chapter electric fields 22€¦ · a +40-μc charge is positioned on the x axis at x = +4.0 cm. to...

Dr. M. F. Al-Kuhaili – PHYS 102 – Chapter 22

PHYS102 Previous Exam Problems–

CHAPTER

22

Electric Fields

Electric field Point charge in an electric field Electric dipole

1. Two identical charges, each of charge Q, are positioned at points A (5.0 m, 0.0 m) and B ( -5.0 m, 0.0 m) to

produce a net electric field of E = - 10 j (N/C) at point C (0.0 m, 5.0 m). Find the value of Q. (Ans: -39 nC)

2. The dipole moment of an electric dipole in a 300-N/C electric field is initially perpendicular to the field, but

it rotates so that it becomes in the same direction as the field. If the electric dipole moment has a magnitude of

2.0×10-9 C.m, how much work is done by the field? (Ans: + 6.0×10-7 J)

3. Two electric charges are arranged as shown in figure 1. If d = 7.2 cm, what is the resultant electric field at

P? (Ans: 1.23×104 N/C making an angle of 45o with + x axis)

4. In figure 2 , a uniform electric field E = -18 j (N/C) exists between two plates that are 4 cm apart. A proton

is fired from the lower plate with a velocity of 8×103 j(m/s). Find the distance from that plate at which the

instantaneous velocity of the proton is zero. [ignore gravity] (Ans: 1.9 cm)

5. An electron with initial velocity 3.5×105 i (m/s) enters a region in which the electric field is 400 i (N/C).

What is the speed of the electron 2.0 ns after it enters the electric field? (Ans: 2.1×105 m/s)

6. A uniform electric field has a magnitude of 2.0×104 N/C and points to the right. An electron is released

from rest in this electric field. How far will the electron travel in two nanoseconds after its release?

(Ans: 7.0 mm to the left)

7. A +40-μC charge is positioned on the x axis at x = +4.0 cm. To produce a net electric field of zero at the

origin, where should a -60 μC charge be placed? (Ans: x = + 4.9 cm)

8. Three point charges q1, q2, and q3 are fixed at the three corners of a right-angle triangle as shown in figure

4. Given that q1 = q2 = +3.2×10-19 C while q3 = -1.6×10-19 C, and b = 5.0 cm, find the net electric field at point P

due to all the three point charges. (Ans: 1.15×10-6 N/C, toward q3)

9. The electric field between two long and parallel charged plates is uniform, and is equal to E = 240 j (N/C).

An electron with velocity components vx = 3.0×105 m/s and vy = 2.0×10 3 m/s enters the region between these

plates. What is the acceleration of the electron when its x coordinate has changed by 2 cm?

(Ans: - 4.2×1013 j m/s)

10. Figure 5 shows a charged ball of mass m = 1.0 g that is suspended by a light string in the presence of a

uniform electric field, E = -3.0×105 i (N/C ). In this field, the ball is in equilibrium at θ = 37o. What is the charge

q on the ball? (Ans: -2.46×10-8 C)


11. A proton is located at the origin and an electron is located on the y axis at y = +1.0 mm. What is the

electric dipole moment of these two particles? (Ans: -1.6×10-22 j C.m)

12. A charged particle with a mass of 2×10-4 kg is held suspended (stationary) by a downward electric field of

300 N/C. What is the charge on the particle? (Ans: – 6.5×10-6 C)

13. In figure 7, two charges q1 = –5.0 μC, q2

= 10 μC, are fixed on the x axis. At what distance, measured from

q1, will the electric field be zero? (Ans: 2.4 m to the left of q1)

14. Six point charges are placed on the corners of a regular hexagon, as shown in the figure 9. Five of them

have a charge of + 1.0 µC and the sixth has a charge of – 1.0 µC. If the distance from the center of the hexagon

to its corner is 1 cm, what is the magnitude of the electric field at the center? (Ans: 1.8×108 N/C)

15. A uniform electric field is set up between two large charged plates, as shown in figure 10. An electron is

released from the negatively charged plate, and at the same time, a proton is released from the positively

charged plate. They cross each other at a distance of 5.00×10-6 m from the positively charged plate. If only the

field due to the charged plates is considered, find the distance between the two plates. [Take the ratio mass of

the electron : mass of the proton = 1 : 1833] (Ans: 9.17 mm)

16. In figure 11, a 0.3-g metallic ball hangs from an insulating string in a vertical electric field of 4000 N/C

directed upward as shown. If the tension in the string is 0.005 N, then what is the charge on the ball?

