1cc. How many electrons does it take to make 1.00 C of charge?a)
1.60 · 1019b) 6.60 · 1019c) 3.20 · 1016d) 6.24 · 1018e) 6.66 · 1017 Get solution
1mcq. When a metal plate is given a positive charge, which of the following is taking place?a) Protons (positive charges) are transferred to the plate from another object.b) Electrons (negative charges) are transferred from the plate to another object.c) Electrons (negative charges) are transferred from the plate to another object, and protons (positive charges) are also transferred to the plate from another object.d) It depends on whether the object conveying the charge is a conductor or an insulator. Get solution
2cc. The hinged conductor moves away from the fixed conductor if a charge is applied to the electroscope, becausea) like charges repel each other.b) like charges attract each other.c) unlike charges attract each other.d) unlike charges repel each other. Get solution
2mcq. The force between a charge of 25 µC and a charge of –10 µC is 8.0 N. What is the separation between the two charges?a) 0.28 mb) 0.53 mc) 0.45 md) 0.15 m Get solution
3cc. You place two charges a distance r apart. Then you double each charge and double the distance between the charges. How does the force between the two charges change?a) The new force is twice as large.b) The new force is half as large.c) The new force is four times larger.d) The new force is four times smaller.e) The new force is the same. Get solution
3mcq. A charge Q1 is positioned on the x-axis at x = a. Where should a charge Q2 = –4Q1 be placed to produce a net electrostatic force of zero on a third charge, Q3 = Q1, located at the origin?a) at the originb) at x = 2ac) at x = –2ad) at x = –a Get solution
4cc. What do the forces acting on the charge q3 in Figure 21.15 indicate about the signs of the three charges?a) All three charges must be positive.b) All three charges must be negative.c) Charge q3 must be zero.d) Charges q1 and q2 must have opposite signs.e) Charges q1 and q2 must have the same sign, and q3 must have the opposite sign.Figure 21.15 The forces exerted on charge 3 by charge 1 and charge 2.... Get solution
4mcq. Which one of these systems has the most negative charge?a) 2 electronsb) 3 electrons and 1 protonc) 5 electrons and 5 protonsd) N electrons and N – 3 protonse) 1 electron Get solution
5cc. Assuming that the lengths of the vectors in Figure 21.15 are proportional to the magnitudes of the forces they represent, what do they indicate about the magnitudes of the charges q1 and q2? (Hint: The distance between x1 and x2 is the same as the distance between x2 and x3.)a) |q1 q2|b) |q1 = q2|c) |q1 > q2|d) The answer cannot be determined from the information given in the figure.Figure 21.15 The forces exerted on charge 3 by charge 1 and charge 2.... Get solution
5mcq. Two point charges are fixed on the x-axis: q1 = 6.0 µC is located at the origin, O, with x1 = 0.0 cm, and q2 = –3.0 µC is located at point A, with x2 = 8.0 cm. Where should a third charge, q3, be placed on the x-axis so that the total electrostatic force acting on it is zero?a) 19 cmb) 27 cmc) 0.0 cmd) 8.0 cme) –19 cm... Get solution
6cc. Three charges are arranged on a straight line as shown in the figure. What is the direction of the electrostatic force on the middle charge?...a) ...b) ...c) ...d) ...e) There is no force on that charge. Get solution
6mcq. Which of the following situations produces the largest net force on the charge Q?a) Charge Q = 1 C is 1 m from a charge of –2 C.b) Charge Q = 1 C is 0.5 m from a charge of –1 C.c) Charge Q = 1 C is halfway between a charge of –1 C and a charge of 1 C that are 2 m apart.d) Charge Q = 1 C is halfway between two charges of –2 C that are 2 m apart.e) Charge Q = 1 C is a distance of 2 m from a charge of –4 C. Get solution
7cc. Three charges are arranged on a straight line as shown in the figure. What is the direction of the electrostatic force on the right charge? (Note that the left charge is double what it was in Concept Check 21.6.)a) ...b) ...c) ...d) ...e) There is no force on that charge. Get solution
7mcq. Two protons placed near one another with no other objects close by woulda) accelerate away from each other.b) remain motionless.c) accelerate toward each other.d) be pulled together at constant speed.e) move away from each other at constant speed. Get solution
