Physics 181.

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

A) , directed upward

59. Which combination of charges would yield the greatest repulsive force between the charges?

A) -2q and -4q

39. If a +2.0 × 10-5 C point charge is placed at P, what is the force exerted on it?

A) 0.2 N, toward the negative plate

15. A charge Q exerts a 1.2 N force on another charge q. If the distance between the charges is doubled, what is the magnitude of the force exerted on Q by q?

A) 0.30 N

28. In the figure, point A is a distance L away from a point charge Q. Point B is a distance 4L away from Q. What is the ratio of the electric field at B to that at A, EB/EA?

A) 1/16

9. An aluminum nail has an excess charge of +3.2 µC. How many electrons must be added to the nail to make it electrically neutral?

A) 2.0 × 10^13

55. A total charge of -6.50 µC is uniformly distributed within a sphere that has a radius of 0.150 m. What is the magnitude and direction of the electric field at 0.300 m from the surface of the sphere?

A) 2.89 × 105 N/C, radially inward

52. What is the electric flux passing through a Gaussian surface that surrounds a +0.075 C point charge?

A) 8.5 × 109 N×m2/C

36. What is the magnitude of the electric field due to a 6.0 × 10-9 C charge at a point located 0.025 m from the charge?

A) 8.6 × 102 N/C

14. Two positive point charges Q and 2Q are separated by a distance R. If the charge Q experiences a force of magnitude F when the separation is R, what is the magnitude of the force on the charge 2Q when the separation is 2R ?

A) F/4

44. A rigid electric dipole is free to move in the electric field represented in the figure. Which one of the following phrases most accurately describes the initial motion of the dipole if it is released from rest in the position shown?

A) It moves to the left.

26. Determine an expression for the magnitude and sign of Q so that the net force on the charge at A is zero newtons.

Ans: B

25. Is it possible to choose the value of Q (that is non-zero) such that the force on Q is zero? Explain why or why not.

Ans: E

45. An electric dipole is released from rest in a uniform electric field with the orientation shown. Which entry in the table below correctly describes the net torque and the net force on the dipole?

B) net torque:clockwise net force: zero

50. A conducting sphere carries a net charge of +6 µC. The sphere is located at the center of a conducting spherical shell that carries a net charge of -2 µC. Determine the excess charge on the outer surface of the spherical shell.

B) +4 µC

61. Determine the excess charge on the inner surface of the outer sphere (a distance b from the center of the system).

B) -6 mC

23. Three charges are located along the x axis as shown in the drawing. The mass of the -1.2 µC is 4.0 × 10-9 kg. Determine the magnitude and direction of the acceleration of the -1.2 µC charge when it is allowed to move if the other two charges remain fixed.

B) 1 × 105 m/s2, to the left

58. Two identical conducting spheres carry charges of +5.0 mC and -1.0 mC, respectively. The centers of the spheres are initially separated by a distance L. The two spheres are brought together so that they are in contact. The spheres are then returned to their original separation L. What is the ratio of the magnitude of the electric force on either sphere after the spheres are touched to that before they were touched?

B) 4/5

53. A uniform electric field with a magnitude of 125 000 N/C passes through a rectangle with sides of 2.50 m and 5.00 m. The angle between the electric field vector and the vector normal to the rectangular plane is 65.0°. What is the electric flux through the rectangle?

B) 6.60 × 105 N×m2/C

13. Four point charges, each of the same magnitude, with varying signs are arranged at the corners of a square as shown. 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?

B) B {there is a square pictured, it is the vector pointing SW from NE corner on the neg line}

8. A charged conductor is brought near an uncharged insulator. Which one of the following statements is true?

B) Both objects will attract each other.

43. The figure shows the electric field lines in the vicinity of two point charges. Which one of the following statements concerning this situation is true?

B) The magnitude of the ratio (q2/ q1) is less than one.

7. Complete the following statement: When a glass rod is rubbed with silk cloth, the rod becomes positively charged as

B) negative charges are transferred from the rod to the silk.

