19. (II) Three point charges are arranged at the corners

1. (I) How much work does the electric field do in moving a -7.7 fiC charge from ground to a point whose potential is +55 V higher?

2. (I) How much work does the electric field do in moving a proton from a point with a potential of +125 V to a point where it is 55 V? Express your answer both in joules and electron volts.

3. (I) How much kinetic energy will an electron gain (in joules and eV) if it accelerates through a potential difference of 23,000 V in a TV picture tube?

4. (I) An electron acquires 7.45 x 10-IAJ of kinetic energy when it is accelerated by an electric field from plate A to plate B. What is the potential difference between the plates, and which plate is at the higher potential?

5. (I) How strong is the electric field between two parallel plates 5.8 mm apart if the potential difference between them is 220 V?

6. (I) An electric field of 640 V/m is desired between two parallel plates 11.0 mm apart. How large a voltage should be applied?

7. (I) The electric field between two parallel plates connected to a 45-V battery is 1500 V/m. How far apart are the plates?

8. (I) What potential difference is needed to give a helium nucleus (Q = 2e) 65.0 kcV of kinetic energy?

9. (II) Two parallel plates, connected to a 200-V power supply, are separated by an air gap. How small can the gap be if the air is not to become conducting by exceeding its breakdown value of E = 3 x 10A V/m?

10. (II) The work done by an external force to move a -8.50/tC charge from point a to point b is 15.0 x 104J. If the charge was started from rest and had 4.82 x 10 4 J of kinetic energy when it reached point b, what must be the potential difference between a and b?

11. (II) What is the speed of an electron with kinetic energy (a) 750-eV. and (b) 3.2-keV?

12. (II) What is the speed of a proton whose kinetic energy is 3.2 keV?

13. (II) An alpha particle (which is a helium nucleus. Q = +2e, in = 6.64 X 10-27kg) is emitted in a radioactive decay with ke = 5.53 MeV. What is its speed?

14. (I) What is the electric potential 15.0 cm from a 4.00nC point charge?

15. (I) A point charge Q creates an electric potential of +125 V at a distance of 15 cm. What is Q?

16. (II) A +35/xC point charge is placed 32cm from an identical +35/xC charge. How much work would be required to move a +0.50juC test charge from a point midway between them to a point 12 cm closer to either of the charges?

17. (II) Draw a conductor in the shape of a football. This conductor carries a net negative charge. -Q. Draw in a dozen electric field lines and two equipotential lines.

18. (II) (a) What is the electric potential a distance of 2.5 x 10-l5m away from a proton? (b) What is the electric potential energy of a system that consists of two protons 2.5 x 10-,5m apartas might occur inside a typical nucleus?

19. (II) Three point charges are arranged at the corners of a square of side L as shown in Fig. 17-25. What is the potential at the fourth corner (point A), taking V = 0 at a great distance?

20. (II) An electron starts from rest 32.5 cm from a fixed point charge with Q= -0.125/tC. How fast will the electron be moving when it is very far away?

21. (II) Two identical +9.5/xC point charges are initially 3.5 cm from each other. If they are released at the same instant from rest, how fast will each be moving when they are very far away from each other? Assume they have identical masses of 1.0 mg.

22. (II) Two point charges. 3.0/uC and -2.0/xC. are placed 5.0 cm apart on the .y axis. At what points along the .v axis is (a) the electric field zero and (b) the potential zero? Let V = 0 at r = oo.

23. (II) How much work must be done to bring three electrons from a great distance apart to 1.0 x 10- ,om from one another (at the comers of an equilateral triangle)?

24. (II) Consider point a which is 72cm north of a -3.8 /xC point charge, and point b which is 88 cm west of the charge (Fig. 17-26). Determine (a) = Vb - VA and (/?) Eb - Ea (magnitude and direction).

25. (Ill) How much voltage must be used to accelerate a proton (radius 1.2 X 1015m) so that it has sufficient energy to just penetrate a silicon nucleus? A silicon nucleus has a charge of + 14e, and its radius is about 3.6 x 10-15 m. Assume the potential is that for point charges.

