Dr. M. F. Al-Kuhaili – PHYS 102 – Chapter 21 Page 1

PHYS102 Previous Exam Problems –

CHAPTER

21

Electric Charge

Charge quantization Charge conservation Conductors & insulators Coulomb’s law

1. Particle 1 with charge q1, and particle 2 with charge q2 are on the x axis, with particle1 at x = 4.0 cm and

particle 2 at x = −2.0 cm. Find the relationship between q1 and q2 so that the net force on a third particle of

charge q located at the origin, be zero. (Ans: q2 = q1 / 4)

2. A particle with charge 2.0 µC is placed at the origin. An identical particle, with the same charge, is placed

2.0 cm from the origin on the positive x axis. A third identical particle, with the same charge, is placed 2.0 cm

from the origin on the positive y axis. What is the magnitude of the force on the particle at the origin?

(Ans: 1.3×102 N)

3. In figure 1, charge Q = - 3.7 nC. For what value of charge q1 will charge q2 be in static equilibrium?

(Ans: 15 nC)

4. Two neutral metal spheres are separated by 0.3 km. How much electric charge must be transferred from

one sphere to the other so that their electrical attraction is 103 N? (Ans: 0.1 C)

5. A negative charge is placed at the center of a square. Each corner of the square has a fixed charge of 1.00

μC. If the resulting force acting on each charge is zero, what is the magnitude of the negative charge?

(Ans: 0.96 μC)

6. Consider two conducting spheres, A and B, having the same size. Sphere A carries a charge of - 2.0 μC,

and sphere B carries a charge of + 6.0 μC. The spheres are touched together and then separated. What is the final

charge on sphere A? (Ans: + 2.0 μC)

7. Two point charges q1= + 2.0×10-6 C and q2 = -8.0×10-6 C are located at (0.0, 0.0) cm and (10.0, 0.0) cm,

respectively. Another positive point charge q3 is to be located somewhere, on x axis, such that the net

electrostatic force on it due to q1 and q2 is zero. What is the location of q3? (Ans: (-10.0,0.0) cm)

8. Two identical positively charged ions are separated from each other by a distance of 6.8×10-9 m. If the

electrostatic force between them is 4.5×10-9 N, how many electrons are missing from each ion? (Ans: 30)

9. Consider the charges shown in figure 4. Find the magnitude and sign of charge Q4 so that the net

electrostatic force on charge Q5 is zero. (Ans: + 1.8 nC)

10. Two small identical conducting spheres, initially uncharged are separated by a distance of 1.0 m. Find

the number of electrons that must be transferred from one sphere to the other in order to produce an attractive

force of 2×104 N between the spheres. (Ans: 9.3×1015)

Dr. M. F. Al-Kuhaili – PHYS 102 – Chapter 21 Page 2

11. Consider three charges fixed on the x axis as follows: q1 = 2.0 µC located at x1 = 0.0 m, q2 located at x2 =

4.0 m, and q3 = - 1.0 µC located at x3 = 6.0 m. What is the value of q2 such that the force on q3 is zero?

(Ans: q2 = - 0.22 µC)

12. Consider two identical conducting spheres, S1 and S2. Initially, sphere S1 has a charge of - 40 µC and

Sphere S2 has a charge of + 20 µC. If the spheres are touched together and then separated by a distance of 0.20

m, what is the resultant force between them? (Ans: 23 N, repulsive)

13. Two 1.0-g spheres are charged equally and placed 2.0 cm apart. When released, each one begins to

accelerate at 225 m/s2. What is the magnitude of the charge on each sphere? (Ans: 1.0×10-7 C)

14. Two positive charges (+8.0 C and +2.0 C) are separated by 300 m. A third charge is placed a distance r

from the +8.0 C charge so that the resultant electric force on the third charge due to the other two charges is

zero. What is the distance r? (Ans: 200 m)

15. In figure5, Q = 60 μC, q = 20 μC, a = 3.0 m, and b = 4.0 m. Calculate the total electric force on q.

(Ans: 0.69 i N)

16. In figure 6, if Q = 30 μC, q = 5.0 μC, and d = 0.3 m, find the net force on q. (Ans: zero)

17. Two small charged objects repel each other with a force F when separated by a distance d. If the charge on

each object is reduced to one-fourth of its original value and the distance between them is reduced to d/2, what

will be the force? (Ans: F/4)

