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Physics 9: Static Electricity A. Electric Nature of Matter 1. subatomic particles a. summary chart (Coulomb, C, unit of charge) particle Proton Neutron Electron mass (kg) 1.67 x 10-27 1.67 x 10-27 9.11 x 10-31 charge (C) +1.60 x 10-19 0 -1.60 x 10-19 b. + and – attract (+ and + or – and – repel) c. attraction between protons and electrons holds matter together/apart explains Fs, Ff, Fn, etc. 2. conductors and insulators a. metals are conductors because valence electrons are loosely held by individual atoms and can travel from atom to atom (excess charge on a conductor spreads out on the outside surface) b. non-metals are insulators because valence electrons are restricted to individual atoms (excess charge on an insulator stays localized) c. metalloids (semiconductors) are intermediate between metals and nonmetals 3. adding static charge to insulators a. rubbing dissimilar insulators together transfers electrons from one to the other b. excess electrons = negatively charged deficient electrons = positively charged c. total charge is unchanged (conservation of charge) 4. adding static charge to conductors a. conduction: charged conductor contacts neutral conductor; electrons flow until equal electric potential (water tanks analogy) Name __________________________ 2. electric field, E = k|Q|/r2 (N/C) a. Michael Faraday's concept is useful to explain forces at a distance, where space around –Q is curved inward so that +q is drawn in as if it were pulled (no physical contact is necessary) +q r -Q b. c. electric field lines (lines of force) 1. lines directed into cone show direction of field 2. away from +Q and toward –Q 3. perpendicular to the conductor's surface 4. (concentric rings are equipotential lines, V, which are discussed in the next section) oppositely charged plates edge effect E=0 E is constant (except edge effect) E kQ/r2 E = 0 inside a conductor (hollow or solid; charged or uncharged) solving E and Fe from multiple charges problems (determining the magnitude and direction of the solid line at point p) 1. 2. 3. b. induction 1. neutral conductor is connected to the earth by a grounded wire (a) 2. charged conductor approaches the neutral conductor, but doesn’t touch, so that electrons flow away from the charged conductor and down into the earth (b) 3. excess charge spreads evenly over surface (c) E1 E2 • +Q1 B. Electric Force and Field 1. electric force, Fe = k|qQ|/r2 (N) a. charges Q and q or Q1 and Q2 in (C) b. k = 1/(4єo) = 9.0 x 109 N•m2/ C2 c. єo = 8.85 x 10-12 C2/N•m2 1. permittivity of free space 2. measures the degree that an electric field is "permitted" in a vacuum d. r is distance between Q's from center to center e. charge sign is not included in calculation, but is used to determine direction of Fe f. similar to Fg = -GMm/r2, except electric force can attract (–) or repel (+) 4. p –Q2 determine E1and E2, at position, p, due to Q1 and Q2: E = k|Q|/r2 (don't include charge sign in calculation) determine direction of E1 and E2 (+), –)) add vectorily o same direction: Etot = E1 + E2 o opposite direction: Etot = E1 – E2 o right angles: Etot = (Ex-tot2 + Ey-tot2)½, tan = Ey/Ex determine the electric force on q at point p o magnitude, Fe = |q|Etot o direction +q: Fe is in the same direction as E –q: Fe is in the opposite direction as E solve x where E = 0 problems D Q1 Q2 location is closer to weaker charge like charges (x < D), unlike charge (x > D) (|+Q1| > |+Q2|): kQ1/x2 = kQ2/(D – x)2; solve for x (|+Q1| > |–Q2|): kQ1/x2 = kQ2/(x – D)2; solve for x math shortcut: take the square root of both sides before cross multiplying Electric Potential Energy and Voltage 1. potential energy between point charges, Q and q a. Ue = kqQ/r (J) b. Ue = 0, when Q and q are infinitely far apart c. scalar quantity d. sign of charge is included in calculation e. analogous to gravitational potential energy 1. Ug = -GMm/r (Ug = 0 when r = ) 2. negative sign in Ug to convert positive M and m into negative Ug 2. electric potential (also called "potential" or "voltage") due to point charge Q a. V = kQ/r (V)—volt b. is relative to where V = 0 1. infinitely far from a point charge (theoretical) 2. practical to set earth as V = 0 ("ground") c. letter V has three uses (confusing!) 