26. (Ill) Two equal but opposite charges are separated by a distance d. as shown in Fig. 17-27. Determine a formula for VjjA = Vu - VA for points B and A on the line between the charges.

27. (Ill) In the Bohr model of the hydrogen atom, an electron orbits a proton (the nucleus) in a circular orbit of radius 0.53 X 10-lom. (a) What is the electric potential at the electrons orbit due to the proton? (b) What is the kinetic energy of the electron? (c) What is the total energy of the electron in its orbit? (<7) What is the ionization energy that is. the energy required to remove the electron from the atom and take it to r = oo. at rest? Express the results of parts b, c and d in joules and eV.

28. (I) An electron and a proton are 0.53 x 10-lom apart. What is their dipole moment if they are at rest?

29. (II) Calculate the electric potential due to a dipole whose dipole moment is 4.8 x 10-30C*m at a point 1.1 X l(T9m away if this point is (a) along the axis of the dipole nearer the positive charge: (b) 45 above the axis but nearer the positive charge; (c) 45 above the axis but nearer the negative charge.

30. (Ill) The dipole moment, considered as a vector, points from the negative to the positive charge. The water molecule, Fig. 17-28. has a dipole moment p which can be considered as the vector sum of the two dipole moments. Pi and p2, as shown. The distance between each H and the O is about 0.96 X 10_,m. Itie lines joining the center of the O atom with each H atom make an angle of 104, as shown, and the net dipole moment has been measured to be p = 6.1 x 10_3oC-m. Determine the charge q on each H atom.

31. (I) The twro plates of a capacitor hold +2500/xC and -2500 pC of charge, respectively, when the potential difference is 850 V. What is the capacitance?

32. (I) A 9500-pF capacitor holds plus and minus charges of 16.5 X 1(TSC. What is the voltage across the capacitor?

33. (I) The potential difference between two short sections of parallel wire in air is 120 V.Thev carry equal and opposite charge of magnitude 95 pC. What is the capacitance of the two wires?

34. (I) How much charge flowrs from each terminal of a 12.0-V battery when it is connected to a 7.00- /xF capacitor?

35. (I) A 0.20-F capacitor is desired. What area must the plates have if they arc to be separated by a 2.2-mm air gap?

36. (II) The charge on a capacitor increases by 18/uC when the voltage across it increases from 97 V to 121 V. What is the capacitance of the capacitor?

37. (II) An electric field of 8.50 x 10s V/m is desired between tw'o parallel plates, each of area 35.0 cm2 and separated by 2.45 mm of air. What charge must be on each plate?

38. (II) If a capacitor has opposite 5.2pC charges on the plates, and an electric field of 2.0kV/mm is desired between the plates, what must each plates area be?

39. (II) How strong is the electric field between the plates of a 0.80-juF air-gap capacitor if they are 2.0 mm apart and each has a charge of 72 pCl

40. (Ill) A 1.1-p capacitor is charged by a 125-V battery (Fig. 17-29a) and then is disconnected from the battery. When this capacitor (Ci) is then connected (Fig. 17-29b) to a second (initially uncharged) capacitor. C2, the final voltage on each capacitor is 15 V. What is the value of C2 ? [Hint, charge is conserved.]

41. (Ill) A 2.50-/xF capacitor is charged to 857 V and a 6.80-/xF capacitor is charged to 652 V. These capacitors are then disconnected from their batteries. Next the positive plates are connected to each other and the negative plates are connected to each other. What will be the potential difference across each and the charge on each? [Hinv. charge is conserved.)

42. (I) What is the capacitance of two square parallel plates 5.5 cm on a side that are separated by 1.8 mm of paraffin?

43. (I) What is the capacitance of a pair of circular plates with a radius of 5.0 cm separated by 3.2 mm of mica?

44. (II) A 3500-pF air-gap capacitor is connected to a 22-V battery. If a piece of mica is placed between the plates, how much charge will flow from the battery?