(Ans: -0.52 μC)

17. A particle (m = 5.0 g, q = 40 mC) moves in a region of space where the electric field is uniform and is

given by E = -5.5 i (N/C). If the velocity of the particle at t = 0 is given by v = 50 j (m/s), find the speed of the

particle at t = 2 s. (Ans: 101 m/s)

18. In figure 12, what is the magnitude of the electric field at point P, center of the equilateral triangle? [Take

d = 2 m, q = 1 nC] (Ans: zero)

19. In figure 13, find the magnitude of the electric field at point R: (0,4) mm due to the two-point charges q (1

μC) and - q placed at points A: (-3, 0) mm and B: (3, 0) mm, respectively. (Ans: 4.3×108 N/C)

20. A point charge of 4.0 nC is located at a point having coordinates (30.0 cm, 40.0 cm). At what point will

the electric field be 72 N/C and pointing in the negative y direction? (Ans: (30.0, -30.7) cm)

21. Two large metal plates are 10.0 cm apart and have a uniform electric field between them as shown in

figure 16. An electron is released from rest from the negative plate at the same time a proton is released from

rest from the positive plate. Find the ratio of the distance covered by proton to that of electron when they pass

each other. (Ans: 5.46×10-4)

22. The electric field 20 mm from a certain point charge has a magnitude |E|. What is the magnitude of the

electric field 10 mm from the point charge? (Ans: 4.0|E|)

23. Figure 17 shows a particle with positive charge +Q and a particle with negative charge –Q, both fixed in

place. What is the electric field at point P? [Take = 1.00 μC] (Ans: = 432 j N/C)

24. Consider two negative point charges q1 at (10, 0) cm and q2 at (0, 20) cm. Find the ratio of the magnitudes

of these two point charges |q1/q2| so that the electric field at the origin makes an angle = 45º with the +x axis.

(Ans: 1/4)

25. A uniform electric field is given by E = 500 i (N/C). What is the net force on a 5.0-μC charge placed at

(3.0 m, 4.0 m)? (Ans: 2.5 i mN)


26. A 1.0-nC charged particle is located at the origin. Determine the electric field at the point x = 1.0 m, y =

1.0 m. (Ans: 3.2 ( i + j ) N/C)

27. Two charges lie on the x axis: Q1 = -1×10-8

C is at x = 0.01 m, Q2

= 5×10-8

C is at x = 0.03 m, what is the

electric field at the origin? (Ans: 4.0×105 N/C along + x axis)

28. An electron is moving along the positive x axis with a constant speed of 1.5×108 m/s. When it is at a point

+ 500 m from the origin, an electric field of magnitude 2.0×103 N/C and directed along the positive x axis is

switched on. At what point will the electron stop momentarily? (Ans: x = 532 m)

29. An electric dipole, of electric charge 9.3×10-12 C and distance 1.0×10-3 m, is in an electric field of strength

1100 N/C. What is the difference in potential energy corresponding to dipole orientations parallel and anti-

parallel to the field? (Ans: 2.05×10-11 J)

30. Three point charges are fixed on the y axis, as shown in figure 19, with q = +1.0 μC. The net electric field

at point P is zero. What is the charge Q? (Ans: - 0.43 μC)

31. An electric dipole consists of two opposite charges, each of magnitude 2.0 nC. A uniform electric field of

magnitude 300 N/C makes an angle of 25° with the dipole moment of the dipole. If the torque exerted by the

field has a magnitude of 2.5 × 10-11 N.m, what is the distance between the two charges of the dipole?

(Ans: 99 μm)

32. A point charge Q = - 500 nC and two unknown point charges, q1 and q2, are placed as shown in figure 20.

The net electric field at the origin O , due to charges Q, q1 and q2, is equal to zero. What are the charges q1 and

q2, respectively? (Ans: + 131 nC, −106 nC)

33. An electric dipole of electric dipole moment p = (5.0×10-10 C.m) i is placed in an external electric field

given by E = (2.0×106 N/C) i + (2.0×106 N/C) j . What is magnitude of the maximum torque experienced by the

dipole? (Ans: 1.4×10-3 N.m)

34. An electric dipole consists of two opposite charges, each of magnitude 5.00×10−19 C, separated by a

distance d = 1.00×10−9 m. The dipole is placed in a uniform electric field of strength 2.45×105 N/C. Calculate

the torque exerted on the dipole when the dipole moment is perpendicular to the electric field, as shown in

figure 22. (Ans:1.23×10−22 N.m, into the page)

