15_electric charge-forces-fields
TRANSCRIPT
Lecture Outline
Chapter 15
College Physics, 7th Edition
Wilson / Buffa / Lou
© 2010 Pearson Education, Inc.
Chapter 15Electric Charge, Forces, and
Fields
© 2010 Pearson Education, Inc.c
Units of Chapter 15
Electric Charge
Electrostatic Charging
Electric Force
Electric Field
Conductors and Electric Fields
Gauss’s Law for Electric Fields: A Qualitative Approach
© 2010 Pearson Education, Inc.
15.1 Electric Charge
Electric charge is a fundamental property of matter; electric charges may be positive or negative.
The atom consists of a small positive nucleus surrounded by a negative electron cloud.
© 2010 Pearson Education, Inc.
15.1 Electric Charge
Like charges repel; unlike charges attract.
© 2010 Pearson Education, Inc.
15.1 Electric Charge
SI unit of charge: the coulomb, C. All charges are integer multiples of the charge on the electron:
© 2010 Pearson Education, Inc.
15.1 Electric Charge
Charge is conserved:
The net charge of an isolated system remains constant.
© 2010 Pearson Education, Inc.
15.2 Electrostatic Charging
Conductors transmit charges readily.
Semiconductors are intermediate; their conductivity can depend on impurities and can be manipulated by external voltages.
Insulators do not transmit charge at all.
© 2010 Pearson Education, Inc.
15.2 Electrostatic ChargingAn electroscope may be used to determine if an object is electrically charged.
© 2010 Pearson Education, Inc.
15.2 Electrostatic Charging
Charging by friction: This is the process by which you get “charged up” walking across the carpet in the winter. It is also the process that creates “static cling” in your laundry, and makes it possible for you to rub a balloon on your hair and then stick the balloon to the wall.
© 2010 Pearson Education, Inc.
15.2 Electrostatic Charging
An electroscope can be given a net charge by conduction—when it is touched with a charged object, the excess charges flow freely onto the electroscope.
© 2010 Pearson Education, Inc.
15.2 Electrostatic Charging
An electroscope may also be charged by induction, if there is a way of grounding it while charge is being induced.
© 2010 Pearson Education, Inc.
15.2 Electrostatic Charging
Charge may also be moved within an object—without changing its net charge—through a process called polarization.
© 2010 Pearson Education, Inc.
Question 15.1a Electric Charge I
a) one is positive, the other
is negative
b) both are positive
c) both are negative
d) both are positive or both
are negative
Two charged balls are Two charged balls are
repelling each other as repelling each other as
they hang from the ceiling. they hang from the ceiling.
What can you say about What can you say about
their charges?their charges?
Question 15.1a Electric Charge I
The fact that the balls repel each
other can tell you only that they
have the same chargesame charge, but you do
not know the sign. So they can
be either both positive or both
negative.
a) one is positive, the other
is negative
b) both are positive
c) both are negative
d) both are positive or both
are negative
Two charged balls are Two charged balls are
repelling each other as repelling each other as
they hang from the ceiling. they hang from the ceiling.
What can you say about What can you say about
their charges?their charges?
Follow-upFollow-up:: What does the picture look like if the two balls are oppositely What does the picture look like if the two balls are oppositely charged? What about if both balls are neutral?charged? What about if both balls are neutral?
a) have opposite charges
b) have the same charge
c) all have the same charge
d) one ball must be neutral (no charge)
From the picture, From the picture,
what can you what can you
conclude about conclude about
the charges?the charges?
Question 15.1b Electric Charge II
a) have opposite charges
b) have the same charge
c) all have the same charge
d) one ball must be neutral (no charge)
From the picture, From the picture,
what can you what can you
conclude about conclude about
the charges?the charges?
The GREEN and PINK balls must
have the same charge, since they
repel each other. The YELLOWYELLOW
ball also repels the GREEN, so it
must also have the same charge
as the GREEN (and the PINK).