1. voltage (electric potential) = V 2. potential difference, V = V 3. volt = V d. scalar quantity (include sign in calculation) 3. solving V and Ue from multiple charges problems (determine the value of the dashed line at point p) V1 + V2 D. Capacitor 1. battery connected to parallel conducting plates fills plates with opposite, but equal, charges a. Vplates = Vbattery b. charge can't pass directly from one plate to the other so plates remain charged when battery is removed c. stores charge and energy 2. electric field, E = V/d (NOT kQ/r2) a. solid arrows b. constant c. V/m = N/C 3. equipotentials, V a. all points at the same V b. dashed lines c. perpendicular to E d. decrease evenly with d e. analogous to elevation lines on contour map 4. capacitance, C =єoA/d (F) a. "capacity" to store charge b. єo = 8.85 x 10-12 C2/N•m2 c. A = common area of plates d. d = distance between plates e. farad, F = C/V 5. stored charge, Q = CV a. charge increases as voltage increase Q • +Q1 p slope = C –Q2 Work = Area under line = Uc 4. 5. determine V1 and V2 at position p, due to Q1 and Q2: V = kQ/r (include charge sign in calculation) add the voltages together, Vtot = V1 + V2 determine electric potential energy for charge q at point p: Ue = qVtot solve x where V = 0 problems D +Q1 –Q2 only meaningful for unlike charges (between charges and closer to weaker charge) (|+Q1| > |–Q2|): kQ1/x = kQ2/(D – x); solve for x cathode ray tube a. device for accelerating a beam of electrons (cathode rays)—video monitors V potential energy, Uc = ½QV Steps Algebra W = ½bh start with W = area under line substitute Q for h and V for b W = ½QV Uc = ½QV substitute Uc for W Uc = ½CVV = ½CV2 substitute CV for Q Uc = ½C(Q/C)2 = ½Q2/C substitute Q/C for V 6. variable capacitor a. connect/disconnect voltage source (battery) 1. connected: voltage V is constant 2. disconnected: charge Q is constant b. increase/decrease area A or distance d Capacitance Battery Variable Connected Disconnected Capacitor C = єoA/d Q =C x V Q = C x V A d 7. uses a. RAM memory (charged = 1, uncharged = 0) b. computer keyboard (variable capacitor—d) c. camera flash (energy/charge storage) d. heart defibrillator (energy/charge storage) b. b. c. design 1. high voltage used to charge two plates 2. electrons accelerate from cathode (– plate) to anode (+ plate) 3. anode has small opening into evacuated tube calculating the velocity of the electrons: |Ue| = K |qe(Vhigh – Vlow)| = ½mev2 me = 9.11 x 10-31 kg qe = 1.6 x 10-19 C constant constant C. Practice Problems 1. A. Electric Nature of Matter A positively charged rod is brought close to a neutral conducting sphere. What is the charge on A? ++++++++++++++++++ A (A) positive (B) negative (C) neutral Questions 2-3 A positively charged rod is brought close to two neutral conducting spheres connected by a wire. ++++++++++++++++++ 2. 3. 4. A B The wire is disconnected, and then the rod is removed. What are the charges on A and B? (A) +A, -B (B) -A, +B (C) both neutral The rod is removed first, and then the wire is disconnected. What are the charges on A and B? (A) +A, -B (B) -A, +B (C) both neutral Consider the two ways to charge a conductor. a. Label the picture that illustrate conduction and the picture that illustrates induction b. What could be done to make the metal rod in the right side set of pictures have a net negative charge? 5. A neutral glass rod is rubbed with a neutral piece of silk. The rod acquires an excess charge of + 1 C. What is the excess charge on the piece of silk? 6. A positively charged piece of metal is used to charge a neutral piece of metal. Which technique, conduction or induction, can make the neutral metal? positively charged negatively charged B. Electric Force and Field Question 7-12 Sphere B is r meters from sphere A, which has a charge of +1 C. The electric force between them is 1 N. A 7. r 18. When the proton and electron are released, they move (A) away from each other (B) toward each other 19. How does the electric force change as they move? (A) increase (B) same (C) decrease 20. The acceleration of the electron compare to the proton is (A) greater (B) equal (C) less 21. At which position will the proton and electron collide? (A) 1 (B) 2 (C) 3 Questions 13-16 Sphere A, Q = +1 C and m = 0.4 kg, is suspended from the ceiling near a charged Wall. Forces F1, F2 and F3 act on A. 53o F1 B What is the direction of the force on B if QB = +1 C? (A) (B) 8. What is the magnitude of the force on B if QB = +2 C? (A) ¼ N (B) ½ N (C) 2 N (D) 4 N 9. What is the magnitude of the force on A if QB = +2 C? (A) ¼ N (B) ½ N (C) 2 N (D) 4 N 10. What is the magnitude of the force on B if QA = QB = +2 C? (A) ¼ N (B) ½ N (C) 2 N (D) 4 N QA = QB = +1 C 11. What is the magnitude of the force on B if r is doubled? (A) ¼ N (B) ½ N (C) 2 N (D) 4 N 12. What is the magnitude of the force on B