35. For the arrangement of charges shown in figure 23, what is the electric field at point P? [q = 1.0 μC and d

= 50 cm] (Ans: − 47 j kV/m)

36. Four point charges are placed at the corners of a square as shown in figure 25.What is the magnitude of

the electric field at the center of the square? (Ans: 5.66kq/a2)

37. As shown in figure 27, an electric dipole is placed in a uniform electric field of magnitude E = 5.0×105

N/C. The charges are ±1.6×10-19 C, and are separated by 0.125 nm. Find the magnitude and direction of the

torque. (Ans: 5.7×10-24 N·m, out of the page)

38. Two point charges, Q1 and Q2, are shown in figure 28. Q1 = −5.00 μC, and the net electric field at point P

is E = -6.00×10-4 i (N/C). Find the charge Q2.

39. Four charges are placed on the circumference of a circle of radius R = 1.00 m and centered at the origin as

shown in figure 30. Find the electric field at the origin. (Ans: -9.0×104 j N/C)


40. Two charges, +2.00 nC and −2.00 nC, are positioned at the coordinates (1.00 m , 0) and (0, 1.00 m)

respectively in an isolated space. What is the magnitude and direction of the electric field at the origin?

(Ans: 25.5 N/C, 1350 from positive x-axis)

41. An electric dipole moment of magnitude p = 3.02×10-25 C.m makes an angle 64o with a uniform electric

field of magnitude E = 46.0 N/C. How much work is required to turn the electric dipole by 90o?

(Ans: 1.85×10-23 J)

42. As shown in figure 33, two parallel plates are 2.0 cm apart and the electric field strength between them is

1.42×104 N/C. An electron is launched at 45° from the positive plate with an initial speed vo = 1.00×107 m/s.

Determine the speed of the electron at the midpoint between the plates. (Ans: 7.1×106 m/s)

43. It requires an external agent a work of 1.30×10-23 J to turn an electric dipole 180o in a uniform electric

field if p = 3.00×10-25 C.m, and the initial angle with respect to the electric field direction is 76o. Find the

magnitude of electric filed. (Ans: 90 N/C)

44. A charged particle with mass 2.0×10-4 kg is moving vertically down with acceleration 2.0 m/s2 under the

action of gravity and a downward electric field of 300 N/C. What is the charge on the particle? (Ans: -5.2 μC)

45. A uniform electric field, with a magnitude of 4 N/C, points in the positive x direction. When a charge is

placed at the origin, the resulting electric field on the x axis at x = 2 m becomes zero. With the charge still at the

origin, what is the magnitude of the electric field at x = +4 m? (Ans: 3 N/C)

46. In figure 38, eight particles form a square in which the distance d = 4.0 cm. The charges are q1 = -4e,

q2 = -e, q3 = -5e, q4 = +2e, q5 = -4e, q6 = -e, q7 = -5e, and q8 = -e. In unit-vector notation, what is the net electric

field at the center of the square?(e is the magnitude of the charge of the electron) (Ans: –2.7 × 10−6 i N/C)

47. A positively charged sphere of mass 1.00 g falls from rest from a height of 5.00 m, in a uniform electric

field of magnitude 1.00×104 N/C that is directed vertically downward. The sphere hits the ground with a speed

of 20.0 m/s. What is the charge on the sphere? (Ans: 3.02 µC)

48. A charged particle (mass = 5.0 g and charge = 4.9 μC) is shot horizontally with an initial velocity

2.0 i km/s between two plates where the electric field is E = 1.0 × 104 j (N/C), as shown in figure 40. What will

be the velocity of the particle after moving for two seconds between the plates? (Ans: 2.0 i km/s)

49. Three point charges are located on a circular arc as shown in figure 41. What is the magnitude of net

electric field at point P, the center of the arc? (Ans: 2.61 × 103 N/C)

50. A certain electric dipole is placed in a uniform electric field E

of magnitude 10 N/C. The magnitude of

torque on the dipole plotted as a function of the angle between E

and the dipole moment p is shown in figure

42. How much work is needed by an external agent to turn the electric dipole from 300 to 600 with respect to E

field? (Ans: +1.83 ×10-1 J)

51. Figure 44 shows an arrangement of three charged particles, with angle θ =30.0o and distance d = 2.00 cm.

Particle 1 has charge q1= +12.0 × 10-6 C while particles 2 and 3 have charges q2 = q3 = −2.00 × 10-6 C. What is

distance D between the origin and particle 1 if the net electrical field at point P due to the three particles is zero?