41. Complete the following statement: The magnitude of the electric field at a point in space does not depend upon

B) the sign of the charge causing the field.

10. Two uncharged, conducting spheres, A and B, are held at rest on insulating stands and are in contact. A positively charged rod is brought near sphere A as suggested in the figure. While the rod is in place, someone moves sphere B away from A. How will the spheres be charged, if at all?

C) Sphere A: negative Sphere B: positive

2. Five styrofoam balls are suspended from insulating threads. Several experiments are performed on the balls; and the following observations are made: I. Ball A attracts B and A repels C. II. Ball D attracts B and D has no effect on E. III. A negatively charged rod attracts both A and E. What are the charges, if any, on each ball?

C) + - + 0 0

49. What is the magnitude and direction of the electric force on a -3.0 µC charge at a point where the electric field is 2800 N/C and is directed along the +y axis.

C) 0.0084 N, -y direction

57. A helium nucleus is located between the plates of a parallel-plate capacitor as shown. The nucleus has a charge of +2e and a mass of 6.6 × 10-27 kg. What is the magnitude of the electric field such that the electric force exactly balances the weight of the helium nucleus so that it remains stationary?

C) 2.0 × 10-7 N/C

56. A circular loop of wire with a diameter of 0.626 m is rotated in a uniform electric field to a position where the electric flux through the loop is a maximum. At this position, the electric flux is 7.50 × 105 N×m2/C. Determine the magnitude of the electric field.

C) 2.44 × 106 N/C

37. Which one of the following statements concerning the direction of the electric field between the plates is true?

C) It points toward the negative plate.

29. At which point (or points) is the electric field zero N/C for the two point charges shown on the x axis?

C) The electric field is zero somewhere on the x axis to the right of the -2q charge.

1. Which one of the following statements best explains why tiny bits of paper are attracted to a charged rubber rod?

C) The paper becomes electrically polarized by induction.

63. Which one of the following figures shows a qualitatively accurate sketch of the electric field lines in and around this system?

C) c, double layer, all arrows point out of circle

34. Which path would be followed by a helium atom (an electrically neutral particle)?

C) path 3

62. Determine the excess charge on the outer surface of the outer sphere (a distance c from the center of the system).

D) +12 mC

16. At what separation will two charges, each of magnitude 6.0 mC, exert a force of 0.70 N on each other?

D) 0.68 m

19. A -4.0-µC charge is located 0.45 m to the left of a +6.0-µC charge. What is the magnitude and direction of the electrostatic force on the positive charge?

D) 1.1 N, to the left

42. Four point charges are placed at the corners of a square as shown in the figure. Each side of the square has length 2.0 m. Determine the magnitude of the electric field at the point P, the center of the square.

D) 1.8 × 104 N/C

40. A small sphere of mass 2.5 × 10-5 kg carries a total charge of 6.0 × 10-8 C. The sphere hangs from a silk thread between two large parallel conducting plates. The excess charge on each plate is equal in magnitude, but opposite in sign. If the thread makes an angle of 30° with the positive plate as shown, what is the magnitude of the charge density on each plate?

D) 2.1 × 10-8 C/m2

20. Determine the ratio of the electrostatic force to the gravitational force between a proton and an electron, FE/FG. Note: k = 8.99 × 109 N-m2/C2; G = 6.672 × 10-11 N-m2/kg2; me = 9.109 × 10-31 kg; and mp = 1.672 × 10-27 kg.

D) 2.26 × 10^39

48. The magnitude of the electric field at a distance of two meters from a negative point charge is E. What is the magnitude of the electric field at the same location if the magnitude of the charge is doubled?

D) 2E

21. In Frame 1, two identical conducting spheres, A and B, carry equal amounts of excess charge that have the same sign. The spheres are separated by a distance d; and sphere A exerts an electrostatic force on sphere B that has a magnitude F. A third sphere, C, which is handled only by an insulating rod, is introduced in Frame 2. Sphere C is identical to A and B except that it is initially uncharged. Sphere C is touched first to sphere A, in Frame 2, and then to sphere B, in Frame 3, and is finally removed in Frame 4.