18. In figure 8, a point charge q1 = +Q is placed at the center of a square, and a second point charge q2 = −Q is

placed at the upper-left corner. It is observed that an electrostatic force of 2.0 N acts on the positive charge at the

center. What is the magnitude of the force that acts on the center charge if a third charge q3 = −Q is placed at the

lower-left corner as shown? (Ans: 2.8 N)

19. Three point charges Q1, Q2 = 20 μC and Q3 = 50 μC are located as shown in figure 9. If the net force on Q3

is in the direction of the negative y axis, find the charge of Q1. (Ans: – 10 μC)

20. Particles A and B are electrically neutral and are separated by 5.0 μm. If 5.0×106 electrons are

transferred from particle A to particle B, what is the magnitude of the electric force between them?

(Ans: 2.3×10-4 N)

21. In figure 10, the net force on the 1 nC charge is zero. What is the charge q, if a = 3 cm and b = 2 cm?

(Ans: +0.68 nC)

22. In figure 12, three positively charged particles form a right angle triangle with two equal sides a = 50 cm.

The charges are q1 = q3 = 2Q and q2 = Q. Find the value of the charge q2 if the magnitude of the net electrostatic

force on it is 0.23 N. (Ans: 1.5 μC)

23. Three fixed point charges are arranged as shown in figure 14, where initially Q1 = 10 μC, Q2 = –15 μC,

and Q3 = –25 μC. If charges Q2 and Q3 are connected by a very thin conducting wire and then disconnected,

what is the net electric force that now acts on charge Q1? (Ans: (+2000 i + 2000 j ) N)

24. Figure 16 shows three charges +q,–q and Q along with net force F on charge – q. If θ = 45° , what is the

value of charge Q? (Ans: +4q)

Dr. M. F. Al-Kuhaili – PHYS 102 – Chapter 21 Page 3

25. Four identical metal spheres (A, B, C, D) have charges of qA = – 8.0 μC, qB = – 2.0 μC, qC = + 5.0 μC, and

qD = + 12.0 μC. Then, three of the metal spheres are brought together so that they touch each other

simultaneously, and then they are separated. Which of the three spheres were touched together, if the final

charge on each of the three spheres is + 3.0 μC? (Ans: A, C, D)

26. Consider two neutral point particles of mass 5.0 g each. A total of 4.0 × 1012 electrons are transferred

from one neutral particle to the other. How far apart must the two particles be if the magnitude of the

electrostatic force between them is equal to the magnitude of the weight of one of the particles on earth surface?

(Ans: 27 cm)

A B C D E Conceptual Problems

1. Four point charges, each of the same magnitude, are arranged at the corners of a square, as shown in figure

2. Which of the arrows labeled A, B, C, and D gives the correct direction of the net force that acts on the charge

at the upper right corner?

A. B

B. A

C. C

D. D

E. The net force on that charge is zero.

2. Three identical point charges, Q, are placed at the corners of an equilateral triangle, as shown in the figure

3. The length of each side of the triangle is d. Determine the magnitude and direction of the total electrostatic

force on the charge at the top of the triangle.

3. An electrical insulator is a material

A. through which electrons do not flow easily.

B. containing no electrons.

C. that has more electrons than protons on its surface.

D. through which electrons flow easily.

E. has very low resistance.

4. Specify the wrong statements:

A. In solid metal conductors electrons as well as positive ions can move.

B. Charge is quantized.

C. Charge is conserved

D. Coulomb’s law gives the force between static point charges.

E. The principle of superposition means that the force between two static particles is

not affected by the presence of other particles.

Dr. M. F. Al-Kuhaili – PHYS 102 – Chapter 21 Page 4

5. Consider three point charges q1, q2 and q3. If q1

repels q3

and q3

attracts q2, then one possibility is that:

A. q1 and q3

are positive and q2

is negative.

B. q1 is negative, q2

and q3

are positive.

C. q1 is positive, q2

and q3

are negative.

D. q1, q2 and q3

are all positive.

E. q1, q2 and q3

are all negative.

6. A charge q is placed at the center of the line joining two equal charges Q. All charges will be in

equilibrium if q is equal to

A. – Q/4

B. – Q/2

C. Q/4

D. Q/2

E. Q/3

7. Which of the following charges cannot be found in nature?

A. 0.8 ×10-19

C

B. 64 ×10-19

C

C. 16 ×10-19

C

D. 4.8 ×10-19

C

E. 3.2 ×10-19

C

8. Two positively charged particles q1 and q2 (with q2 > q1) are fixed in place on the x axis at the positions

shown in figure 7. A third charge q3 is to be placed somewhere on the x axis such that the net electrostatic force

on q3 is zero. Which one of the following statements is true?

