1. 4 point charges (+1 C, +3 C, -4 C and
-5 C) are fixed at the vertices of a square.
When a charge of +10 C is placed at the
center of the square, it experiences a force
of 107 N. What is the magnitude of the
electric field at the center of the square?
(a) This cannot be determined since the
dimensions of the square are unknown.
(b) 107 N/C
(c) 106 N/C
(d) 105 N/C
(e) 104 N/C
2. Two small, uniformly charged spheres
A and B are suspended as shown below.
The entire system is in electrostatic and
mechanical equilibrium. Sphere A has
mass mA and sphere B has mass mB. The
spheres A & B carry charges QA and QB,
respectively, with QA > Q B. Assume that
the centers of the two spheres lie on the
same horizontal. Which of the following
statements is CORRECT?
(a) The tension in the string attached to
sphere A = mA g sinθ B
(b) Sphere A exerts more force on sphere
B than sphere B exerts on sphere A.
(c) The tension in the string attached to
sphere B = mB g cosθ B
(d) The force exerted by sphere B on
sphere A = mA g tanθ A
(e) Since the two spheres exert equal and
opposite forces on each other, θ A =
θ B.
θA
Sphere A
θB
Sphere B
.
2
3. Suppose you place an excess negative
charge on a plastic pen by rubbing it on
your sweater and then bring the pen close
to a thin metal foil on a very dry day.
Which of the following statements is
correct?
Metal Foil
PEN
4. The figure below shows two charged
particles of charge +9Q and -Q fixed in
place at x = 0 and x = L, respectively. At
what point (other than infinitely far away)
can a proton be placed so that it is in
equilibrium?
+9Q
x=0
(a) Since the metal is an insulator and
does not have freely mobile electrons, it
will not react to the charged pen.
(b) The metal foil will be repelled since
the pen will repel electrons from one side
of the foil to the other.
(c) The metal foil will be attracted by the
pen because a positive charge will be
induced on the side of the foil closest to
the pen.
(d) The metal foil will be repelled by the
pen because a negative charge will be
induced on the side of the foil closest to
the pen.
(e) The metal foil will be attracted by the
pen because a negative charge will be
induced on the side of the foil closest to
the pen.
(a) x = -L/2
(b) x = -10L/2
(c) x = +3L/2
(d) x = +L/2
(e) x = +9L/8
-Q
x=L
3
5. Jennifer peels apart two neutral pieces
of scotch tape that are stuck together. She
finds that (a) they attract each other and
(b) the force of attraction increases
strongly when the distance between the
tapes is reduced. Which of the following
fundamental laws of nature is
qualitatively illustrated by this simple
experiment?
(a) The quantization of charge.
(b) The conservation of charge.
(c) Gauss’ Law.
(d) Coulomb’s Law.
(e) Both Coulomb’s Law and the
conservation of charge.
6. A molecule of water acts like an
electric dipole in which the charges are
“effectively” separated by a distance of
10-12 m. The magnitude of the electric
field at a point located 10-9 m away on the
perpendicular bisector of this electric
dipole is 106 N/C. What is the magnitude
of the electric field at a point located 2 x
10-9 m away on the perpendicular
bisector?
(a) 4 x 106 N/C
(b) 2 x 106 N/C
(c) 5 x 105 N/C
(d) 2.5 x 105 N/C
(e) 1.25 x 10 5 N/C
7. The figure below shows 5 point
charges arranged on the perimeter of a
circle of radius 10 cm centered at the
origin of the x-y co-ordinate system.
The +8 C charges are at opposite ends of
a diameter, as are the -5C charges.
Determine the magnitude & direction of
the electric field at the center of the circle.
(a) 5.67 x 10 12 N/C, making an angle of
-820 with the +x axis.
(b) 8.65 x 1012 N/C, making an angle of 320 with the +x axis.
(c) 9 x 108 N/C, directed along +y
direction
(d) 9 x 1012 N/C, directed along -y
direction.
(e) 9 x 1012 N/C, directed along +y
direction
y
-5C
150
x
+8C
+8C
150
-5C
-10C
4
8. In the figure below, two curved plastic
rods, one of charge +2 q and the other of
charge + q, form a circle of radius R in an
xy plane. The x-axis passes through their
connecting points, and the charge is
distributed uniformly on both rods. What
are the magnitude and direction of the
electric field at the center of the circle?
y
(a) (kq)/( πR2 ), along -y.
(b) kq/R2 , along +y.
(c) kq/R2 , along -y.
(d) (2kq)/(πR2 ), along +y.
(e) (2kq)/( πR2 ), along -y.
+2q
R
x
+q
`
9. The figure below shows the electric
field lines in some region of space. All
three lines shown are straight lines.
Which one of the following statements is
incorrect?
A
B
(a) The force experienced by an electron
at B is less than the force it would
experience at A.
(b) An electron released from rest at B
will move with decreasing acceleration
towards A.
(c) A proton released from rest at A will
move with decreasing acceleration
towards B.
(d) The force experienced by a proton at
A is greater than the force it would
experience at B.
(e) An electron released from rest at B
will move towards A with increasing
speed.