if r is halved? (A) ¼ N (B) ½ N (C) 2 N (D) 4 N Questions 17-21 An electron and proton are 1 m apart. p 1 2 3 e 17. The proton's electric force compared to the electron is (A) greater (B) equal (C) less F2 A F3 13. What the charge on the wall? (A) positive (B) negative 14. What is F3? (A) 3 N (B) 4 N (C) 5 N 15. What is F1? (A) 3 N (B) 4 N (C) 5 N 16. What is F2? (A) 3 N (B) 4 N (C) 5 N Questions 22-25 The electric field strength is E at point p, which is r distance way from sphere A with charge +Q. +Q •p 22. What is the direction of the electric field at p? (A) (B) 23. If Q is doubled, what is the electric field at point p? (A) ¼E (B) ½E (C) 2E (D) 4E 24. If r is doubled, what is the electric field at point p? (A) ¼E (B) ½E (C) 2E (D) 4E Questions 25-27 What is the direction of the electric field at point p half way between charges of equal magnitude? 25. +Q •p +Q (A) (B) (C) E = 0 26. +Q •p –Q (A) (B) (C) E = 0 27. –Q •p +Q (A) (B) (C) E = 0 Questions 28-31 Where is the electric field equal to zero? 28. A +4Q B C –Q D 29. A –4Q B C 30. A +Q B C –Q +4Q –4Q D D 31. A +Q B C D Questions 32-34 What is the direction of electric field at point p? 32. +Q •p +Q (A) (B) (A) –Q (B) (C) –Q •p (A) (B) 33. 34. (C) +Q •p (D) (D) –Q (C) (D) Questions 35-37 What is the direction of the field at point p, which is in the center of the box? 35. –Q +Q •p –Q +Q (A) (B) (C) (D) E = 0 36. +Q +Q •p +Q +Q (A) (B) (C) (D) E = 0 37. +Q –Q •p –Q +Q (A) (B) (C) (D) E = 0 38. In a simplified model of a hydrogen atom, an electron orbits a proton at a distance of 5.3 x 10-11 m. a. What is the electric force between the electron and proton? b. What is the gravitational force between the electron and proton? (G = 6.67 x 10-11 N•m2/kg2) 42. Where is the net charge located on a good conductor? 43. What is the orientation of the electric field with respect to a conductor's surface? 44. The electric field lines are drawn around charged spheres and plates. Indicate whether the charged spheres or plates are positive or negative. a. b. 45. A 50 C charge and a 1 C charge are 0.1 m apart. a. Which charge generates the stronger field at 0.1 m? b. Which charge exerts the greater force on the other? 46. What is the electric field 3 m away from a +10C charge? 47. Determine the magnitude and direction of the electric field at point p. Q1 = -5 C Q2 = +10 C • p 1m c. What is the velocity of the electron in its orbit? 39. Two small identical metal spheres contain excess charge of -10 C and +8 C, respectively ( = 10-6). The spheres are 0.4 m apart. a. Determine the magnitude and direction of the force between the spheres. The spheres touch and then returned to their original 0.4-m separation. b. Determine the charge on each sphere. c. 3m 48. Determine the magnitude and direction of the electric field at point p. Q1 = -5 C Q2 = +10 C 1m p• 3m Determine the magnitude and direction of the force between the spheres. 40. Two charged spheres of equal mass and charge, suspended from a common point by threads that are 0.5 m long, rest a distance of 0.5 m apart. a. Label the three forces acting on the right sphere (Fg, Ft, Fe) on the vector 30o sum diagram below. 49. Determine the magnitude and direction of the electric field at the center of a square 2 m on an edge if charges of +8 C each are at three of the corners of the square. +8C 2m +8 C 2m +8C 0.5 m b. What is the charge on each sphere if the mass of each sphere is 0.030 kg? 41. What is the strength of an electric field inside a conductor? 50. What is the magnitude and direction of the electric force on a -3 x 10-7 C charge in a 500 N/C electric field directed toward the west? 51. Calculate the magnitude and direction of the force on Q2. Q1 = +10 C Q2 = +2 C Q3 = -10 C 0m 5m 15 m 52. A +40 C and -10 C charge are 10 m apart. +40 C -10 C 0m 10 m a. Determine the magnitude and direction of the electric field at a point half way between. b. c. Which charge generates the stronger field at a point half way between the two charges? d. Determine the magnitude and direction of the electric field at the midpoint. A -1 C charge is placed at the midpoint e. Determine the magnitude and direction of the electric force on the -1 C charge at the midpoint. f. Determine where the -1 C charge can be placed where it would experience a net electric force of zero. 59. A proton traveling at 3 x 106 m/s enters a region where the electric field has a magnitude of 3 x 105 N/C. The electric field is uniform and slows the proton's motion. Determine a. the acceleration on the proton. Determine where the electric field is zero. 53. A drop of water has a net charge of 150 electrons. What is its mass if it is suspended in an electric field is 300 N/C? 54. A particle of mass 1 x 10-6 kg has an excess charge of +1 C. The particle is located in a region between two oppositely charged parallel plates where the electric field is uniform and has a magnitude of 1000 N/C. Determine the a. the force acting on the particle. b. b. the distance the proton will travel before coming to a momentary halt. c. the time required for the proton to travel this distance. 