Question 15.1b Electric Charge II
Question 15.2a Conductors I
a) positive
b) negative
c) neutral
d) positive or neutral
e) negative or neutral
A metal ball hangs from the ceiling
by an insulating thread. The ball is
attracted to a positive-charged rod
held near the ball. The charge of
the ball must be:
Clearly, the ball will be attracted if its
charge is negativenegative. However, even if
the ball is neutralneutral, the charges in the
ball can be separated by inductioninduction
(polarization), leading to a net
attraction.
a) positive
b) negative
c) neutral
d) positive or neutral
e) negative or neutral
A metal ball hangs from the ceiling
by an insulating thread. The ball is
attracted to a positive-charged rod
held near the ball. The charge of
the ball must be:
Remember the ball is a conductor!
Question 15.2a Conductors I
Follow-upFollow-up:: What happens if the What happens if the metal ballmetal ball is replaced by a is replaced by a plastic ballplastic ball??
Two neutral conductors are connected
by a wire and a charged rod is brought
near, but does not touch. The wire is
taken away, and then the charged rod
is removed. What are the charges on
the conductors?
Question 15.2b Conductors IIa) 0 0
b) + –
c) – +
d) + +
e) – –
0 0
? ?
While the conductors are connected, positive positive
charge will flow from the blue to the green charge will flow from the blue to the green
ball due to polarizationball due to polarization. Once disconnected,
the charges will remain on the separate charges will remain on the separate
conductorsconductors even when the rod is removed.
Two neutral conductors are connected
by a wire and a charged rod is brought
near, but does not touch. The wire is
taken away, and then the charged rod
is removed. What are the charges on
the conductors?
Question 15.2b Conductors IIa) 0 0
b) + –
c) – +
d) + +
e) – –
0 0
? ?Follow-upFollow-up:: What will happen when the What will happen when the
conductors are reconnected with a wire?conductors are reconnected with a wire?
15.3 Electric ForceThe force exerted by one charged particle on another is given by:
© 2010 Pearson Education, Inc.
15.3 Electric Force
If there are multiple point charges, the force vectors must be added to get the net force.
© 2010 Pearson Education, Inc.
QQ QQF1 = 3 N F2 = ?
a) 1.0 N
b) 1.5 N
c) 2.0 N
d) 3.0 N
e) 6.0 N
What is the magnitude What is the magnitude
of the force of the force FF22??
Question 15.3a Coulomb’s Law I
The force F2 must have the same magnitudesame 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 reverseforce of one on the other of a pair is the same as the reverse.
Note that this sounds suspiciously like Newton’s 3rd law!!Note that this sounds suspiciously like Newton’s 3rd law!!
QQ QQF1 = 3 N F2 = ?
a) 1.0 N
b) 1.5 N
c) 2.0 N
d) 3.0 N
e) 6.0 N
What is the magnitude What is the magnitude
of the force of the force FF22??
Question 15.3a Coulomb’s Law I
Question 15.3b Coulomb’s Law II
a) 3/4 N
b) 3.0 N
c) 12 N
d) 16 N
e) 48 N
If we increase one charge to If we increase one charge to 44QQ, ,
what is the magnitude ofwhat is the magnitude of F F11??
44QQ QQF1 = ? F2 = ?
QQ QQF1 = 3 N F2 = ?
Question 15.3b Coulomb’s Law II
Originally we had:
F1 = k(Q)(Q)/r2 = 3 N
Now we have:
F1 = k(4Q)(Q)/r2
which is 4 times bigger4 times bigger than before.
a) 3/4 N
b) 3.0 N
c) 12 N
d) 16 N
e) 48 N
If we increase one charge to If we increase one charge to 44QQ, ,
what is the magnitude of what is the magnitude of FF11??
44QQ QQF1 = ? F2 = ?
QQ QQF1 = 3 N F2 = ?
Follow-upFollow-up:: Now what is the magnitude of Now what is the magnitude of FF22??
A proton and an electron are
held apart a distance of 1 m
and then released. As they
approach each other, what
happens to the force between
them?
a) it gets bigger
b) it gets smaller
c) it stays the same
p e
Question 15.5a Proton and Electron I
By Coulomb’s law, the force between the force between the
two charges is inversely proportional to two charges is inversely proportional to
the distance squaredthe distance squared. So, the closer they get to each other, the bigger the electric force between them gets!
