Two charged balls are
repelling each other as
they hang from the ceiling.
What can you say about
their charges?
one is positive, the
other is negative
both are positive
both are negative
both are positive or
both are negative
From the picture,
what can you
conclude about
the charges?
A)
have opposite charges
B)
have the same charge
C)
all have the same charge
D) one ball must be neutral (no charge)
A metal ball hangs from the ceiling
A) positive
by an insulating thread. The ball is
B) negative
attracted to a positive-charged rod
C) positive or neutral
held near the ball. The charge of
D) negative or neutral
the ball must be:
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?
0
0
?
?
A)
0
0
B)
+
–
C)
–
+
D)
–
–
Two uniformly charged spheres are firmly fastened to and
electrically insulated from frictionless pucks on an air
table. The charge on sphere 2 is three times the charge
on sphere 1. Which force diagram correctly shows the
magnitude and direction of the electrostatic forces?
A
D
B
E
C
F
A) 3/4 N
If we increase one
charge to 4Q, what
is the magnitude of
F1?
F1 = 3N
F1 = ?
Q
4Q
B) 3.0 N
C) 12 N
D) 16 N
Q
Q
F2 = ?
F2 = ?
A) 9 F
The force between two charges
B) 3 F
separated by a distance d is F. If
the charges are pulled apart to a
C) 1/3 F
distance 3d, what is the force on
D) 1/9 F
each charge?
F
F
Q
Q
d
?
?
Q
Q
3d
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?
+4Q
+Q
3R
A) yes, but only if Q0 is
positive
B) yes, but only if Q0 is
negative
C) yes, independent of
the sign (or value) of
Q0
D) no, the net force can
never be zero
A) yes, but only if Q0 is
positive
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?
B) yes, but only if Q0 is
negative
C) yes, independent of the
sign (or value) of Q0
D) no, the net force can
never be zero
– 4Q
+Q
3R
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?
p
e
A) it gets bigger
B) it gets smaller
C) it stays the
same
Which of the
A
B
arrows best
C
represents the
direction of the
D
d
+2Q
+Q
net force on
charge +Q due to
the other two
charges?
d
+4Q
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?
A) 2 E0
B) E0
C) 1/2 E0
D) 1/4 E0
Between the red and
the blue charge, which
experiences the
greater electric field
due to the yellow
charge?
+1
d
+2
A)
+1
B)
+2
C) it’s the same for both
+1
d
+1
Between the red and
the blue charge, which
experiences the
greater electric force
due to the yellow
charge?
+1
d
+2
A)
+1
B)
+2
C) it’s the same for both
+1
d
+1
Which arrow
-2 C
A
best represents
the electric field
at the center of
B
-2 C
the square?
D) E = 0
C
What is the
-Q
+Q
direction of the
electric field at the
position of the X ?
B
C
A
D
+Q
Field Lines
Field lines point in the direction of the
Coulomb force on a positive test charge
due to the charge creating the field
Electric fields add up vectorially
Asymmetric charge distribution
yields asymmetric field
Parallel Plates
•Constant electric field
far away from the top
and the bottom
•Constant direction
•Constant strength
A proton and an
A) proton
electron are held apart a
B) electron
distance of 1 m and then
C) both the
same
released. Which
particle has the larger
acceleration at any one
moment?
p
e
A proton and an
electron are held
apart a distance
of 1 m and then
let go. Where
would they meet?
A) in the middle
B) closer to the
electron’s side
C) closer to the
proton’s side
p
e
Flux through an Area
Curved
Surface and
non-uniform
Field
Changing for
every point on
surface:
– Strength of E
– Direction of E
– Direction of A
Angle determines sign of flux
What is the Flux through the
Surfaces?
A1 pos., A2 neg
A2 pos., A1 neg
Both zero
None of the
above
A gaussian cylinder is placed in a uniform electric
field of magnitude E, aligned with the cylinder
axis. For each of the surfaces 1, 2, 3, is the
electric flux
positive,
B. negative, or
C. zero?
A.
3
2
1
E
A gaussian cylinder encloses a negative charge.
For each of the surfaces 1, 2, 3, is the electric flux
positive,
B. negative, or
C. zero?
A.
3
2
–Q
1
A positive charge is located outside a gaussian
cylinder as shown. For each of the surfaces 1, 2,
3, is the electric flux
A. positive,
B. negative, or
C. zero?
3
2
1
+Q
Which statement do you agree with?
“Since each Gaussian surface encloses the same charge, the net
flux through each should be the same.”
B. “Gauss’s law doesn’t apply here. The electric field at the Gaussian
surface in case B is weaker than in case A, because the surface is
farther from the charge. Since the flux is proportional to the electric
field strength, the flux must also be smaller in case B.”
