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Ch 20: Electrostatics
M Sittig
AP Physics B
Summer Course 2012
2012年AP物理B暑假班
Apologies


Electricity (and magnetism) is a huge topic
and we’re going to go quickly, learning just
enough to score a 5 on the AP Exam.
If you take a full-year class, you will get a
better, fuller picture that is not possible now
due to time restraints.
Electric Charge
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The forces between electric charges hold
the world together.
But we rarely notice them because, unlike
gravity, electric particles come in positive
and negative, so they mostly cancel out
across large distances.
Electric Charge
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Charge is a property of matter, like mass.
Three charged particles: + (protons),
– (electrons) and neutral (neutrons).
Our bodies, for example, contain a huge
amount of protons, but also a huge amount of
electrons.
So on a large scale, most objects are neutral.
Charge is measured in Coulombes (C).
Charge of an electron is 1.6×10-19 C.
ConcepTest 16.1a 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 16.1a 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 only can tell you 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 16.1b 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 16.1b 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).
Interaction between Charges
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Opposite charges attract (attractive force).
Like charges repel (repulsive force).
Using charge to create “induced charge”:
(Object is still net neutral. Balloon on wall demo.)
Electrons and Protons
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Protons are stuck in the nucleus, don’t move.
Electrons are freer to move/flow, especially in
metals.
Metals are good conductors = electrons can
flow through them.
Materials that don’t conduct electrons =
insulators.
Interaction between Charges
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Like charges on a conductor will move as far
away from each other as possible.
Charges will stay on the surface of
conductors.
Charges will collect on sharp points and
edges.
ConcepTest 16.2a 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 16.2a 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?
ConcepTest 16.2b 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 16.2b 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?
Electric Fields
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Fields were invented to explain how objects
could interact without “touching”.
Objects with mass have gravitational fields,
other masses in the field interact and feel a
gravitational force.
Objects with (electric) charge have electric
fields, other charges in the field interact and
feel an electric force.
Electric fields
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Electric fields are vector fields: each point in
the field has a strength (E) and a direction.
The force felt by a charge in an electric field is
F = qE.
E and F are in the same direction if q is
positive (q > 0), opposite directions if q < 0.
Another way to say it: positive charges feel a
force in the same direction as the field,
negative charges in the opposite direction.
Unit of E is N/C.
Example Problem
Practice Problem

In a uniform electric field in empty space, a
4 C charge is placed and it feels an electrical
force of 12 N. If this charge is removed and
a 6 C charge is placed at that point instead,
what force will it feel?
Practice Problem
Electric Potential
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The potential energy due to a charge’s
position in an electric field, PE = qV.
For gravity, we usually choose PE = 0 at the
ground. For electricity, we usually choose PE
= 0 at an infinite distance away.
Note: PE is usually measured in Joules, but
we can also use electron volts (eV), the
energy gained by the charge of 1 electron
moving across 1 V.
Electric Potential
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V is called “voltage” or “potential”, unit is J/C
or volts (V).
V is the potential energy provided at each
point in a field to a unit charge.
Usually potential difference is more
important, as a measure of energy required
to move a charged particle.
Also, it’s a scalar. Can you see why? (Hint:
PE=qV)
Electric Potential

You increase the electric potential of an
object or space by adding positive charge to
it (or taking away negative charge from it).
Example Problem
Practice Problem
Example Problem
Equipotential Lines
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Lines of equal potential, equal distance from
point/surface of zero potential energy.
A charged particle can be moved along an
equipotential line without work being done.
Always perpendicular to the electric field
lines.
Equipotential Lines
Practice Problem

Draw the equipotential lines for two
positive particles close to each other.
ConcepTest 17.7a Work and Electric Potential I
1) P  1
Which requires the most work,
to move a positive charge from
P to points 1, 2, 3 or 4 ? All
points are the same distance
from P.
2) P  2
3) P  3
4) P  4
5) all require the same
amount of work
3
2
1
P

E
4
ConcepTest 17.7a Work and Electric Potential I
Which requires the most work,
to move a positive charge from
P to points 1, 2, 3 or 4 ? All
points are the same distance
from P.
For path #1, you have to push the
positive charge against the E field,
which is hard to do. By contrast,
path #4 is the easiest, since the
field does all the work.
1) P  1
2) P  2
3) P  3
4) P  4
5) all require the same
amount of work
3
2
1
P

E
4
ConcepTest 17.7b Work and Electric Potential II
1) P  1
Which requires zero work, to
move a positive charge from
P to points 1, 2, 3 or 4 ? All
points are the same distance
from P.
2) P  2
3) P  3
4) P  4
5) all require the same
amount of work
3
2
1
P

E
4
ConcepTest 17.7b Work and Electric Potential II
Which requires zero work, to
move a positive charge from
P to points 1, 2, 3 or 4 ? All
points are the same distance
from P.
1) P  1
2) P  2
3) P  3
4) P  4
5) all require the same
amount of work
For path #3, you are moving in a
direction perpendicular to the field
lines. This means you are moving
along an equipotential, which
requires no work (by definition).
Follow-up: Which path requires the least work?
3
2
1
P

