Quantitative
1) How much work does it take to move an electron 7.0 m at an angle of 30.0° to r, in the
presence of a uniform electric field E = 5.0 r N/C?
A) 6.1 eV
2) Consider the group of charges in this figure. All three charges have Q = 2.4 nC. What is their
electric potential energy?
A) 4.1 × 10-6 J
3) Three electrons are placed at the vertexes of an equilateral triangle with side length of 5.1
nm. A proton is placed at the center of the triangle. What is the potential energy of this
arrangement of charges?
A) -9.9 × 10-38 J
4) A 6.0 μC negative charge is attracted to a large, well-anchored, positive charge. How much
kinetic energy does the negatively charged object gain if the potential difference through
which it moves is 3 mV?
A) 18 nJ
Solve the problem. (The value of k is 9.0 × 109 N∙m2/C2.)
7) Three 6.0 μC point charges are located at an extreme distance of 100,000 km from the origin,
and are configured as an equilateral triangle with sides of length 1.0 mm. How much work
does it take to move the three charges to a position centered about the origin while
preserving the geometry of the configuration?
A) 0 J
8) An electron was accelerated from rest through a potential difference of 9900 V. What is its
speed?
A) 5.9 × 107 m/s
12) Two 3.0 μC charges lie on the x-axis, one at the origin and the other at 24.0 m. A third point
is located at 72.0 m. What is V72.0m ? (The value of k is 9.0 × 109 N∙m2/C2.)
A) 940 V
Solve the problem. (The value of k is 9.0 × 109 N∙m2/C2.)
13) A 3.0 μC point charge and a 9.0 μC point charge are initially infinitely far apart. How much
work does it take to bring the 3.0 μC point charge to x = 3.0 mm, y = 0.0 mm and the 9.0 μC
point charge to x = -3.0 mm, y = 0.0 mm?
A) 41 J
14) A charge of 3.0 μC and a second charge are initially far apart. If it takes 29 J of work to bring
them to a final configuration in which the 3.0 μC is at x = 1.0 mm, y = 1.0 mm, and the other
charge is at x = 1.0 mm, y = 3.0 mm, find the magnitude of the unknown charge.
A) 2.15 μC
18) Three charges form an equilateral triangle with 1.6 cm long sides. What is the electric
potential at the point indicated with the dot?
A) zero
Solve the problem. (The value of k is 9.0 × 109 N∙m2/C2.)
19) Eight 3.0 μC charges are located at the vertices of a unit cube centered about the origin with
1.0 mm edges. How much work does it take to bring a 5.0 μC charge from infinity to the
origin?
A) 1200 J
True/False
1) Suppose you have two point charges, +Q and -q. As you pull them farther and farther apart,
you increase the potential energy of this system relative to infinity.
Answer: TRUE
2) Two equal positive charges are separated by a fixed distance. If you put a third positive
charge midway between these two charges, its electrical potential energy (relative to infinity)
is zero because the electrical forces due to the two fixed charges just balance each other.
Answer: FALSE
3) Suppose you have two positive point charges and want to move them closer together. To do
the least amount of work, you should move them directly toward each other; any other path
will require more work because the charges must move through a greater distance.
Answer: FALSE
4) If an object is at zero potential, it must be uncharged.
Answer: FALSE
5) You want to put an electron somewhere between the plates of a parallel plate capacitor so
that it will have the maximum electrical potential energy relative to one of the plates. The
best place to put it is at the inner surface of the negative plate.
Answer: TRUE
6) If the electrical potential is 100 V at 1.0 cm from a point charge, the potential will be 25 V if
you go twice as far away.
Answer: FALSE
7) Two equal but opposite point charges are held a distance D apart, and a third point charge Q
is placed midway between them. When Q is released it will remain at rest because its
potential energy is zero at the midpoint.
Answer: FALSE
8) Four identical positive point charges lie at the corners of a square. The electrical potential at
the center of this square is zero because the electric fields all cancel at that point.
Answer: FALSE
Conceptual
1) Why is it possible to label any potential level as zero with respect to a given charge?
Answer: The choice of 0 V is arbitrary. The interest is in potential difference.
2) Why is it not proper to discuss an absolute potential at a given point?
Answer: Potential is a difference, hence it requires two points to have meaning.
3) As an electron moves from a high potential to a low potential, its electrical potential energy
A) increases.
B) decreases.
C) remains constant.
Answer: A
4) A point charge of q and a second of 2q are initially infinitely far apart. It takes W joules of
work to bring them to a distance of 1 m apart. Explain how, since the charges differ, the
work is the same regardless of which charge moves.
Answer: Vr  is proportional to the charge that does not move, so W is proportional to the
product of both charges.
5) If work is done by an electric field on a charged particle, the particle's velocity increases.
Explain this in terms of conservation of energy.
Answer: Potential energy decreases, so kinetic energy increases.
6) An electron at a certain electrical potential is surrounded by a spherical surface at a higher
potential, which is surrounded by a second concentric spherical surface at the original
potential. What is the approximate probability the electron will migrate to the outer surface?
Answer: Zero
7) A parallel plate capacitor contains a positively charged plate on the left, and a negatively
charged plate on the right. An electron in between the plates is moving to the right. Which
statement is true?
A) The potential energy of the electron is increasing and it is moving to a region having a
lower potential.
10) A hydrogen atom consists of a proton and an electron. If the orbital radius of the electron
increases, the potential energy of the electron
A) increases.