Download PSE4_Lecture_1_Ch21

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
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Units of Chapter 21
• Field Lines
• Electric Fields and Conductors
• Motion of a Charged Particle in an Electric
Field
• Electric Dipoles
• Electric Forces in Molecular Biology: DNA
• Photocopy Machines and Computer
Printers Use Electrostatics
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21-1 Static Electricity; Electric
Charge and Its Conservation
Objects can be charged by rubbing
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21-1 Static
Electricity; Electric
Charge and Its
Conservation
Charge comes in two
types, positive and
negative; like charges
repel and opposite
charges attract.
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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?
ConcepTest 21.1b Electric Charge II
From the picture,
what can you
conclude about
the charges?
1)
have opposite charges
2)
have the same charge
3)
all have the same charge
4) one ball must be neutral (no charge)
ConcepTest 21.1b Electric Charge II
From the picture,
what can you
conclude about
the charges?
1)
have opposite charges
2)
have the same charge
3)
all have the same charge
4) one ball must be neutral (no charge)
The GREEN and PINK balls must
have the same charge, since they
repel each other. The YELLOW
ball also repels the GREEN, so it
must also have the same charge
as the GREEN (and the PINK).
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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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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ConcepTest 21.2a Conductors I
A metal ball hangs from the ceiling
1) positive
by an insulating thread. The ball is
2) negative
attracted to a positive-charged rod
3) neutral
held near the ball. The charge of
4) positive or neutral
the ball must be:
5) negative or neutral
ConcepTest 21.2a Conductors I
A metal ball hangs from the ceiling
1) positive
by an insulating thread. The ball is
2) negative
attracted to a positive-charged rod
3) neutral
held near the ball. The charge of
4) positive or neutral
the ball must be:
5) negative or neutral
Clearly, the ball will be attracted if its
charge is negative. However, even if
the ball is neutral, the charges in the
ball can be separated by induction
(polarization), leading to a net
attraction.
Remember
the ball is a
conductor!
Follow-up: What happens if the metal ball is replaced by a plastic ball?
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.
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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 the electric force
between two charges is proportional to the
product of the charges and 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.
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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.
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ConcepTest 21.3a Coulomb’s Law I
What is the magnitude
1) 1.0 N
2) 1.5 N
of the force F2?
3) 2.0 N
F1 = 3 N
Q
Q
F2 = ?
4) 3.0 N
5) 6.0 N
ConcepTest 21.3a Coulomb’s Law I
What is the magnitude
1) 1.0 N
2) 1.5 N
of the force F2?
3) 2.0 N
F1 = 3 N
Q
Q
F2 = ?
4) 3.0 N
5) 6.0 N
The force F2 must have the same magnitude as F1. This is
due to the fact that the form of Coulomb’s law is totally
symmetric with respect to the two charges involved. The
force of one on the other of a pair is the same as the reverse.
Note that this sounds suspiciously like Newton’s 3rd law!!
ConcepTest 21.3b Coulomb’s Law II
F1 = 3 N
Q
Q
F2 = ?
2) 3.0 N
If we increase one charge to 4Q,
what is the magnitude of F1?
F1 = ?
4Q
Q
1) 3/4 N
F2 = ?
3) 12 N
4) 16 N
5) 48 N
ConcepTest 21.3b Coulomb’s Law II
F1 = 3 N
Q
Q
F2 = ?
2) 3.0 N
If we increase one charge to 4Q,
what is the magnitude of F1?
F1 = ?
4Q
Q
1) 3/4 N
F2 = ?
3) 12 N
4) 16 N
5) 48 N
Originally we had:
F1 = k(Q)(Q)/r2 = 3 N
Now we have:
F1 = k(4Q)(Q)/r2
which is 4 times bigger than before.
Follow-up: Now what is the magnitude of F2?