*45. (II) The electric field between the plates of a paper-separated (K = 3.75) capacitor is 8.24 x 104V/m. The plates are 1.95 mm apart, and the charge on each plate is 0.775 pC. Determine the capacitance of this capacitor and the area of each plate.

46. (I) 650 V is applied to a 2200-pF capacitor. How much energy is stored?

47. (I) A cardiac defibrillator is used to shock a heart that is beating erratically. A capacitor in this device is charged to 5.0 kV and stores 1200 J of energy. What is its capacitance?

48. (II) Howr much energy is stored by the electric field between two square plates, 8.0 cm on a side, separated by a 1 5-mm air gap? The charges on the plates are equal and opposite and of magnitude 420 pC.

49. (II) A homemade capacitor is assembled by placing two 9-in. pie pans 5 cm apart and connecting them to the opposite terminals of a 9-V battery. Estimate (a) the capacitance. (b) the charge on each plate, (c) the electric field halfway between the plates, and (d) the work done by the battery to charge the plates, (e) Which of the above values change if a dielectric is inserted?

50. (II) A parallel-plate capacitor has fixed charges +Q and -Q. The separation of the plates is then doubled. (a) By what factor does the energy stored in the electric field change? (b) How' much work must be done in doubling the plate separation from d to 2</? Hie area of each plate is A.

51. (II) How docs the energy stored in a capacitor change if (d) the potential difference is doubled, and (b) the charge on each plate is doubled, as the capacitor remains connected to a battery?

52. (Ill) A 2.70-juF capacitor is charged by a 12.0-V battery. It is disconnected from the battery and then connected to an uncharged 4.00-/uF capacitor (Fig. 17-29). Determine the total stored energy (a) before the two capacitors are connected, and (b) after they are connected, (c) What is the change in energy?

53. (Ill) In a given CRT, electrons arc accelerated horizon tally by 7.0 kV. They then pass through a uniform electric field E for a distance of 2.8 cm. which deflects them upward so they reach the screen top 22 cm away, 11 cm above the center. Estimate the value of E.

* 54. (Ill) Electrons are accelerated by 6.0 kV in a CRT The screen is 30 cm wide and is 34 cm from the 2.6-cm-long deflection plates. Over what range must the horizontally deflecting electric field vary to sweep the beam fully across the screen?

55. An electron starting from rest acquires 6.3 keV of KE in moving from point A to point B. (a) How much ke would a proton acquire, starting from rest at B and moving to point A? (6) Determine the ratio of their speeds at the end of their respective trajectories.

56. A lightning flash transfers 4.0 C of charge and 4.2 MJ of energy to the Earth, (a) Across what potential difference did it travel? (b) How much water could this boil and vaporize, starting from room temperature?

57. There is an electric field near the Earth's surface whose magnitude is about 150 V/m. How much energy is stored per cubic meter in this field?

58. In a television picture tube, electrons are accelerated by thousands of volts through a vacuum. If a television set were laid on its back, would electrons be able to move upward against the force of gravity? What potential difference, acting over a distance of 3.0 cm. would be needed to balance the downward force of gravity so that an electron would remain stationary? Assume that the electric field is uniform.

59. A huge 4.0-F capacitor has enough stored energy to heat 2.5 kg of water from 21 C to 95 C. What is the potential difference across the plates?

60. An uncharged capacitor is connected to a 24.0-V battery until it is fully charged, after which it is disconnected from the battery. A slab of paraffin is then inserted between the plates. What will now be the voltage between the plates?

61. Dry air will break down if the electric field exceeds 3.0 X 10h V/m. What amount of charge can be placed on a parallel-plate capacitor if the area of each plate is 56 cm2?

62. Three charges are at the corners of an equilateral triangle (side L) as shown in Fig. 17-30. Determine the potential at the midpoint of each of the sides.

63. A 3.4 fiC and a -2.6 fiC charge are placed 1.6 cm apart. At what points along the line joining them is (a) the electric field zero, and (b) the electric potential zero?

64. A 2600-pF air-gap capacitor is connected to a 9.0-V battery. If a piece of Pyrex glass is placed between the plates, how much charge will then flow from the battery?