A. q3 should be placed at a point between q1 and q2 but closer to q1.

B. q3 should be placed at the midpoint between q1 and q2.

C. q3 should be placed at a point between q1 and q2 but closer to q2.

D. q3 should be placed to the left of q1.

E. q3 should be placed to the right of q2.

9. Three point charges are fixed on the x axis. Charge q1 is at x = +1 m, charge q2 is at x = 0, and charge q3 is

at x = –1 m. For the net electrostatic force on q3 to be zero:

A. q1 and q2 must have opposite signs and |q1| > |q2|.

B. q1 and q2 must have the same sign and |q1| > |q2|.

C. q1 and q2 must have opposite signs and |q1| < |q2|.

D. q1 and q2 must have the same magnitude and have the same sign.

E. q1 and q2 must have opposite signs and their magnitudes depend on q3.

10. Charges q1 and q2 are on the x axis. q1 is at x = a and q2 is at x = 2a. The net force on a third charge at the

origin is zero. Which of the following statements is true?

A. q2 = -4q1

B. q2 = -2q1

C. q2 = -q1

D. q2 = 2q1

E. q2 = 4q1

Dr. M. F. Al-Kuhaili – PHYS 102 – Chapter 21 Page 5

11. Two small charged objects attract each other with a force F when separated by a distance d. If the charge

on each object is reduced to one-fourth of its original value and the distance between them is reduced to d/2 the

force becomes:

A. F/4

B. F/2

C. F/16

D. F

E. F/8

12. Two particles, each with charge Q, and a third particle, with charge q, are placed at the corners of an

equilateral triangle, as shown in figure 11. The total force on the particle with charge q is:

A. Perpendicular to the bottom side of the triangle.

B. Parallel to the bottom side of the triangle.

C. Parallel to the right side of the triangle.

D. Parallel to the left side of the triangle.

E. Perpendicular to the right side of the triangle.

13. Figure 13 shows three pairs of identical small conducting spheres that are to be touched together and then

separated. The initial charges on them are indicated in the figure (e is the elementary charge and has the value

1.6×10-19 C). Rank the pairs according to the magnitude of the charges transferred during touching.

A. 3, 1, 2

B. 1, 2, 3

C. 3, 2, 1

D. 1, 3, 2

E. all tie

14. Consider an object having a charge Q. Charge q is removed from it and is placed on a second initially

uncharged object. The two objects are placed 1.0 m apart. What should be the value of q such that the force

between the two objects is maximum?

A. Q/2

B. 2Q

C. Q

D. Q/4

E. 0

15. A particle of charge q1 = –14.4 × 10-19 C is placed at the origin of the x-axis. Two other particles of

charges q2 and q3 are placed at x2 = 1 cm and x3 = 3 cm, respectively, as shown in figure 15. How many

electrons or protons should charge q2 have in order to create a zero net electric force on charge q3?

A. Four protons

B. Four electrons

C. Six protons

D. Six electrons

E. Three electrons

Dr. M. F. Al-Kuhaili – PHYS 102 – Chapter 21 Page 6

16. Two identical conducting spheres A and B carry equal charge Q, and are separated by a distance much

larger than their diameters. Initially the electrostatic force between them is F. A third identical uncharged

conducting sphere C is first touched to A, then to B, and then moved away. As a result of this, the electrostatic

force between A and B becomes:

A) 3F/8

B) F/4

C) F/2

D) F/16

E) F

17. Figure 17 shows four situations in which a central proton (P) is surrounded by protons or electrons fixed

in place along a half-circle. The angles θ = φ = 30°. What is the direction of the net force on the central proton P

due to the other particles?

A) d

B) a

C) b

D) f

E) c

Dr. M. F. Al-Kuhaili – PHYS 102 – Chapter 21 Page 7

Figure1 Figure 2 Figure 3

Figure 4 Figure 5 Figure 6

Figure 7 Figure 8 Figure 9

Figure 10 Figure 11 Figure 12

Figure 13 Figure 14 Figure 15

Dr. M. F. Al-Kuhaili – PHYS 102 – Chapter 21 Page 8

Figure 16 Figure 17