ConcepTest 21.3c Coulomb’s Law III
The force between two charges
1) 9F
separated by a distance d is F. If
2) 3F
the charges are pulled apart to a
3) F
distance 3d, what is the force on
4) 1/3F
each charge?
5) 1/9F
F
F
Q
Q
d
?
?
Q
Q
3d
ConcepTest 21.3c Coulomb’s Law III
The force between two charges
1) 9F
separated by a distance d is F. If
2) 3F
the charges are pulled apart to a
3) F
distance 3d, what is the force on
4) 1/3F
each charge?
5) 1/9F
F
Originally we had:
F
Q
Q
Fbefore = k(Q)(Q)/d2 = F
Now we have:
Fafter = k(Q)(Q)/(3d)2 = 1/9F
d
?
?
Q
Q
3d
Follow-up: What is the force if the original distance is halved?
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
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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21-5 Coulomb’s Law
The proportionality constant k can also be
written in terms of ε0, the permittivity of free
space:
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21-5 Coulomb’s Law
Conceptual Example 21-1: Which charge
exerts the greater force?
Two positive point charges, Q1 = 50 μC
and Q2 = 1 μC, are separated by a
distance . Which is larger in magnitude,
the force that Q1 exerts on Q2 or the force
that Q2 exerts on Q1?
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21-5 Coulomb’s Law
Example 21-2: Three charges in a line.
Three charged particles are arranged in a line,
as shown. Calculate the net electrostatic force
on particle 3 (the -4.0 μC on the right) due to the
other two charges.
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ConcepTest 21.4a Electric Force I
Two balls with charges +Q and +4Q
are fixed at a separation distance of
3R. Is it possible to place another
charged ball Q0 on the line between
the two charges such that the net
force on Q0 will be zero?
1) yes, but only if Q0 is positive
2) yes, but only if Q0 is negative
3) yes, independent of the sign
(or value) of Q0
4) no, the net force can never
be zero
+4Q
+Q
3R
ConcepTest 21.4a Electric Force I
Two balls with charges +Q and +4Q
are fixed at a separation distance of
3R. Is it possible to place another
charged ball Q0 on the line between
the two charges such that the net
force on Q0 will be zero?
1) yes, but only if Q0 is positive
2) yes, but only if Q0 is negative
3) yes, independent of the sign
(or value) of Q0
4) no, the net force can never
be zero
A positive charge would be repelled
by both charges, so a point where
these two repulsive forces cancel
+4Q
+Q
can be found. A negative charge
would be attracted by both, and the
same argument holds.
Follow-up: What happens if both charges are +Q?
Where would the F = 0 point be in this case?
3R
ConcepTest 21.4c Electric Force III
Two balls with charges +Q and –4Q
are fixed at a separation distance of
3R. Is it possible to place another
charged ball Q0 anywhere on the
line such that the net force on Q0
will be zero?
1) yes, but only if Q0 is positive
2) yes, but only if Q0 is negative
3) yes, independent of the sign
(or value) of Q0
4) no, the net force can never
be zero
– 4Q
+Q
3R
ConcepTest 21.4c Electric Force III
Two balls with charges +Q and –4Q
are fixed at a separation distance of
3R. Is it possible to place another
charged ball Q0 anywhere on the
line such that the net force on Q0
will be zero?
1) yes, but only if Q0 is positive
2) yes, but only if Q0 is negative
3) yes, independent of the sign
(or value) of Q0
4) no, the net force can never
be zero
A charge (positive or negative) can be
placed to the left of the +Q charge,
– 4Q
+Q
such that the repulsive force from the
+Q charge cancels the attractive
3R
force from –4Q.
Follow-up: What happens if one charge is +Q and the other is –Q?
21-5 Coulomb’s Law
Example 21-3: Electric force using vector
components.
Calculate the net electrostatic force on charge Q3
shown in the figure due to the charges Q1 and Q2.
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21-5 Coulomb’s Law
Conceptual Example
21-4: Make the force
on Q3 zero.