8cc. Consider three charges placed along the x-axis, as shown in the figure....The values of the charges are q1 = –8.10 μC, q2 = 2.16 μC, and q3 = 2.16 pC. The distance between q1 and q2 is d1 = 1.71 m. The distance between q1 and q3 is d2 = 2.62 m. What is the magnitude of the total electrostatic force exerted on q3 by q1 and q2?a) 2.77 · 10–8 Nb) 7.92 · 10–6 Nc) 1.44 · 10–5 Nd) 2.22 · 10–4 Ne) 6.71 · 10–2 N Get solution
8mcq. Two lightweight metal spheres are suspended near each other from insulating threads. One sphere has a net charge; the other sphere has no net charge. The spheres willa) attract each other.b) exert no net electrostatic force on each other.c) repel each other.d) do any of these things depending on the sign of the net charge on the one sphere. Get solution
9cc. Three charges are arranged at the corners of a square as shown in the figure. What is the direction of the electrostatic force on the lower-right charge?...a) ...b) ...c) ...d) ...e) There is no force on that charge. Get solution
9mcq. A metal plate is connected by a conductor to a ground through a switch. The switch is initially closed. A charge +Q is brought close to the plate without touching it, and then the switch is opened. After the switch is opened, the charge +Q is removed. What is the charge on the plate then?a) The plate is uncharged.b) The plate is positively charged.c) The plate is negatively charged.d) The plate could be either positively or negatively charged, depending on the charge it had before +Q was brought near.... Get solution
10cc. Four charges are arranged at the corners of a square as shown in the figure. What is the direction of the electrostatic force on the lower-right charge?...a) ...b) ...c) ...d) ...e) There is no force on that charge. Get solution
10mcq. You bring a negatively charged rubber rod close to a grounded conductor without touching it. Then you disconnect the ground. What is the sign of the charge on the conductor after you remove the charged rod?a) negativeb) positivec) no charged) cannot be determined from the information given Get solution
11cc. The proton’s mass is ~2000 times larger than the electron’s mass. Therefore, the ratio Fe/Fg for two protons is ______________ the value calculated in Example 21.4 for two electrons.a) ~4 million times smaller thanb) ~2000 times smaller thanc) the same asd) ~2000 times larger thane) ~4 million times larger thanExample 21.4Forces between Electrons...... Get solution
11mcq. When a rubber rod is rubbed with rabbit fur, the rod becomesa) negatively charged.b) positively charged.c) neutral.d) either negatively charged or positively charged, depending on whether the fur is always moved in the same direction or is moved back and forth. Get solution
12mcq. When a glass rod is rubbed with a polyester scarf, the rod becomesa) negatively charged.b) positively charged.c) neutral.d) either negatively charged or positively charged, depending on whether the scarf is always moved in the same direction or is moved back and forth. Get solution
13mcq. Consider an electron with mass m and charge –e moving in a circular orbit with radius r around a fixed proton with mass M and charge +e. The electron is held in orbit by the electrostatic force between itself and the proton. Which one of the following expressions for the speed of the electron is correct?a) ...b) ...c) ...d) ...e) ... Get solution
14mcq. Consider an electron with mass m and charge –e located a distance r from a fixed proton with mass M and charge +e. The electron is released from rest. Which one of the following expressions for the magnitude of the initial acceleration of the electron is correct?a) ...b) ...c) ...d) ...e) ... Get solution
15cq. If two charged particles (the charge on each is Q) are separated by a distance d, there is a force F between them. What is the force if the magnitude of each charge is doubled and the distance between them changes to 2d? Get solution
16cq. Suppose the Sun and the Earth were each given an equal amount of charge of the same sign, just sufficient to cancel their gravitational attraction. How many times the charge on an electron would that charge be? Is this number a large fraction of the number of charges of either sign in the Earth? Get solution