60. Q1 = +9 C, and Q2 = +1 C, are located on the x-axis at x = 0 m and x = 6 m, respectively. Q1 = +9 C Q2 = +1C the acceleration of the particle. The plates are 0.01 m apart and the particle is initially at rest at a point close to the positive plate. c. Determine the velocity of the particle "just" before it strikes the negative plate. 0m 6m a. Determine where a third charge, Q3 = +1 C, can be placed and experience no net force. b. 55. What is the electric field 5 m away from a +10C charge? 56. What is the electric force between an electron and proton that are 1.0 x 10-10 m apart? 57. What is the magnitude and direction of the electric force on a +5 x 10-7 C charge in a 200 N/C electric field directed toward the west? 58. A +32 C and +8 C charge are 2 m apart. +32 C +8C 0m 2m a. What is the electric force on the +8 C charge? b. What is the electric force on the +32 C charge? Charge Q2 is replaced with a -1 C charge located at x = 6 m. Determine where a third charge, Q3 = +1 C, can be placed and experience no net force. C. Electric Potential Energy and Voltage 61. A proton and electron are released within a constant electric field generated between parallel plates. p + – e Which has more kinetic energy when it reaches the plate? (A) electron (B) proton (C) tie 62. Which system has +Ue? +– + + – – A B C (A) A (B) B (C) C (D) B and C 63. Which pair of equal charges takes positive work to bring together from a very large initial distance apart? +– + + A B (A) A (B) B (C) A and B Questions 64-66 Consider the square with four equal charges on the corners. +– + + + – 75. What is the voltage at 25 cm from a 10-C charge? 76. a. Calculate the electric field E and voltage V from 1 m to 4 m from Q (1 C). r (m) E V +– + + – + A B C 64. Which arrangement has V > 0 at the center? (A) A (B) B (C) C (D) none 65. Which arrangement(s) is V = 0 at the center? (A) A (B) B (C) C (D) A and C 66. Which arrangement(s) is V = 0 and E = 0 at the center? (A) A (B) B (C) C (D) A and C Questions 67-69 A charge is placed at point p in the electric field, whose direction is indicated by the dashed arrows. The particle is moved along equal length paths indicated by the solid arrows. 1 2 3 4 b. 8000 A 6000 C p Which path requires the most work to move a positive charge? (A) A (B) B (C) C (D) B and C Which path requires negative work to move a negative charge? (A) A (B) B (C) C (D) B and C Which path requires zero work to move any charge? (A) A (B) B (C) C (D) B and C Which point(s) have the same potential as point X around these two equal put opposite charges? B 67. 68. 69. 70. X• A• Graph E and V on the same grid. E and V B• C• (A) A (B) B (C) C (D) all above 71. What is the potential energy between a -1-C charge and a +10-C charge that are 25 m apart? 4000 2000 0 c. 1 3 r (m) Draw a tangent to the V vs. r graph at r = 3 m and compare its slope with the value of E and 3 m. 77. a. Determine the voltage at point p, which is at 1 m. -5 C +10 C p 1m 3m b. How much work is required to bring an electron from infinitely far away to point p? (1) In joules 72. A +2-C charge is infinitely far away from a +20-C charge. a. What is the electric potential energy? (2) in eV (q = -1—measured in terms of electrons) The +2-C charge is moved to 2 m from the +20-C charge. b. What is the electric potential energy now? c. c. How much work is needed to move the +2-C charge from infinity to 2 m from the +20-C charge? Determine the voltage at point p, which is located as shown -5 C +10 C 1m 3m p 73. Q1 (+10 C) is 10 m from Q2 (-1 C). a. What is the electric potential energy? Q1 accelerates to a distance of 2 m from Q2. b. What is the electric potential energy now? c. What is the velocity of Q1 (0.2 kg) at 2 m from Q2? 74. What is the voltage between points if 10 J of work is required to move 5 C from one point to the other? 