In the figure, where
could you place a
fourth charge, Q4 = -50
μC, so that the net
force on Q3 would be
zero?
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1
ConcepTest 21.6 Forces in 2D
2
3
Which of the arrows best
4
represents the direction
of the net force on charge
d
+2Q
+Q
+Q due to the other two
charges?
d
+4Q
5
1
ConcepTest 21.6 Forces in 2D
2
3
Which of the arrows best
4
represents the direction
of the net force on charge
d
+2Q
+Q
+Q due to the other two
d
charges?
+4Q
The charge +2Q repels +Q toward the
right. The charge +4Q repels +Q
upward, but with a stronger force.
Therefore, the net force is up and to
+2Q
the right, but mostly up.
Follow-up: What would happen if
the yellow charge were +3Q?
+4Q
5
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:
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ConcepTest 21.7 Electric Field
You are sitting a certain distance from
a point charge, and you measure an
electric field of E0. If the charge is
doubled and your distance from the
charge is also doubled, what is the
electric field strength now?
1) 4E0
2) 2E0
3) E0
4) 1/2E0
5) 1/4E0
ConcepTest 21.7 Electric Field
You are sitting a certain distance from
a point charge, and you measure an
electric field of E0. If the charge is
doubled and your distance from the
charge is also doubled, what is the
electric field strength now?
1) 4E0
2) 2E0
3) E0
4) 1/2E0
5) 1/4E0
Remember that the electric field is: E = kQ/r2.
Doubling the charge puts a factor of 2 in the
numerator, but doubling the distance puts a factor
of 4 in the denominator, because it is distance
squared!! Overall, that gives us a factor of 1/2.
Follow-up: If your distance is doubled, what must you do to
the charge to maintain the same E field at your new position?
21-6 The Electric Field
Force on a point
charge in an
electric field:
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21-6 The Electric Field
Example 21-6: Electric field of a single point
charge.
Calculate the magnitude and direction of the
electric field at a point P which is 30 cm to the
right of a point charge Q = -3.0 x 10-6 C.
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21-6 The Electric Field
Example 21-7: E at a point between two charges.
Two point charges are separated by a distance of 10.0 cm.
One has a charge of -25 μC and the other +50 μC. (a)
Determine the direction and magnitude of the electric field
at a point P between the two charges that is 2.0 cm from
the negative charge. (b) If an electron (mass = 9.11 x 10-31
kg) is placed at rest at P and then released, what will be its
initial acceleration (direction and magnitude)?
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21-6 The Electric Field
Example 21-8: E
above two point
charges.
Calculate the
total electric
field (a) at point
A and (b) at
point B in the
figure due to
both charges, Q1
and Q2.
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ConcepTest 21.9a Superposition I
-2 C
What is the electric field at
2
1
the center of the square?
3
5) E = 0
-2 C
4
ConcepTest 21.9a Superposition I
-2 C
What is the electric field at
2
1
the center of the square?
3
5) E = 0
-2 C
For the upper charge, the E field vector at the center
of the square points toward that charge. For the lower
charge, the same thing is true. Then the vector sum
of these two E field vectors points to the left.
Follow-up: What if the lower charge were +2 C?
What if both charges were +2 C?
4
21-6 The Electric Field
Problem solving in electrostatics: electric
forces and 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 vectorially to get result.
4. Check your answer!
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Summary of Chapter 21 Sec. 1-6
• Two kinds of electric charge – positive and
negative.
• Charge is conserved.
• Charge on electron:
e = 1.602 x 10-19 C.
• Conductors: electrons free to move.
• Insulators: nonconductors.
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Summary of Chapter 21 Sec. 1-6
• Charge is quantized in units of e.
• Objects can be charged by conduction or
induction.
• Coulomb’s law:
•Electric field is force per unit charge:
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Summary of Chapter 21 Sec. 1-6
• Electric field of a point charge:
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