C. “I was comparing A and C. In C the charge outside the Gaussian
surface changes the field over the whole surface. The areas are the
same so the fluxes must be different.”
D. None of these statements is correct.
A.
A
B
C
-6Q
+Q
+Q
+Q
Gauss’s law problem solving
1. Symmetry of charge distributions  Gaussian
2.
3.
4.
5.
6.
surface
Draw Gaussian surface through point where you
want to know E field
Determine direction of E field from symmetry of
charge distribution
Calculate electric flux through Gaussian surface
Calculate charge enclosed by surface
Solve for E as a function of distance from charge
using Gauss’ law
What is the symmetry of a long
straight wire with line charge
density λ?
Cylindrical
Elliptical
Spherical
Planar
What is the symmetry of a nonconducting hollow sphere with
charge density ρ?
Cylindrical
Elliptical
Spherical
Planar
Which Gaussian surface should we
choose to calculate the electric field
of a non-conducting hollow sphere
with charge density ρ ?
Cylinder
Pillbox
Sphere
Other
Which radius should the Gaussian
sphere of a non-conducting hollow
sphere with charge density ρ have?
Less than inner radius of hollow sphere
More than outer radius of hollow sphere
Between inner and outer radius of hollow
sphere
Depends on where you are interested in
the electric field
Which is the symmetry of a sheet
of metal with surface charge
density σ?
Cylindrical
Elliptical
Spherical
Planar
Which Gaussian surface should we
choose to calculate the electric field
of a metal sheet with surface
charge density σ?
Cylinder
Pillbox
Sphere
Other
Which of the three surfaces of the
pillbox has a non-zero electric flux?
Top (outside conductor)
Mantle (half-submerged)
Bottom
All three
Electric field of a solid charged
sphere
Choose gaussian
surface A1 to
calculate E field
outside sphere
Choose gaussian
surface A2 to
calculate E field
inside sphere
Electric field of solid charged
sphere
How does the electric field of a long
wire depend on R?
Not, Const.
R
1/R
1/R2
Non-conducting solid cylinder and cylindrical
tube, both carry charge density 15μC/m3;
R1=1/2R2=R3/3=5cm. Calculate the electric field.
Group 1: inside
solid cylinder
Group 2: between
cylinders
Group 3: inside
hollow cylinder
Group 4: outside
both cylinders
Electric Field as a function of
distance from axis
10.0
6.0
4
E (10 N/C)
8.0
4.0
2.0
0.0
0.0
2.5
5.0
7.5
10.0
R (cm)
12.5
15.0
17.5
20.0
The analogy of the potential energy
of two rocks are charges between
charged plates. Which plate should
be on top?
Positive
Negative
Depends
The analogy of the potential energy
of two rocks are charges between
charged plates. What does the
small rock represent?
More charge
Less charge
Negative charge
Depends
The analogy of the potential energy
of two rocks are charges between
charged plates. What is a correct
analogy?
Neg. plates up and neg.
charges high
Neg. plates down and neg.
charges high
Pos. plates and neg.
charges up/high
None of the above
What is correct?
Potential would be lower at b for negative
charges
The potential at b is higher for the larger charge
Negative charges go from low to high potential
None of the above
A proton is moved from position i to position
f below. Is the change in its potential
energy
A. positive,
B. negative, or
C. zero?
+
 i
 f
In each of the situations shown below, an electron
is moved from position i to position f. Is the
change in its potential energy
A. positive,
B. negative, or
C. zero?
1.
2.
 i
+
 f
3.
 i
-
-
+
 f
+
 i
 f
Draw the field lines & equipotential lines of two
charges plates
+
-
Draw the field lines & equipotential lines of
a point charge
+
Draw the field lines & equipotential lines of
two opposite point charges
+
-
Draw the field lines & equipotential lines of
two point charges
+
+
Four point
charges are
arranged at the
corners of a
square.
-Q
+Q
-Q
Draw the field
lines &
equipotential lines
+Q
Four point
charges are
arranged at the
corners of a
square. What are
the electric field E
and potential V at
the center of the
square? Draw the
field lines &
equipotential lines
A) E = 0
V=0
B) E = 0
V0
C) E  0
V0
D) E  0
V=0
-Q
+Q
-Q
+Q
The electric potential is shown at four
points in space below. Estimate the
electric field (magnitude and direction!) at
the dot.
25 V
10 V

E ?
7.1mm
10 V
15 V
An electron is shot directly towards a 2mm
diameter plastic bead with charge –1 nC
from very far away. It “reflects” from the
bead reaching a turning point 1mm from
the surface of the bead. What was the
initial speed of the electron?
-1 nC
1mm
The potential of a point charge Q is
assessed at different distances. Sort
the potential starting from the highest.