A proton and an electron are
held apart a distance of 1 m
and then released. As they
approach each other, what
happens to the force between
them?
a) it gets bigger
b) it gets smaller
c) it stays the same
1 22
=Q Q
F kr
p e
Question 15.5a Proton and Electron I
a) proton
b) electron
c) both the same
p e
Question 15.5b Proton and Electron II
A proton and an electron are held
apart a distance of 1 m and then
released. Which particle has the
larger acceleration at any one
moment?
The two particles feel the same forcesame force. Since F = ma, the particle with the smaller smaller
massmass will have the larger accelerationlarger acceleration.
This is the electron.This is the electron.
a) proton
b) electron
c) both the same
p e
Question 15.5b Proton and Electron II
A proton and an electron are
held apart a distance of 1 m
and then released. Which
particle has the larger
acceleration at any one
moment?
1 22
=Q Q
F kr
Which of the arrows best
represents the direction
of the net force on charge
+Q due to the other two
charges?
+2Q
+4Q
+Q
a bc
d
ed
d
Question 15.6 Forces in 2D
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 net force is up and to
the right, but mostly upthe right, but mostly up.
+2Q
+4Q
+Q
a bc
d
ed
d
+2Q
+4Q
Question 15.6 Forces in 2D
Which of the arrows best
represents the direction
of the net force on charge
+Q due to the other two
charges?
15.4 Electric Field
Definition of the electric field:
The direction of the field is the direction the force would be on a positive charge.
© 2010 Pearson Education, Inc.
15.4 Electric FieldCharges create electric fields, and these fields in turn exert electric forces on other charges.
Electric field of a point charge:
© 2010 Pearson Education, Inc.
a) 44EE00
b) 22EE00
c) EE00
d) 1/21/2EE00
e) 1/44EE00
You are sitting a certain distance from You are sitting a certain distance from
a point charge, and you measure an a point charge, and you measure an
electric field of electric field of EE00. If the charge is . If the charge is
doubleddoubled and your distance from the and your distance from the
charge is also charge is also doubleddoubled, what is the , what is the
electric field strength now?electric field strength now?
Question 15.7 Electric Field
Remember that the electric field is: E = kQ/r2.
Doubling the chargeDoubling the charge puts a factor of 2factor of 2 in the
numerator, but doubling the distancedoubling the distance puts a factor factor
of 4of 4 in the denominator, because it is distance
squared!! Overall, that gives us a factor of 1/2factor of 1/2.
a) 44EE00
b) 22EE00
c) EE00
d) 1/21/2EE00
e) 1/44EE00
You are sitting a certain distance from You are sitting a certain distance from
a point charge, and you measure an a point charge, and you measure an
electric field of electric field of EE00. If the charge is . If the charge is
doubleddoubled and your distance from the and your distance from the
charge is also charge is also doubleddoubled, what is the , what is the
electric field strength now?electric field strength now?
Question 15.7 Electric Field
+2 +1+1 +1d d
a)
b)
c) the same for both
Between the red and the
blue charge, which of
them experiences the
greater electric field due
to the green charge?
Question 15.8a Field and Force I
+2
+1
Both charges feel the same electric same electric
fieldfield due to the green charge because
they are at the same point in spacesame point in space!
+2 +1+1 +1d d
a)
b)
c) the same for both
2r
QkE
Between the red and the
blue charge, which of
them experiences the
greater electric field due
to the green charge?
Question 15.8a Field and Force I
+2
+1
+2 +1+1 +1d d
a)
b)
c) the same for both
Between the red and the
blue charge, which of
them experiences the
greater electric force due
to the green charge?
Question 15.8b Field and Force II
+2
+1
The electric field is the sameelectric field is the same for both charges,
but the forceforce on a given charge also depends
on the magnitude of that specific chargemagnitude of that specific charge.