65. An electron is accelerated horizontally from rest in a television picture tube by a potential difference of 5500 V. It then passes between two horizontal plates 6.5 cm long and 1.3 cm apart that have a potential difference of 250 V (Fig. 17-31). At what angle H will the electron be traveling after it passes between the plates?

66. A capacitor of capacitance C\ carries a charge Q{). It is then connected directly to a second, uncharged, capacitor of capacitance C2. as shown in Fig. 17-32. What charge will each carry now? What will be the potential difference across each?

67. To get an idea how big a farad is. suppose you want to make a 1-F air-filled parallel-plate capacitor for a circuit you arc building. To make it a reasonable size, suppose you limit the plate area to 1.0 cm2. What would the gap have to be between the plates? Is this practically achievable?

68. Near the surface of the Earth there is an electric field of about 150 V/m which points downward. Two identical balls with mass m = 0.540 kg are dropped from a height of 2.00 m. but one of the balls is positively charged with <7| = 650 fiC, and the second is negatively charged with <72 = -650/iC. Use conservation of energy to determine the difference in the speed of the two balls when they hit the ground. (Neglect air resistance.)

69. The power supply for a pulsed nitrogen laser has a 0.050-/xF capacitor with a maximum voltage rating of 30 kV. (a) Estimate how much energy could be stored in this capacitor. (b) If 12% of this stored electrical energy is converted to light energy in a pulse that is 8.0 microseconds long, what is the power of the laser pulse?

70. In lightning storms, the potential difference between the F.arth and the bottom of the thunderclouds can be as high as 35.000.000 V. The bottoms of the thunderclouds are typically 1500 m above the Earth, and can have an area of 110 km2. Modeling the Earth-cloud system as a huge capacitor, calculate (tf) the capacitance of the Earth-cloud system, (/?) the charge stored in the capacitor." and (c) the energy stored in the "capacitor.

71. In a photocell, ultraviolet (UV) light provides enough energy to some electrons in barium metal to eject them from a surface at high speed. See Fig. 1733. To measure the maximum energy of the electrons, another plate above the barium surface is kept at a negative enough potential that the emitted electrons are slowed down and stopped, and return to the barium surface. If the plate voltage is -3.02 V (compared to the barium) when the fastest electrons are stopped, what was the speed of these electrons when they were emitted?

72. A +33 /xC point charge is placed 36 cm from an identical + 33 fxC charge. A -1.5 /xC charge is moved from point a to point b in Fig. 17-34. What is the change in potential energy?

73. A capacitor is made from two 1.1-cm-diameter coins separated by a 0.15-mm-thick piece of paper (K = 3.7). A 12-V battery is connected to the capacitor. How much charge is on each coin?

74. A +4.5 fxC charge is 23 cm to the right of a 8.2/tC charge. At the midpoint between the two charges, (a) what are the potential and (b) the electric field?

75. A parallel-plate capacitor with plate area 2.0cm2 and air-gap separation 0.50 mm is connected to a 12-V batten,-, and fully charged. The battery is then disconnected, (a) What is the charge on the capacitor? (b) ITie plates are now pulled to a separation of 0.75 mm. What is the charge on the capacitor now? (c) What is the potential difference across the plates now? (d) How much work was required to pull the plates to their new separation?

76. A 2.5-fxb' capacitor is fully charged by a 6.0-V battery. The battery is then disconnected. The capacitor is not ideal and the charge slowly leaks out from the plates. 'ITie next day. the capacitor has lost half its stored energy. Calculate the amount of charge lost.

77. Two point charges are fixed 4.0 cm apart from each other. Their charges are Q\ = Qi = 5.0 aiC, and their masses are mi = 1.5mg and mi = 2.5 mg. (a) If Q\ is released from rest, what will be its speed after a very-long time? (b) If both charges arc released from rest at the same time, what will be the speed of Q\ after a very-long time?

78. Two charges are placed as shown in Fig. 17-35 with Cf\ = 1.5 /xC and q> = 3.3 yuC. Find the potential difference between points A and B.