78. A +40-C charge and a -10-C charge are 10 m apart. +40 C -10 C a. 0m 10 m Calculate the voltage at a point half way between. b. Determine where the voltage is zero. 79. An electron accelerates through a voltage of 750 J/C. a. What is the change in the electric potential energy? b. 85. Two point charges, q1 (3.0 C) and q2 (-1.5 C), are placed 0.30 m apart on the x-axis. What is the velocity of the electron? 80. 1 electron that moves from 10 V to 20 V in an electric field. a. The electron (gains or loses) potential energy. b. What is the change in potential energy (in eV)? 81. Four charged have the same magnitude Q, but two are positive and two are negative. +Q –Q +Q –Q –Q +Q +Q –Q Arrangement 1 Arrangement 2 In the center of which arrangement is the electric field equal to zero the voltage equal to zero 82. Consider the three pairs of charges in the figures below (shaded charges are positive, unshaded are negative). (1) (2) (3) Has positive potential energy Has negative potential energy Requires the most work to separate 83. What is the potential at the center of a 1-m square for each situation below? Q1 1m Q2 1m a. Q3 Q1 = Q2 = Q3 = +10 C? b. Q1 = Q2 = +10 C and Q3 = -25 C? a. Determine the x-coordinate of the point on the line between the two charges where V = 0. b. How much work must be done by an external force to bring an electron from infinity to the point where V = 0? Explain your reasoning. D. Capacitor Questions 86-93 The capacitor with capacitance C has plate area A, plate separation d, potential difference V, charge Q and potential energy Uc. A V d 86. What is the charge if the voltage goes from V to 2V? (A) ¼Q (B) ½Q (C) 2Q (D) 4Q 87. What is the potential energy if the voltage goes from V to 2V? (A) ¼Uc (B) ½Uc (C) 2Uc (D) 4Uc 88. What is the capacitance if the area goes from A to 2A? (A) ¼C (B) ½C (C) 2C (D) 4C 89. What is the capacitance if the separation goes from d to 2d? (A) ¼C (B) ½C (C) 2C (D) 4C 90. The battery remains connected and the plate separation goes form d to 2d. What happens to the voltage? (A) ½V (B) V (C) 2V (D) 0 91. The battery remains connected and the plate separation goes form d to ½d. What happens to the charge? (A) ½Q (B) Q (C) 2Q (D) 0 92. The battery is disconnected and the plate area goes from A to 2A. What happens to the charge? (A) ½Q (B) Q (C) 2Q (D) 0 93. The battery is disconnected and the plate area goes from A to 2A. What happens to the voltage? (A) ½V (B) V (C) 2V (D) 0 94. Highlight the correct option for the following capacitor. A 84. Consider the arrangement of charges below. A• B• 40 cm 30 cm 40 cm 60 cm 52 cm a. Q1 = +50 C Q2 = -50 C Calculate the voltage at point A due to the two charges. B Plate (A or B) has the higher electric potential. The dashed lines are (equipotentials or electric field). The solid arrows are (equipotentials or electric field). Each dashed line equals 5 V. The potential difference between the two plates is (0, 5, 10 or 20) V. e. The plates are 0.01 m apart. The electric field is (1000, 2000, 4000 or 8000) V/m. 95. A 330-pF (p = 10-12) capacitor is connected to a 12 V battery. a. How much charge is stored on the capacitor? a. b. c. d. b. b. Calculate the voltage at point B due to the two charges. How much energy is stored in the capacitor? 96. A capacitor stores 10 C when charged with 12 V. a. What is the capacitance? b. How much energy does the capacitor store? e. What vertical velocity do the electrons acquire while passing through the vertical deflection plates? 97. Millikan, an American physicist, determined the charge of an electron by suspending an oil drop in midair with an electric field. f. How much time does it take the beam to travel from the vertical deflection plates to the fluorescent screen if there is 22 cm between them? g. What is the vertical displacement of the bright spot on the fluorescent screen? a. What is the force of gravity on the oil drop if it has a mass of 2.8 x 10-15 kg? b. What is the electric field strength between the plates if the plates have a potential difference of 340 V and a separation of 1.0 cm? c. What charge is necessary to suspend the oil drop between the two plates? d. How many excess electrons are on the oil drop? 98. A cathode ray tube is diagramed below. The heater current causes electrons to leave the cathode and accelerate toward the anode, where they pass through a small opening. Then the beam of electrons, cathode rays, are turned horizontally by the horizontal deflection plates and turned vertically by the vertical deflection plates, so that they form a bright spot on the fluorescent screen. The moving bright spot and the alternation of on and off generate an image on a TV picture tube. a. How much kinetic energy do the emerging electrons have if they are accelerated horizontally by 7.0 kV? b. What is the velocity of the emerging electrons? c. What vertical acceleration do the emerging electrons experience if a 2.9 x 105 N/C electric field exists between the vertical deflection plates? d. How much time does it take the beam to cross the vertical deflection plate if it is 2.8 cm long? Practice Multiple Choice Briefly explain why the answer is correct in the space provided. 