+2 +1+1 +1d d
a)
b)
c) the same for both
Between the red and the
blue charge, which of
them experiences the
greater electric force due
to the green charge?
qEF
Question 15.8b Field and Force II
+2
+1
15.4 Electric FieldFor multiple charges, the total electric field is found using the superposition principle:For a configuration of charges, the total, or net, electric field at any point is the vector sum of the electric fields due to the individual charges.
© 2010 Pearson Education, Inc.
15.4 Electric Field
It is convenient to represent the electric field using electric field lines, or lines of force. These lines are drawn so the field is tangent to the line at every point.
© 2010 Pearson Education, Inc.
15.4 Electric Field
Rules for drawing electric field lines:
1. Closer lines mean a stronger field.
2. The field is tangent to the lines at every point.
3. Field lines start on positive charges and end on negative charges.
4. The number of lines entering or leaving a charge is proportional to the magnitude of the charge.
5. Field lines never cross.© 2010 Pearson Education, Inc.
What is the electric field at What is the electric field at
the center of the square?the center of the square?
dc
b a
-2 C
-2 C
Question 15.9a Superposition I
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 leftpoints to the left.
What is the electric field at What is the electric field at
the center of the square?the center of the square?
dc
b a
-2 C
-2 C
Question 15.9a Superposition I
Follow-upFollow-up:: What if the lower charge were +2 C? What if the lower charge were +2 C? What if both charges were +2 C? What if both charges were +2 C?
What is the direction of
the electric field at the
position of the X ?
d
cb
a
+Q
-Q +Q
e
Question 15.9c Superposition III
The two +Q charges give a resultant E field
that is down and to the rightdown and to the right. The –Q charge
has an E field up and to the leftup and to the left, but smallersmaller
in magnitude. Therefore, the total electric total electric
field is down and to the rightfield is down and to the right.
What is the direction of
the electric field at the
position of the X ?
d
cb
a
+Q
-Q +Q
e
Question 15.9c Superposition III
Follow-upFollow-up:: What if all three charges reversed their signs? What if all three charges reversed their signs?
15.4 Electric FieldElectric field lines of a dipole:
© 2010 Pearson Education, Inc.
15.4 Electric Field
Electric field lines due to very large parallel plates:
© 2010 Pearson Education, Inc.
15.4 Electric Field
Electric field lines due to like charges: (a) equal charges; (b) unequal charges.
© 2010 Pearson Education, Inc.
a) charges are equal and positive
b) charges are equal and negative
c) charges are equal and opposite
d) charges are equal, but sign is
undetermined
e) charges cannot be equal
Q2Q1 x
y
E
Two charges are fixed along Two charges are fixed along
the the xx axis. They produce an axis. They produce an
electric field electric field EE directed along directed along
the negative the negative yy axis at the axis at the
indicated point. Which of indicated point. Which of
the following is true?the following is true?
Question 15.10 Find the Charges
The way to get the resultant PINK vector
is to use the GREEN and BLUE vectors.
These E vectors correspond to equal equal
chargescharges (because the lengths are equal)
that are both negativeboth negative (because their
directions are toward the charges). Q2Q1 x
y
E
Two charges are fixed along Two charges are fixed along
the the x x axis. They produce an axis. They produce an
electric field electric field EE directed along directed along
the negative the negative yy axis at the axis at the
indicated point. Which of indicated point. Which of
the following is true?the following is true?
a) charges are equal and positive
b) charges are equal and negative
c) charges are equal and opposite
d) charges are equal, but sign is
undetermined
e) charges cannot be equal
Question 15.10 Find the Charges
Q
In a uniform electric field in empty In a uniform electric field in empty
space, a 4 C charge is placed and it space, a 4 C charge is placed and it
feels an electric force of 12 N. If this feels an electric force of 12 N. If this
charge is removed and a 6 C charge charge is removed and a 6 C charge
is placed at that point instead, what is placed at that point instead, what
force will it feel?force will it feel?