E
4
Parallel plates
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Oppositely charged.
Useful because electric field between the is
uniform in strength and direction (except at
the edges).
E = V/d
Because qΔV=ΔPE=W=F·d=qE·d
Capacitor
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Parallel plates added to a circuit.
Charge is added by a battery (movie).
Take out the battery, and charge flows back.
How much charge can a capacitor hold?
Q = CV (V is voltage of the battery)
How big is C?
C = ε0A/d
ε0 is permittivity of free space, A is area of
plates (m2), d is separation of the plates (m).
Unit of C is Farads (F).
Practice Problem
ConcepTest 17.8 Capacitors
Capacitor C1 is connected across
1) C1
a battery of 5 V. An identical
2) C2
capacitor C2 is connected across
a battery of 10 V. Which one has
3) both have the same charge
4) it depends on other factors
the most charge?
+Q –Q
ConcepTest 17.8 Capacitors
Capacitor C1 is connected across
1) C1
a battery of 5 V. An identical
2) C2
capacitor C2 is connected across
a battery of 10 V. Which one has
the most charge?
3) both have the same charge
4) it depends on other factors
+Q –Q
Since Q = C V and the two capacitors are
identical, the one that is connected to the
greater voltage has the most charge,
which is C2 in this case.
ConcepTest 17.9a Varying Capacitance I
What must be done to
1) increase the area of the plates
a capacitor in order to
2) decrease separation between the plates
increase the amount of
3) decrease the area of the plates
charge it can hold (for
a constant voltage)?
4) either (1) or (2)
5) either (2) or (3)
+Q –Q
ConcepTest 17.9a Varying Capacitance I
What must be done to
1) increase the area of the plates
a capacitor in order to
2) decrease separation between the plates
increase the amount of
3) decrease the area of the plates
charge it can hold (for
a constant voltage)?
4) either (1) or (2)
5) either (2) or (3)
+Q –Q
Since Q = C V, in order to increase the charge
that a capacitor can hold at constant voltage,
one has to increase its capacitance. Since the
capacitance is given by C   0 A , that can be
d
done by either increasing A or decreasing d.
ConcepTest 17.9c Varying Capacitance III
A parallel-plate capacitor initially has
a potential difference of 400 V and is
then disconnected from the charging
battery. If the plate spacing is now
doubled (without changing Q), what
is the new value of the voltage?
+Q
–Q
1) 100 V
2) 200 V
3) 400 V
4) 800 V
5) 1600 V
ConcepTest 17.9c Varying Capacitance III
A parallel-plate capacitor initially has
a potential difference of 400 V and is
then disconnected from the charging
battery. If the plate spacing is now
doubled (without changing Q), what
is the new value of the voltage?
Once the battery is disconnected, Q has to
remain constant, since no charge can flow
either to or from the battery.
Since
C   0 A when the spacing d is doubled, the
d
capacitance C is halved. And since Q = C V,
that means the voltage must double.
1) 100 V
2) 200 V
3) 400 V
4) 800 V
5) 1600 V
+Q
–Q
Point charges
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Electric field: E = kQ/r2
Electric potential: V = kQ/r
Electric force: F = kQ1Q2/r2
Electric field points away from positive
charges, toward negative charges.
Electric potential is high, + near positive
charges; low, - near negative charges.
Example Problem
Practice Problem
Practice Problem

Calculate the electric field and electric
potential at point A.
ConcepTest 17.4 Hollywood Square
Four point charges are
arranged at the corners of a
square. Find the electric
field E and the potential V at
the center of the square.
1) E = 0
V=0
2) E = 0
V0
3) E  0
V0
4) E  0
V=0
5) E = V regardless of the value
-Q
+Q
-Q
+Q
ConcepTest 17.4 Hollywood Square
Four point charges are
arranged at the corners of a
square. Find the electric
field E and the potential V at
the center of the square.
1) E = 0
V=0
2) E = 0
V0
3) E  0
V0
4) E  0
V=0
5) E = V regardless of the value
The potential is zero: the scalar
contributions from the two positive
charges cancel the two minus charges.
However, the contributions from the
electric field add up as vectors, and
they do not cancel (so it is non-zero).
Follow-up: What is the direction
of the electric field at the center?
-Q
+Q
-Q
+Q
ConcepTest 17.5a Equipotential Surfaces I
1
5) all of them
At which point
does V = 0?
2
+Q
3
4
–Q
ConcepTest 17.5a Equipotential Surfaces I
1
5) all of them
At which point
does V = 0?
2
+Q
3
–Q
4
All of the points are equidistant from both charges. Since
the charges are equal and opposite, their contributions to
the potential cancel out everywhere along the mid-plane
between the charges.
Follow-up: What is the direction of the electric field at all 4 points?
ConcepTest 17.5b Equipotential Surfaces II
Which of these configurations gives V = 0 at all points on the x-axis?
+2mC
+1mC
+2mC
+1mC
x
-1mC
-2mC
+2mC
-2mC
x
-2mC
-1mC
1)
x
2)
4) all of the above
+1mC
-1mC
3)
5) none of the above
ConcepTest 17.5b Equipotential Surfaces II
Which of these configurations gives V = 0 at all points on the x-axis?
+2mC
+1mC
+2mC
+1mC
x
-1mC
-2mC
+2mC
-2mC
x
-2mC
-1mC
1)
x
2)
4) all of the above
+1mC
-1mC
3)
5) none of the above
Only in case (1), where opposite charges lie
directly across the x-axis from each other, do
the potentials from the two charges above the
x-axis cancel the ones below the x-axis.