1. Gravitational forces differ from electrostatic forces in that gravitational forces are (A) attractive only (B) repulsive only (C) both attractive and repulsive 2. A positive charge of 1 x 10-6 C is placed on an insulated solid conducting sphere. Which is true? (A) The charge resides uniformly throughout the sphere. (B) The electric field inside the sphere is constant in magnitude, but not zero. (C) An insulated metal object acquires a net positive charge when brought near to, but not in contact with, the sphere. (D) When a second conducting sphere is connected by a conducting wire to the first sphere, charge is transferred until the electric potentials of the two spheres are equal. 3. If the distance separating an electron and a proton is halved, the electric force between them will be (A) unchanged (B) quartered (C) doubled (D) quadrupled 4. Forces between two objects which are inversely proportional to the square of the distance between the objects include which of the following? I. Gravitational force between two celestial bodies II. Electrostatic force between two electrons III. Spring force between two masses (A) I only (B) II only (C) III only (D) I and II only 5. Metal sphere A has a charge of -2 units and an identical metal sphere, B, has a charge of -4 units. If the spheres are brought into contact with each other and then separated, the charge on sphere B will be (A) 0 units (B) -3 units (C) -2 units (D) +4 units Questions 6-7 Two ⅓-kg metallic spheres, A and B, are 0.3 m apart. The charge on each sphere is +1.0 x 10-6 C. 6. 7. 0.3 m What is the electric force between the two charged spheres? (A) 0.1 N (B) 0.3 N (C) 0.25 N (D) 1.0 N Which arrow represents the direction of the electric field at point P due to the charges on spheres A and B? (A) (B) (C) (D) 8. 9. In the diagram, P is a point near a negatively charged sphere. 17. The hollow metal sphere is positively charged. Point C is the center and point P is any other point within the sphere. What is the direction of the electric field at point P? (A) (B) (C) (D) Two metal spheres, A and B, have charges of +2 x 10-6 C and +1 x 10-6 C, respectively. Which is true of the electric field at these points? (A) It is zero at both points. (B) It is zero at C, but is directed inward at P. (C) It is zero at C, but is directed outward at P. (D) It is zero at P, but is not zero at C. 18. What is the electric field 2-m from the center of a 1-m hollow metal sphere, which carries a charge of 4 x 10-6 C? (A) 9.0 x 103 N/C (B) 1.8 x 104 N/C 4 (C) 2.4 x 10 N/C (D) 3.6 x 104 N/C 19. Where is the electric field closet to zero? QA = 4 C QB = -1 C A B C D 20. Charges -Q and +Q are located on the x- and y-axes, respectively, each at a distance d from the origin 0. The electric force on A due to B is 2.4 N. What is the electric force on B due to A? (A) I.2 N (B) 4.8 N (C) 2.4 N (D) 9.6 N Questions 10-11 An electron placed between oppositely charged parallel plates A and B moves toward plate A. The electric field strength between the two plates is 3,000 N/C. 10. What is the direction of the electric field between the plates? (A) toward plate A (B) toward plate B 11. What is the force on the electron? (A) 4.8 x 10-16 N (B) 2.4 x 10-16 N -16 (C) 6.4 x 10 N (D) 1.2 x 10-16 N 12. Which of the following is true about the net force on an uncharged conducting sphere in a uniform electric field? (A) It is zero. (B) It is in the direction of the field. (C) It is in the direction opposite to the field. 13. An electron is accelerated from rest by an electric field that exerts a force of 8.0 x 10-15 N. What is the the electric field? (A) 8.0 x 10-24 N/C (B) 9.1 x 10-22 N/C (C) 8.0 x 10-6 N/C (D) 5.0 x 104 N/C 14. Which location will have the greatest electric field strength as measured from the center of a positively charged hollow metal sphere of radius R? (A) 0 (B) 3/4R (C) 5/4R (D) 2R 15. Point B is twice as far away from +Q as point A. What is the direction of the electric field at the origin 0? (A) (B) (C) (D) Questions 21-22 Point P is 0.5 m from a charge of -5 x 10-6 C. 21. The intensity of the electric field at point P is most nearly (A) 1.8 x 105 N/C (B) 3.6 x 105 N/C 6 (C) 1.8 x 10 N/C (D) 7.2 x 106 N/C A second charge, q2 = 1 x 10-6 C is placed at point P. 22. What is the electric force on q2 at point P? (A) 1.8 N (B) 0.18 N (C) 3.6 N (D) 0.09 N 23. Two charges, QA = -4 C and QB = +1 C are 6 m apart. 