C.
Electric charge is quantized in units
of the electron charge.
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21-2 Electric Charge in the Atom
Polar molecule: neutral overall, but charge not
evenly distributed
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21-3 Insulators and Conductors
Conductor:
Insulator:
Charge flows freely
Almost no charge flows
Metals
Most other materials
Some materials are semiconductors.
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21-4 Induced Charge; the
Electroscope
Metal objects can be charged by conduction:
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21-4 Induced Charge; the
Electroscope
They can also be charged by induction, either
while connected to ground or not:
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21-4 Induced Charge; the
Electroscope
Nonconductors won’t become charged by
conduction or induction, but will experience
charge separation:
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21-4 Induced Charge; the
Electroscope
The electroscope
can be used for
detecting charge.
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21-4 Induced Charge; the
Electroscope
The electroscope can be charged either by
conduction or by induction.
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21-4 Induced Charge; the
Electroscope
The charged electroscope can then be used to
determine the sign of an unknown charge.
Copyright © 2009 Pearson Education, Inc.
ConcepTest 21.2b Conductors II
Two neutral conductors are connected
1)
0
0
by a wire and a charged rod is brought
2)
+
–
3)
–
+
4)
+
+
5)
–
–
near, but does not touch. The wire is
taken away, and then the charged rod
is removed. What are the charges on
the conductors?
0
0
?
?
ConcepTest 21.2b Conductors II
Two neutral conductors are connected
1)
0
0
by a wire and a charged rod is brought
2)
+
–
3)
–
+
4)
+
+
5)
–
–
near, but does not touch. The wire is
taken away, and then the charged rod
is removed. What are the charges on
the conductors?
While the conductors are connected, positive
0
0
?
?
charge will flow from the blue to the green
ball due to polarization. Once disconnected,
the charges will remain on the separate
conductors even when the rod is removed.
Follow-up: What will happen when the
conductors are reconnected with a wire?
21-5 Coulomb’s Law
Experiment shows that 1) the electric force
between two charges is proportional to the
product of the charges and 2) inversely
proportional to the distance between them.
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21-5 Coulomb’s Law
Coulomb’s law:
This equation gives the magnitude of
the force between two charges.
In vector form:
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Q1Q2
F21  k 2 rˆ21
r21
21-5 Coulomb’s Law
Unit of charge: coulomb, C.
The proportionality constant in Coulomb’s
law is then:
k = 8.99 x 109 N·m2/C2.
Charges produced by rubbing are
typically around a microcoulomb:
1 μC = 10-6 C.
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21-5 Coulomb’s Law
The proportionality constant k can also be
written in terms of ε0, the permittivity of free
space:
1C 1C 

1N  k
2
1m 
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1 statC 1 statC 

or in cgs units 1dyne 
2
1cm 
21-5 Coulomb’s Law
The force is along the line connecting the
charges, and is attractive if the charges are
opposite, and repulsive if they are the same.
Newton’s Third Law applies!
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21-5 Coulomb’s Law
Example: Three charges in a line.
Three charged particles are arranged in a line,
as shown. Calculate the net electrostatic force
on particle 2 (the +3.0 μC in the middle) due to
the other two charges.
Copyright © 2009 Pearson Education, Inc.
ConcepTest 21.4b Electric Force II
Two balls with charges +Q and +4Q are separated by 3R. Where
should you place another charged ball Q0 on the line between
the two charges such that the net force on Q0 will be zero?
+4Q
+Q
1
2
3
4
2R
R
3R
5
ConcepTest 21.4b Electric Force II
Two balls with charges +Q and +4Q are separated by 3R. Where
should you place another charged ball Q0 on the line between
the two charges such that the net force on Q0 will be zero?
+4Q
+Q
1
2
3
4
5
2R
R
3R
The force on Q0 due to +Q is:
F = k(Q0)(Q)/R2
The force on Q0 due to +4Q is:
F = k(Q0)(4Q)/(2R)2
Since +4Q is 4 times bigger than +Q, Q0 needs to be farther
from +4Q. In fact, Q0 must be twice as far from +4Q, since
the distance is squared in Coulomb’s law.
21-5 Coulomb’s Law
Force is a vector quantity:
Example: Calculate the
net electrostatic force on
charge q3 shown in the
figure due to the charges
q1 and q2.
q1  q3  5.00 C
q2  2.00 C
a  0.100 m
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q1q2
F12  k 2 rˆ12
r12
Coulomb’s Law
r  r
q q
q q
 F  k 2  k 2  k q q
r
r
 F  attractive
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 1
1 
 r2  r2   0
   
21-6 The Electric Field
The electric field is defined as the force on a
small charge, divided by the magnitude of the
charge:
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21-6 The Electric Field
An electric field surrounds every charge.
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21-6 The Electric Field
For a point charge:
F
Q
E  r  is a vector: E pt   k 2 rˆ
q
r
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21-6 The Electric Field
Force on a point
charge in an
electric field:
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21-6 The Electric Field
Example: Calculate the
total electric field at
point P due to both
charges, q and -q.
Hint: exploit symmetry!
What direction would E
point if both charges were
equal, not opposite?
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21-6 The Electric Field
Problem solving in electrostatics: electric
forces and/or electric fields
1. Draw a diagram; show all charges, with
signs, and electric fields and forces with
directions.
2. Calculate forces using Coulomb’s law.
3. Add forces vectorally to get result.
4. Check your answer!
Copyright © 2009 Pearson Education, Inc.
ConcepTest 21.9b Superposition II
What is the electric field at
-2 C
2
-2 C
1
the center of the square?
3
5) E = 0
-2 C
4
-2 C
ConcepTest 21.9b Superposition II
What is the electric field at
-2 C
2
-2 C
1
the center of the square?
3
5) E = 0
-2 C
The four E field vectors all point outward
from the center of the square toward their
respective charges. Because they are all
equal, the net E field is zero at the center!!
Follow-up: What if the upper two charges were +2 C?
What if the right-hand charges were +2 C?
4
-2 C
Questions?
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