5
10. A thin plastic ring is uniformly
charged with a positive charge as shown
in the adjacent figure. Which of the plots
below correctly depicts the qualitative
variation with of the magnitude of the
electric field at a point on the axis of the
circle? (In the plots, z varies from 0 to
some large distance, with z = 0 at the
center of the ring.)
z
(b)
(a)
E
(c)
E
z
E
z
z
(e)
(d)
E
E
z
z
6
11. An electron of charge -e and mass m
is launched with an initial speed v at an
angle of 30 0 to a uniform electric field E
as shown below. After how much time
does its speed reach its minimum value?
v
E
30 0
12. In the figure below, a nonconducting
rod of length L has charge q uniformly
distributed along its length. Also shown
is a differential element of length dx along
the rod. Which of the following
expressions correctly gives the magnitude
of the electric field from this element of
charge at the point P shown in the figure?
P
vm
2eE
0.87vm
(b)
eE
vm
(c)
eE
2vm
(d)
eE
(e) Never, because it constantly
accelerates.
(a)
(a)
(b)
kq
L(x + y 2 )
kqdx
2
L x2 + y 2
kdx
(c)
L(x2 + y 2 )
kqdx
(d)
L(x2 + y 2 )
kq
(e) 2
x +y2
y
dx
x
7
13. A spherical balloon made of nonconducting material has a positive charge
on its surface. The balloon is now
expanded. Which of the following
statements is FALSE?
(a) The magnitude of the electric field at a
point that is inside the balloon before
and after expansion does not change.
(b) The magnitude of the electric field at a
point that is outside the balloon before
and after expansion does not change.
(c) The magnitude of the electric field at a
point on the surface of the balloon
does not change.
(d) The magnitude of the electric field at
a point that was outside the balloon
before expansion but is now inside
decreases.
(e) The magnitude of the electric field at a
point that is always inside the balloon
is zero.
14. An infinitely long line of charge with
a linear charge density λ passes through
the axis of a cylinder as shown below.
The cylinder has a length L and a radius
R. What is the magnitude of the electric
flux through the surface of the cylinder?
(a) λL/ε0
(b) 2πλRL/ε0
(c) 2πRL/ε0
(d) (2πRL + 2πR2 )/ε0
(e) (2πRL + 2πR2 )λ /ε0
L
8
15. A very large plastic sheet with a
uniform positive surface charge density σ
on both surfaces is placed parallel to
another very large plastic sheet with a
negative surface charge density -σ on
both surfaces as shown in the edge-on
view below. What is the electric field in
the region between the two sheets?
(a)
(b)
(c)
(d)
(e)
+
+
+
+
+
+
+
+
+
+
+
+
+
+
-
-
-
-
16. A net charge Q is distributed
uniformly throughout the volume of a
sphere of radius R. What is the
magnitude of the electric field within the
sphere at a distance r < R from the center
of the sphere?
2σ
pointing to the left
ε0
σ
pointing to the right
ε0
Zero
σ
pointing to the left
ε0
2σ
pointing to the right.
ε0
Qr
4πε 0 R2
Q
(b)
4πε 0r 2
Q
(c)
4πε 0 R2
Qr
(d)
4πε 0 R3
(a)
Qr 3
(e)
4πε 0 R3
9
17. The figure below shows a point
charge +Q located at the center of a
spherical conducting shell of inner radius
A and outer radius B. The distance r is
measured from the center of the sphere.
Which of the following statements is
FALSE?
+Q
(a) The total charge on the outside surface
of the shell = +Q.
(b) The total charge on the inside surface
of the shell = -Q.
(c) The electric field in the region
A < r < B is zero.
(d) The electric flux through the shell
does not change if the position of the
charge is changed.
(e) The electric field outside the shell (r >
B) changes if the position of the
charge is changed.
A
B
18. A thin plastic rod with a negative
uniform charge -Q is shaped like a circle
of radius R. How much work would you
need to do to bring a negative charge -q
from infinity to the center of the circle?
(a) Zero since the electric field at the
center is zero.
kQq
(b) −
R
kQ
(c) −
R
kQq
(d) +
R
kQ
(e) +
R
10
19. The figure below shows 3
equipotentials shaped like concentric
ellipses: the center ellipse is at 0V, the
middle one at +100 V and the outer one at
+200 V. The points A, B and C lie on the
outer, middle and inner ellipses,
respectively, and form a straight line that
is perpendicular to the equipotentials.
Which of the following statements is
correct?
A
(a) An electron released from rest at point
B will reach point A with a kinetic
energy of 1.6 x 10-17 J.
(b) A proton released from rest at point A
will reach point C with zero kinetic
energy.
(c) You would need to do to 3.2 x 10-17 J
of work to move an electron from
point C to point A.
(d) The electric field at C points towards
B.
(e) The electric field at B points towards
A.
B
C
0V
+100 V
+200 V
20. A solid spherical conductor is given a
net non-zero charge. Which of the
following statements is correct?
(a) The electrostatic potential is largest at
the center.
(b) The electrostatic potential is largest at
the surface.
(c) The electrostatic potential is largest
somewhere in between the center and the
surface.
(d) The electrostatic potential is constant
throughout the volume of the sphere.
(e) We cannot say anything about the
electrostatic potential without more
details.
11
Answer Key to Sample Exam 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
c
d
c
c
e
e
d
e
b
d
b
d
c
a
e
d
e
(Remaining questions on potential do not apply to Mid Term1 in Sp. 99)