0m 6m Where is the electric field equal to zero? (A) 2 m (B) 4.8 m (C) 8 m (D) 12 m 24. Two identical spheres each with a mass of ⅓-kg and charge of +1.0 x 10-6 C are 0.30 m apart. When the spheres are released, what is their initial acceleration? (A) 0.1 m/s2 (B) 0.3 m/s2 (C) 0.25 m/s2 (D) 1.0 m/s2 25. Two identical conducting spheres are charged to +2Q and -Q, respectively, and are separated by a distance d. The The ratio of the electric field strength at point A to the magnitude of the force of attraction on the left sphere is F1. electric field strength at point B is After the two spheres are made to touch and then (A) 8 to 1 (B) 4 to 1 (C) 2 to 1 (D) 1 to 1 separated by distance d, the magnitude of the force on the 16. An electron e and a proton p are simultaneously released left sphere is F2. Which of the following is correct? from rest in a uniform electric field E. (A) 2 F1 = F2 (B) F1 = F2 (C) F1 = 2 F2 (D) F1 = 8 F2 26. The figure shows two particles, each with a charge of +Q, which are located at the opposite corners of a square of At a later time the electron and the proton will have the same side d. (A) direction of motion (B) speed (C) displacement (D) magnitude of force What is the electric force on a particle of charge +q that is held at point P? (A) Zero (B) √2kqQ/d2 (C) kqQ/d2 (D) 2kqQ/d2 Questions 27-30 A charge Q1 = -16 x 10-6 C is on the x-axis at +4 m, and a charge Q2 = +9.0 x 10-6 C is on the y-axis at +3 m. attached to a battery with voltage V and filled with charge Q is altered. Use the options to answer the questions. C' Q' V' C' Q' V' (A) C Q V (B) ½C Q 2V (C) 2C 2Q V (D) 4C Q ¼V 37. The battery is disconnected and then the separation between the plates is doubled. 38. The battery remains connected and the plate area doubles. 39. The battery remains connected and the plate area and plate separation doubles. 40. The battery is disconnected and then the plate area is doubled and the plate separation is halved? 27. What are the electric fields due to Q1 and Q2 at the origin? (A) E1 = 9,000 N/C and E2 = 9,000 N/C (B) E1 = 36,000 N/C and E2 = 27000 N/C (C) E1 = 3,000 N/C and E2 = 4,000 N/C (D) E1 = 18,000 N/C and E2 = 8,000 N/C 28. The overall strength of the electric field at the origin is (A) 18,000 N/C (B) 13,000 N/C (C) 15,000 N/C (D) 5,000 N/C A charge, Q3 = -4 x 10-6 C is placed at the origin. 29. What is the direction of the electric force on Q3? (A) (B) (C) (D) 30. What is the electric force on Q3? (A) 0.05 N (B) 0.5 N (C) 0.75 N (D) 2.0 N 31. If 60 J of work is required to move 5 C of charge between two points in an electric field, what is the potential difference between these points? (A) 5 V (B) 60 V (C) 12 V d. 300 V 32. How much electrical energy is required to move a 4 x 10 -6-C charge through a potential difference of 36 V? (A) 9.00 x 106 J (B) 1.44 x 10-4 J (C) 144 J (D) 1.11 x 10-7 J Questions 33-34 Point P is 0.5 m from a charge of -5 x 10-6 C. 33. The electric potential (voltage) at point P is most nearly (A) -2.5 x 104 V (B) -2.5 x 103 V 4 (C) -9.0 x 10 V (D) -1.8 x 103 V 34. A second charge, q2 = 1 x 10-6 C is placed at point P. What is the electric potential energy of q2 at point P? (A) -1.8 J (B) -0.18 J (C) -3.6 J (D) -0.09 J Questions 35-36 Two conducting plates are 0.04 m apart. The lower plate is at a potential of 2 V and the upper plate is at a potential of 10 V. Point P is 0.01 m above the lower plate. 35. The electric potential at point P is (A) 10 V (B) 8 V (C) 6 V (D) 4 V 36. The electric field at point P is (A) 800 V/m (B) 600 V/m (C) 400 V/m (D) 200 V/m Questions 37-40 Determine the charge Q', Voltage V', and capacitance C' when a capacitor with capacitance C, 41. Two charges, QA = -4 C and QB = +1 C are 6 m apart. Where is the electric potential, voltage, equal to zero? (A) 2 m (B) 4.8 m (C) 8 m (D) 12 m 42. The capacitance of a parallel-plate capacitor can be increased by increasing which of the following? (A) The distance between the plates (B) The charge on each plate (C) The area of the plates (D) The voltage across the plates 43. A parallel-plate capacitor is connected to a battery. The electric field between the plates is 2,000 N/C. If the voltage is doubled and the distance between the plates is reduced to 1/5 the original distance, the new electric field is (A) 1,600 N/C (B) 