(Ans: 2.30 cm)


A B C D E Conceptual Problems

1. Two charges Q1 and Q2 of equal magnitudes and opposite signs are positioned as shown in the figure 3.

Which of the shown arrows represents correctly the electric field at point P?

A. A

B. B

C. C

D. D

E. The electric field is zero.

2. A particle, of mass m and charge q, is placed at rest at point A in a uniform electric field E, as shown in

figure 6. If the particle is released, then what is the kinetic energy it attains after moving a distance y?

3. In a uniform electric field, which statement is correct?

A. All electric field lines are parallel.

B. All charged particles experience the same force.

C. All charged particles move with the same velocity.

D. All electric field lines are directed away from the negative charges.

E. All electric field lines are directed towards the positive charges.

4. What is the electric field on the y axis at a distance b from the origin due to two identical positive point

charges, each of charge q, located on the x axis one at a distance b and the other a distance –b from the origin, as

shown in figure 8?

A. k q/( b2√2) in the positive y-direction. B. k q/(b2√2) in the negative y-direction. C. k q2/ b2

in the positive y-direction.

D. (k q/ b2)/2 in the positive y-direction.

E. (k q/ b2)/2 in the negative y-direction.

5. In figure 14, four charges are placed on the circumference of a circle of diameter 2 m. If an electron is

placed at the center of the circle, then the electron will [Take Q = 60 μC, q = 20 μC]

A. stay at the center.

B. move to the right.

C. move to the left.

D. move upward.

E. move downward.

6. At which point can the electric field due to the two charges shown in figure 15 be zero?

A. point E

B. point A

C. point B

D. point C

E. point D


7. Which statement is false?

A. Electric field lines extend away from negative charge and toward positive charge.

B. Electric fields are vector fields.

C. The principle of superposition applies to electric fields as well as

to electrostatic forces.

D. The electric dipole consists of two charges of the same magnitude but

opposite sign.

E. When an electric dipole is placed in a uniform electric field, the net force on it

is zero.

8. Four electric charges are arranged so that the total electric field at the origin is zero. Which configuration

in figure 18 would achieve this?

A. configuration 1

B. configuration 2

C. configuration 3

D. configurations 1 and 3

E. configurations 2 and 3

9. In figure 21, four positive charges are fixed on the circumference of a circle of diameter 2.0 m. If an

electron is placed at the center of the circle, then the electron will [Take Q = 60 μC, q = 20 μC]

A. move South West.

B. move North East.

C. move toward the West.

D. move toward the South.

E. stay at the center.

10. Two particles of the same mass carrying charges +3Q and -2Q are shot into a region that contains a

uniform electric field as in figure 24. The particles have the same initial velocities in the + x direction. The

direction of the electric field is as shown. What will be the resulting paths for the particles?

A. path 5 for +3Q and path 2 for -2Q

B. path 1 for +3Q and path 4 for -2Q

C. path 3 for +3Q and path 2 for -2Q

D. path 4 for +3Q and path 3 for -2Q

E. path 2 for +3Q and path 5 for -2Q

11. Which one of the following statements is wrong?

A. Electric field lines extend away from negative charges and toward positive charges.

B. Electric field lines form a vector field.

C. The principle of superposition applies to electric fields as well as electrostatic

forces.

D. The electric dipole consists of two charges having the same magnitude but opposite sign.

E. When an electric dipole is placed in a uniform external electric field, the net force on

it is zero.

12. Two point charges, q1 = + 4 μC and q2 = – 2 μC, are fixed on the x axis, as shown in figure 26. Which of

the following statements regarding the electric field produced by the two charges on the x axis is correct?

A. The electric field points to the right at point 1.

B. The electric field points to the right between the two charges.

C. The electric field points to the left at point 1.

D. The electric field points to the left at point 2.

E. The electric filed is zero at the origin.


13. A proton and an electron are released from rest from the same point in a uniform electric field? Which of

the following statements is correct?

A. They will experience the same magnitude of the electric force.

B. They will travel in the same direction.

C. They will experience the same acceleration.

D. They will travel equal distances in equal times.

E. The distance between them will remain constant.

14. Four equal negative point charges are located at the corners of a square centered at the origin, their

positions in the xy plane are (1, 1), (-1, 1), (-1, -1), (1, -1). What is the direction of the electric field at (1, 0)?

