PHY 106 SPRING 2016-2017

MIDTERM 1

March 25, 2017

13:40 PM - 15:30 PM

Exam Booklet: A

Last Name:

First Name:

Student ID:

Instructions:
Do NOT forget to mark the version of your exam booklet on the answer sheet provided.
The exam contains 20 questions, each worth 5 points.
You may work out your solutions in your exam booklet, but you will NOT receive partial credit for any work done. You
MUST mark your responses on the separate answer sheet provided.
Mark only one response for each question. Multiple responses will be considered as incorrect.
Incorrect responses will be penalized; 1.25 points will be deducted for each incorrect response.
Calculators, cell phones and any other electronic devices are NOT allowed. You MUST turn off all your electronic devices
and submit them to your exam proctor(s).

Useful information:
Acceleration due to gravity:
g = 10 m/s2

Fundamental unit of charge:

e = 1.6 × 10 −19 C
Coulomb constant:
k = 9 × 10 9 Nm2/C2
Permittivity of free space:
ε o = 8.85 × 10 −12 C2/N.m2
Values of trigonometric functions for common angles:
sin 30 o = 0.5, cos 30 o = 0.9
sin 37 o = 0.6, cos 37 o = 0.8
sin 45 o = 0.7, cos 45 o = 0.7
sin 53o = 0.8, cos 53o = 0.6
sin 60 o = 0.9, cos 60 o = 0.5

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1. X and Y are two uncharged metal spheres on insulating stands and are in contact with each other. A positively
charged rod R is brought close to X as shown in Figure 1. Sphere Y is then moved away from X as shown in
Figure 2. Which one of the following statements correctly describes the final states of X and Y?

A. Both X and Y are negatively charged

B. Both X and Y are neutral
C. X is positively charged and Y is neutral
D. X is negatively charged and Y is positively charged
E. X is neutral and Y is positively charged

2. As shown in the figure below, one very small charged plastic ball is fixed to the bottom of a test tube. An
identical charged ball of mass m is directly above the first ball. There is no friction between the walls of the
tube and this upper sphere, and the balls are in equilibrium a distance d apart. If the charge on each ball is
doubled, the distance between the balls in the test tube will become

A. 2d
B. 2d
C. 4d
D. 8d
E. d/2

3. A piece of plastic has a net charge of +2.00 µC. How many more protons than electrons does this piece of
plastic have?

A. 3.20 × 1013
B. 3.20 × 1019
C. 1.25 × 1019
D. 1.25 × 1013
E. 8.00 × 1012

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4. Two particles X and Y are a distance d apart. X has a charge of 2Q and Y has a charge of Q. The force of X
on Y

A. has four times the magnitude of the force of Y on X

B. has the same magnitude as the force of Y on X
C. has half the magnitude of the force of Y on X
D. has one-fourth the magnitude of the force of Y on X
E. has twice the magnitude of the force of Y on X

5. Three point charges are placed on the x-axis. The first charge of +2.0 µC is located at the origin, the second
charge of -2.0 µC is located at x = 50 cm, and the third charge of +4.0 µC is located at x = 100 cm. Find the
electrostatic force that acts on the charge located at the origin.

A. −0.036i8 N
B. zero
C. 0.072i8 N
D. 0.036i8 N
E. −0.072i8 N

6. The figure below shows three electric charges labeled Q1, Q2, and Q3, and some electric field lines in the region
surrounding the charges. What are the signs of these three charges?

A. All three charges are positive

B. Q1 is positive, Q2 is positive, and Q3 is negative
C. Q1 is negative, Q2 is positive, and Q3 is negative
D. All three charges are negative
E. Q1 is positive, Q2 is negative, and Q3 is positive

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7. Four equal negative point charges are located at the corners of a square. Their positions (x, y) in the xy-plane
are (1,1) cm, (-1,1) cm, (-1,-1) cm, and (1,-1) cm. Find the direction of the electric field on the x-axis at
(1,0) cm.

A. −i8
B. 8j
C. 8i
D. k8
E. −j8

8. A small sphere of mass 500 g is moving in the positive y-direction when it encounters an electric field of
5i8 N/C. If, due to this field, the sphere suddenly acquires an acceleration of 20i8 m/s2, what is the charge that it
carries? Ignore the effect of gravity.

A. 2C
B. 8C
C. 4C
D. -4 C
E. -2 C

9. Consider the three point charges arranged as shown in the figure below. Find the electrostatic force acting on
Q = 6.00 nC.
Hint: 1 nC = 10−9 C

A. −2.16 × 10−38j N
B. 2.16 × 10−38j N
C. −1.08 × 10−3 8i N
D. 1.08 × 10−38j N
E. 1.08 × 10−3 8i N

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10. Two point charges of +20 µC and -10 µC are separated by a distance of 20 cm. Find the electric field at a point
midway between these two charges.
A. 2.7 × 106 N/C directed toward the negative charge
B. 2.7 × 106 N/C directed toward the positive charge
C. 2.7 × 105 N/C directed toward the negative charge
D. 2.7 × 107 N/C directed toward the positive charge
E. 2.7 × 107 N/C directed toward the negative charge

11. Suppose that there exists a uniform electric field of 4 N/C directed along the positive x-axis. When a point
charge is placed at and fixed to the origin, the resulting electric field on the x-axis at x = 2 m becomes zero.
What is then the magnitude of the resulting electric field on the x-axis at x = 4 m?