a) 12 N
b) 8 N
c) 24 N
d) no force
e) 18 N
Question 15.11 Uniform Electric Field
Since the 4 C charge feels a force, there must
be an electric field present, with magnitude:
E = F / q = E = F / q = 12 N12 N / / 4 C4 C = = 3 N/C3 N/C
Once the 4 C charge is replaced with a 6 C
charge, this new charge will feel a force of:
F = q E = (F = q E = (6 C6 C)()(3 N/C3 N/C) = ) = 18 N18 N
Q
a) 12 N
b) 8 N
c) 24 N
d) no force
e) 18 N
Question 15.11 Uniform Electric Field
In a uniform electric field in empty In a uniform electric field in empty
space, a 4 C charge is placed and it space, a 4 C charge is placed and it
feels an electric force of 12 N. If this feels an electric force of 12 N. If this
charge is removed and a 6 C charge charge is removed and a 6 C charge
is placed at that point instead, what is placed at that point instead, what
force will it feel?force will it feel?
Question 15.12a Electric Field Lines I
What are the signs of the
charges whose electric
fields are shown at right?
a)
b)
c)
d)
e) no way to tell
Question 15.12a Electric Field Lines I
What are the signs of the
charges whose electric
fields are shown at right?
a)
b)
c)
d)
e) no way to tell
Electric field lines originate on originate on
positive chargespositive charges and terminate terminate
on negative chargeson negative charges.
15.5 Conductors and Electric Fields
Electric charges are free to move within a conductor; therefore, there cannot be a static field within the conductor:
The electric field is zero inside a charged conductor.
Excess charges on a conductor will repel each other, and will wind up being as far apart as possible.Any excess charge on an isolated conductor resides entirely on the surface of the conductor.
© 2010 Pearson Education, Inc.
15.5 Conductors and Electric Fields
There cannot be any component of the electric field parallel to the surface of a conductor; otherwise charges would move.The electric field at the surface of a charged conductor is perpendicular to the surface.
© 2010 Pearson Education, Inc.
15.5 Conductors and Electric Fields
The force from neighboring charges is less when the curvature of the surface is large:
Excess charge tends to accumulate at sharp points, or locations of highest curvature, on charged
conductors. As a result, the electric field is greatest at such locations.
© 2010 Pearson Education, Inc.
15.6 Gauss’s Law for Electric Fields: A Qualitative Approach
A surface, called a Gaussian surface, that completely surrounds a point charge intercepts the same number of field lines regardless of its shape. For a positive charge, the lines exit the surface; for a negative one they enter it.
© 2010 Pearson Education, Inc.
15.6 Gauss’s Law for Electric Fields: A Qualitative Approach
If a greater amount of charge is enclosed, more field lines cross the surface.
© 2010 Pearson Education, Inc.
15.6 Gauss’s Law for Electric Fields: A Qualitative Approach
Here, surface 1 surrounds the positive charge and has lines exiting it. Surface 2 surrounds the negative charge and has lines entering it. Surface 3 does not enclose any charge, and the same number of lines exit as enter.
Surface 4 encloses both charges; as they are equal in magnitude, the same number of lines exit the surface as enter it.© 2010 Pearson Education, Inc.
15.6 Gauss’s Law for Electric Fields: A Qualitative Approach
The underlying physical principle of Gauss’s law:The net number of electric field lines passing through an imaginary closed surface is proportional to the amount of net charge enclosed within that surface.
This can be used to show that excess charge on a conductor must reside on the surface.
© 2010 Pearson Education, Inc.
Summary of Chapter 15
Like charges repel; unlike charges attract.
Charge is conserved.
Electrons move freely inside conductors, but not inside insulators.
Objects may be charged electrostatically by friction, conduction, or induction.
Polarization is the separation of positive and negative charge within an object.
© 2010 Pearson Education, Inc.
Summary of Chapter 15
Coulomb’s law:
The electric field, a vector, is the force per unit charge. Electric fields from multiple charges add by superposition.
Electric field lines are used to represent the electric field.
A conductor has zero electric field inside and has all excess charge on its surface.
© 2010 Pearson Education, Inc.
Summary of Chapter 15
The electric field is always perpendicular to the surface of a conductor.
The charge density and electric field are greatest on a conductor where the curvature is largest.
© 2010 Pearson Education, Inc.