A. along the negative x axis

B. along the positive x axis

C. along the positive y axis

D. along the negative y axis

E. along the positive z axis

15. Three electric charges QA = QB = q, and QC

= -2q are located at the points A (x = + a, y = 0), B (x = -a, y =

0), and C (x = 0, y = +2a), respectively. What is the electric field at the origin?

16. Which of the following statements is wrong?

A. A shell of uniform charge density exerts a constant force on a charge inside it.

B. Electric field can exert a torque on an electric dipole.

C. Electric field lines extend away from a positive charge.

D. A shell of uniform charge density exerts a constant force on a charge outside it.

E. The magnitude of the charge on a positive ion is an integer multiple of the

electron charge.

17. For the arrangement of charges shown in figure 29, the electric field at the point p is:

A. 1.3kq/d2 in the negative y-direction.

B. 2.0kq/d2 in the negative y-direction.

C. Zero.

D. 2.0kq/d2 in the positive y-direction.

E. 1.3kq/d2 in the positive y-direction.

18. The strength of the electric field shown in figure 31

A. increases as we go from point a to point b.

B. increases as we go from point b to point a.

C. increases as we go from point b to point c.

D. increases as we go from point c to point b.

E. is the same at points a, b and c.

19. Figure 32 shows 5 possible directions labeled 1, 2, 3, 4, and 5 of the net electric field at point P due to the

charges shown. The correct direction of the net electric field at point P is:

A. 3

B. 2

C. 1

D. 5

E. 4


20. What is NOT TRUE about electric field lines:

A. They are extended away from a negative point charge.

B. They are the path followed by a unit positive charge.

C. Two electric field lines never cross each other.

D. They are imaginary lines used to visualize the patterns in the electric field.

E. The direction of the electric field at a point in the field line is given by the

tangent at that point.

21. An electric field exerts a torque on a dipole ONLY IF:

A. the field is not parallel to the dipole moment

B. the field is parallel to the dipole moment

C. the field is perpendicular to the dipole moment

D. the field is not perpendicular to the dipole moment

E. the field is uniform

22. Four particles, with the same magnitude of charge, are placed at the corners of a square, as shown in

figure 34. Which configuration gives an electric field, at the center of the square, pointing to the right?

A. 3

B. 1

C. 4

D. 2

E. 5

23. An electron traveling horizontally enters a region where a uniform electric field is directed upward, (see

figure 35. What is the direction of the electric force exerted on the electron once it has entered the field?

A. downward

B. upward

C. to the left

D. to the right

E. out of the page

24. Consider three different electric dipoles placed in the same uniform electric field E, as shown in figure 36,

where θ = 60o. Which of these dipoles has (or have) the LOWEST electric potential energy?

A. 2

B. 1

C. 3

D. 1 and 3

E. 2 and 3

25. Three charged particles are fixed at the corners of a square, as shown in figure 37. Consider point P,

which is the top right corner of the square. Which of the indicated arrows represents the direction of the net

electric field at point P?

A. V

B. I

C. II

D. III

E. IV


26. Experimenter A uses a test charge qo and experimenter B uses a test charge -2qo to determine the electric

field in a region having a uniform electric field. Experimenter A finds an electric field that is

A. Identical to the field found by experimenter B.

B. greater in magnitude than the field found by experimenter B.

C. less in magnitude than the field found by experimenter B.

D. opposite in direction to the field found by experimenter B.

E. dependent on the accelerations of the test charges.

27. Figure 39 shows a dipole rotating under the effect of an electric field pointing along the negative x-axis.

Which one of the following statements is TRUE?

A. The potential energy of the dipole is decreasing.

B. The torque on the dipole is directed into of the page.

C. The dipole is rotating clockwise.

D. The work done on the dipole by the field is negative.

E. The dipole will stop when it is pointing parallel to the positive x-axis.

28. Figure 43 shows four possible orientations of an electric dipole p in a uniform electric field E. Rank them

according to the magnitude of the torque exerted on the dipole by the field, least to greatest.

A) 1, 2 and 4 tie, then 3

B) 1, 2, 3, 4

C) 1, 2, 4, 3

D) 3, 2 and 4 tie, then 1

E) 4,3,2,1


Figure 1 Figure 2 Figure 3 Figure 4

Figure 5 Figure 6 Figure 7





Figure 34 Figure 35



Figure 42 Figure 43

Figure 44

chapter electric fields 22€¦ · a +40-μc charge is positioned on the x axis at x = +4.0 cm. to...

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