A. 1 N/C
B. 3 N/C
C. 4 N/C
D. More information is needed to find the magnitude of the resulting electric field at this position
E. 2 N/C

12. A positive charge of 9 × 10−9 C is uniformly distributed along the x-axis from x = 0 to x = 3 m. Which of the
following integrals correctly describes the electric field on the x-axis at x = 4 m?

A. 3

∫ 18dx
0 (4 − x)2
B. 3

∫ 27dx
0 (3 + x)2
C. 3

∫ 27dx
0 (3 − x)2
D. 3

∫ 27dx
0 x2
E. 3

∫ 27dx
0 (4 − x)2

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13. Two rods of equal length, one with a uniform positive linear charge density of +1.5 × 10−9 C/m and the other
with a uniform negative linear charge density of -1.5 × 10−9 C/m, are bent to form semicircles each of radius
0.3 m. These semicircles are then joined to make a full circle. What is the magnitude of the electric field at the
center of the circle?
π π
Hint: ∫ 0
sin θdθ = 2 and ∫ 0
cos θdθ = 0 , OR
π/2 π/2
∫ −π / 2
sin θdθ = 0 and ∫ −π / 2
cos θdθ = 2

A. 60 N/C
B. 180 N/C
C. zero
D. 120 N/C
E. 240 N/C

14. Two point particles of charges q1 and q2 are placed a distance r apart. The electric field is zero at some point P
between the two particles along the line joining them. We can conclude that
A. q1 and q2 must have the same magnitude and sign
B. q1 and q2 must have opposite signs but may have different magnitudes
C. P must be midway between the particles
D. q1 and q2 must have equal magnitudes and opposite signs
E. q1 and q2 must have the same sign but may have different magnitudes

15. An electric dipole is made up of two charges of equal magnitudes and opposite signs. The positive charge of
+1.0 µC is located at the point (x, y, z) = (0.0, 1.0, 0.0) cm, while the negative charge of -1.0 µC is located at the
point (x, y, z) = (0.0, −1.0, 0.0) cm. How much work will be done by an electric field ä E = 3.0 × 106 8i N/C to
align the dipole along the positive x-direction?
Hint: U = −p
ä⋅ä
E

A. 0.060 J
B. 0.040 J
C. 0.020 J
D. zero
E. 0.010 J

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16. Two imaginary concentric spherical surfaces of radii R and 2R surround a positive point charge Q located at
their center. How does the number of electric field lines N1 going through the spherical surface of radius R
compare to the number of electric field lines N2 going through the spherical surface of radius 2R?

A. N2 = N1 / 2
B. N2 = 2N1
C. N2 = N1 / 4
D. N2 = N1
E. N2 = 4N1

17. Three cylinders 1, 2, and 3 are aligned vertically and separated from each other. The values of the electric flux
in Nm2/C through the top, bottom, and curved surfaces of the cylinders are given in the table below. Rank the
total electric charge inside these cylinders from most negative to most positive.
cylinder top surface bottom surface curved surface

1 2 × 10−9 2 × 10−9 −8 × 10−9

2 zero zero −8 × 10−9

3 −2 × 10−9 2 × 10−9 6 × 10−9

A. 1, 3, 2
B. 2, 1, 3
C. 3, 2, 1
D. 2, 3, 1
E. 3, 1, 2

18. Charges q and Q are placed on the x-axis at x = 0.40 m and x = 2.00 m, respectively. If q = −88.5 × 10−12 C and
Q = +30.0 × 10−12 C, determine the net flux through a spherical surface of radius 1.0 m centered at the origin.

A. zero
B. -20.0 Nm2/C
C. +10.0 Nm2/C
D. +20.0 Nm2/C
E. -10.0 Nm2/C

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 E = 8j8 + 2k8 N/C. Calculate the electric flux
19. The electric field in the region of space shown below is given by ä
through the top face of the cube.

A. 36 Nm2/C
B. 12 Nm2/C
C. 18 Nm2/C
D. 72 Nm2/C
E. 54 Nm2/C

20. A thick spherical conducting shell surrounds a point particle of charge -q located at its center. A charge of +3q
is then added to the shell. When static equilibrium is reached, the charges on the inner and outer surfaces of the
shell are respectively

A. +3q and zero

B. -q and +q
C. +2q and +q
D. +q and -q
E. +q and +2q

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PHY 106 SPRING 2016-2017 MIDTERM 1 - VERSION A
Answer Section

MULTIPLE CHOICE

1. ANS: D
2. ANS: B
3. ANS: D
4. ANS: B
5. ANS: C
6. ANS: E
7. ANS: A
8. ANS: A
9. ANS: E
10. ANS: E
11. ANS: B
12. ANS: E
13. ANS: B
14. ANS: E
15. ANS: A
16. ANS: D
17. ANS: B
18. ANS: E
19. ANS: C
20. ANS: E

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