D) 3F/8

5. A conducting sphere has a net charge of -6.4 × 10-17 C. What is the approximate number of excess electrons on the sphere?

D) 400

17. One mole of a substance contains 6.02 × 1023 protons and an equal number of electrons. If the protons could somehow be separated from the electrons and placed in very small, individual containers separated by a million meters, what would be the magnitude of the electrostatic force exerted by one box on the other?

D) 8.4 × 10^7 N

47. Which one of the following statements is true concerning the electrostatic charge on a conductor?

D) The charge is entirely on the surface and it is distributed according to the shape of the object.

46. Which one of the following statements is true concerning the spacing of the electric field lines in the vicinity of two point charges of equal magnitude and opposite sign?

D) The spacing indicates the relative magnitude of the electric field.

30. An electron traveling horizontally enters a region where a uniform electric field is directed upward. What is the direction of the force exerted on the electron once it has entered the field?

D) downward

6. Complete the following statement: When an ebonite rod is rubbed with animal fur, the rod becomes negatively charged as

D) negative charges are transferred from the fur to the rod.

33. In which direction does the electric field point?

D) toward the bottom of the page

4. Each of three objects has a net charge. Objects A and B attract one another. Objects B and C also attract one another, but objects A and C repel one another. Which one of the following table entries is a possible combination of the signs of the net charges on these three objects?

D)- + -

3. Two uncharged conducting spheres, A and B, are suspended from insulating threads so that they touch each other. While a negatively charged rod is held near, but not touching sphere A, someone moves ball B away from A. How will the spheres be charged, if at all?

E) Sphere A: + Sphere B: -

60. Which combination of charges will yield zero electric field at the point x?

E) +4q and +4q

54. A straight, copper wire has a length of 0.50 m and an excess charge of -1.0 × 10-5 C distributed uniformly along its length. Find the magnitude of the electric field at a point located 7.5 × 10-3 m from the midpoint of the wire.

E) 4.8 × 107 N/C

38. What is the magnitude of the electric field at the point P?

E) 9.9 × 103 N/C

27. Which one of the following statements is true concerning the magnitude of the electric field at a point in space?

E) It is a measure of the electric force per unit charge on a test charge.

31. Which one of the following statements is true concerning the strength of the electric field between two oppositely charged parallel plates?

E) It is constant between the plates except near the edges.

12. Two charged particles A and B are located near one another. Both the magnitude and direction of the force that particle A exerts on particle B is independent of

E) The magnitude and direction of the force are dependent on all of the above choices. (the sign of charge B, the sign of charge A, the distance between A and B, the magnitude of the charge on B.)

11. Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of -2.0 µC; sphere B carries a charge of -6.0 µC; and sphere C carries a charge of +4.0 µC. Spheres A and B are touched together and then separated. Spheres B and C are then touched and separated. Does sphere C end up with an excess or a deficiency of electrons and how many electrons is it?

E) There is no excess or deficiency of electrons.

24. Four point charges are held fixed at the corners of a square as shown in the figure. Which of the five arrows shown below most accurately shows the direction of the net force on the charge -Q due to the presence of the three other charges?

E) e

18. Three charges are positioned as indicated in the figure. What are the horizontal and vertical components of the net force exerted on the +15 µC charge by the +11 µC and +13 µC charges?

E) horizontal: 76 N vertical: 370 N

35. Which path would be followed by a charge +6Q?

E) path 5

32. Two particles of the same mass carry charges +3Q and -2Q, respectively. They are shot into a region that contains a uniform electric field as shown. The particles have the same initial velocities in the positive x direction. The lines, numbered 1 through 5, indicate possible paths for the particles. If the electric field points in the negative y direction, what will be the resulting paths for these particles?

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

51. A cubical Gaussian surface is placed in a uniform electric field as shown in the figure. The length of each edge of the cube is 1.0 m. The uniform electric field has a magnitude of 5.0 × 108 N/C and passes through the left and right sides of the cube perpendicular to the surface. What is the total electric flux that passes through the cubical Gaussian surface?

E) zero N×m2/C