2,400 N/C (C) 5,000 N/C (D) 20,000 N/C Questions 44-47 Two ⅓-kg metallic spheres, A and B, are separated by a distance of 0.3 m. The charge on each sphere is +1.0 x 10-6 C. 0m 0.3 m 44. Other than at an infinite distance away, where is the electric potential, voltage, equal to zero? (A) to the left of A (B) to the right of B (C) between A and B (D) at no location 45. What is the electric potential, voltage, at the midpoint? (A) 45,000 V (B) 90,000 V (C) 135,000 V (D) 120,000 V 46. What is the electric potential energy of the two sphere system? (A) 0.02 J (B) 0.05 J (C) 0.03 J (D) 0.15 J 47. The spheres are released. What is the velocity of each sphere when they are infinitely far apart? (A) 0.1 m/s (B) 0.3 m/s (C) 0.25 m/s (D) 1.0 m/s 48. A particle of charge Q and mass m accelerates from rest through a potential difference V attains a velocity v and kinetic energy K. What is the velocity, v', and kinetic energy, K', of a particle of charge 2Q and mass 2m that is accelerated from rest through the same potential difference? v' K' v' K' (A) ½v ¼K (B) ¼v ½K (C) 2v K (D) v 2K 49. The figure shows two particles, each with a charge of +Q, which are located at the opposite corners of a square of side d. Sphere C (+6 C, 0.004 kg) is placed at the midpoint. k. Determine the magnitude and direction of the electric force on sphere C. What is the potential energy of a particle of charge +q that is held at point P? (A) Zero (B) √2kqQ/d (C) kqQ/d (D) 2kqQ/d Practice Free Response 1. l. A 0.04-kg conducting sphere, carrying a charge of -30 C, is suspended by a string at an angle, = 37o, between two parallel plates of a capacitor that are 0.2 m apart. m. Sphere C is released from the midpoint. Determine the velocity of C when it is infinitely far away. a. 2. 0.2 m What is the electric force on the sphere? b. What is the magnitude and direction of the electric field between the plates? c. What is the voltage between the plates? 3. 0m 3m What is the electric force between them? b. the electric potential energy. +5 C 0 f. the velocity. Sphere B is returned to its original position 3 m from sphere A. Determine g. What is the magnitude and direction of the electric field at the midpoint? h. Determine the magnitude and direction of the electric field on the x-axis at x = 4 m. 4. 5. Two point charges, q1 and q2, are placed 0.30 m apart on the x-axis. Charge q1 has a value of -3.0 x 10-9 C. The net electric field at point P is zero. a. What is the sign of charge q2? Justify your answer. b. Calculate the magnitude of charge q2. c. Calculate the magnitude of the electric force on q2 and indicate its direction. A capacitor consists of two metal plates that are separated by 0.01 m and have cross sectional areas of 0.2 m2. a. Determine the capacitance? the voltage at the midpoint. The capacitor is connected to a 50 V battery. b. Determine the charge. i. Where is the electric field equal to zero? c. j. where the voltage equals zero. x -5 C Determine the following for sphere B when it is 1 m from A. d. the potential energy. the kinetic energy. | 4m -3 m Sphere B is released and accelerates toward sphere A. c. What is the magnitude and direction of the acceleration? e. Two charges, Q1 = +5 C and Q2 = -5 C, are located on the y-axis at y = +3 m and y = -3 m, respectively. y +3m Two conducting spheres, A (+9 C, 0.01 kg) and B (-1 C, 0.01 kg) are placed 3 m apart. A (+ 9 C) B (-1 C) a. Determine the electric potential energy of sphere C. Determine the energy. The battery remains attached to the capacitor while the distance between the plates is doubled. d. Determine the new capacitance and charge. The distance is returned to 0.01 m and the battery is disconnected. Now the area of the plates is doubled. e. Determine the new capacitance and voltage. 6. In a CRT monitor, electrons are first accelerated from rest through a high voltage in an electron gun. They then pass between deflecting plates before striking the screen. deflection plates screen electron gun 0.012 m a. d 0.04 m 0.5 m Determine the voltage in the electron gun that accelerates an electron to a velocity of 6.0 x 107 m/s. The deflecting plates are 0.012 m apart, 0.04 m long and have a 600-V potential between them. Determine b. the electric field between the plates. c. the acceleration of the electron while it is in the electric field between the plates. d. the time that the electron is between the plates. e. the vertical velocity of the electron as it leaves the plates. f. the distance, d, where the electron strikes the screen, which is 0.5 m from the deflection plates.