A) V 1cm in front of Q=+2nC
B) V 1m behind Q=+2nC
C) V 1cm left of Q=-4nC
D) V 1m right of Q=-4nC
ABCD
ABDC
DCBA
None of the above
Equipotential Lines
Electric field is perpendicular
to equipotential lines
– Does this determine its
direction fully?
– Why is the right plate at 0V?
Point
charge
Can we
calculate
how big the
charge is?
Is it positive
or negative?
What
would a
negative
charge
change?
Shape of
equipotential
lines
Potentials
would be
negative
Potential would
increase from
center
other
Do the distorted circles on the left
represent the same potential as the
right ones?
No
Yes
Up to a
sign
Depends
A parallel plate capacitor has plates with area A,
separated by a distance d. A battery with voltage
V is connected across the plates. For each
modification listed, state whether the capacitance
A) increases, B) decreases, or C) stays the same.
1. Increase d
2. Increase A
3. Increase V
4. Reverse battery polarity
A parallel plate capacitor has plates with area A,
separated by a distance d. A battery with voltage
V is connected across the plates. For each
modification listed, state whether the capacitance
A) increases, B) decreases, or C) stays the same.
1. Increase d  C=ε0 A/d  C decreases
2. Increase A  C=ε0 A/d  C increases
3. Increase V  C not function of V (device
does not change) C same
Note that charge goes up (Q=CV at constant C),
so electric field goes up (E= ε0 Q/A for plate of
charges) [yet it is constant as a function of
position!], which is, of course, why the potential
difference (V=Ed at constant d) is up.
4. Reverse battery polarity  same, device
does not change
A parallel plate capacitor has plates with area A,
separated by a distance d. A battery with voltage
V is connected across the plates. For each of the
following modifications, state whether the charge
on the plate connected to the positive battery
terminal A) increases, B) decreases, or C) stays
the same.
1. Increase d
2. Increase A
3. Increase V
4. Reverse battery polarity
A parallel plate capacitor has plates with area A,
separated by a distance d. A battery with voltage
V is connected across the plates. For each of the
following modifications, state whether the charge
on the plate connected to the positive battery
terminal A) increases, B) decreases, or C) stays
the same.
1. Increase d  V=const. (same battery), C=ε0
A/d decreases  Q=CV decreases
2. Increase A V=const. (same battery), C=ε0
A/d increases  Q=CV increases
3. Increase V  C=const., so Q=CV increases
4. Reverse battery polarity: Reversing polarity
will first decrease charge, so that charge
built-up is opposite later.
A parallel plate capacitor has plates with area A,
separated by a distance d. A battery with potential
difference V is connected across the plates for a
long time, and then disconnected. For each of the
following modifications, state whether the
potential difference between the plates A)
increases, B) decreases, or C) stays the same.
1. Increase d
2. Increase A
A parallel plate capacitor has plates with area A,
separated by a distance d. A battery with potential
difference V is connected across the plates for a
long time, and then disconnected. For each of the
following modifications, state whether the
potential difference between the plates A)
increases, B) decreases, or C) stays the same.
1. Increase d  Q=const., C decreases 
V=Q/C increases (more voltage needed for
same charge)
2. Increase A Q=const., C increases 
V=Q/C decreases (less voltage needed to
keep same charge)
Consider a simple parallel-plate capacitor whose
plates are given equal and opposite charges and
are separated by a distance d. Suppose the
plates are pulled apart until they are separated by
a distance D > d. The electrostatic energy stored
in the capacitor is now
greater than
B. the same as
C. smaller than
A.
before the plates were pulled apart.
Consider a simple parallel-plate capacitor whose
plates are given equal and opposite charges and
are separated by a distance d. Suppose the
plates are pulled apart until they are separated by
a distance D > d. The electrostatic energy stored
in the capacitor is now
greater than
B. the same as
C. smaller than
A.
before the plates were pulled apart.
Q=const here, so if d is increased, device
changes C goes down, V goes up, U=1/2 QV
goes up.
Consider a simple parallel-plate capacitor which
has been fully charged by a battery with potential
V and left connected to it. Suppose the plates
are pulled apart from their initial separation d to a
separation D > d. The electrostatic energy stored
in the capacitor is now
greater than
B. the same as
C. smaller than
A.
before the plates were pulled apart.
Consider a simple parallel-plate capacitor which
has been fully charged by a battery with potential
V and left connected to it. Suppose the plates
are pulled apart from their initial separation d to a
separation D > d. The electrostatic energy stored
in the capacitor is now
greater than
B. the same as
C. smaller than
A.
before the plates were pulled apart.
Now V=const, charge Q can change. C goes
down, so Q=CV goes down, so U=1/2 QV goes
down.