17cq. It is apparent that the electrostatic force is extremely strong, compared to gravity. In fact, the electrostatic force is the basic force governing phenomena in daily life—the tension in a string, the normal forces between surfaces, friction, chemical reactions, and so forth—except weight. Why then did it take so long for scientists to understand this force? Newton came up with his gravitational law long before electricity was even crudely understood. Get solution
18cq. Occasionally, people who gain static charge by shuffling their feet on the carpet will have their hair stand on end. Why does this happen? Get solution
19cq. Two positive charges, each equal to Q, are placed a distance 2d apart. A third charge, –0.2Q, is placed exactly halfway between the two positive charges and is displaced a distance x ˂˂ d (that is, x is much smaller than d) perpendicular to the line connecting the positive charges. What is the force on this charge? For x ˂˂ d, how can you approximate the motion of the negative charge? Get solution
20cq. Why does a garment taken out of a clothes dryer sometimes cling to your body when you wear it? Get solution
21cq. Two charged spheres are initially a distance d apart. The magnitude of the force on each sphere is F. They are moved closer to each other such that the magnitude of the force on each of them is 9F. By what factor has the distance between the two spheres changed? Get solution
22cq. How is it possible for one electrically neutral atom to exert an electrostatic force on another electrically neutral atom? Get solution
23cq. The scientists who first contributed to the understanding of the electrostatic force in the 18th century were well aware of Newton’s law of gravitation. How could they deduce that the force they were studying was not a variant or some manifestation of the gravitational force? Get solution
24cq. Two charged particles move solely under the influence of the electrostatic forces between them. What shapes can their trajectories have? Get solution
25cq. Rubbing a balloon causes it to become negatively charged. The balloon then tends to cling to the wall of a room. For this to happen, must the wall be positively charged? Get solution
26cq. Two electric charges are placed on a line, as shown in the figure. Is it possible to place a charged particle (that is free to move) anywhere on the line between the two charges and have it not move?... Get solution
27cq. Two electric charges are placed on a line as shown in the figure. Where on the line can a third charge be placed so that the force on that charge is zero? Does the sign or the magnitude of the third charge make any difference to the answer?... Get solution
29cq. When you exit a car and the humidity is low, you often experience a shock from static electricity created by sliding across the seat. How can you discharge yourself without experiencing a painful shock? Why is it dangerous to get back into your car while fueling your car? Get solution
30. How many electrons are required to yield a total charge of 1.00 C? Get solution
32. Another unit of charge is the electrostatic unit (esu). It is defined as follows: Two point charges, each of 1 esu and separated by 1 cm, exert a force of exactly 1 dyne on each other: 1 dyne = 1 g cm/s2 = 1 · 10–5 N.a) Determine the relationship between the esu and the coulomb.b) Determine the relationship between the esu and the elementary charge. Get solution
33. A current of 5.00 mA is enough to make your muscles twitch. Calculate how many electrons flow through your skin if you are exposed to such a current for 10.0 s. Get solution
35. The Earth is constantly being bombarded by cosmic rays, which consist mostly of protons. These protons are incident on the Earth’s atmosphere from all directions at a rate of 1245. protons per square meter per second. Assuming that the depth of Earth’s atmosphere is 120.0 km, what is the total charge incident on the atmosphere in 5.000 min? Assume that the radius of the surface of the Earth is 6378. km. Get solution
36. Performing an experiment similar to Millikan’s oil drop experiment, a student measures these charge magnitudes:3.26 · 10–19 C6.39 · 10–19 C5.09 · 10–19 C4.66 · 10–19 C1.53 · 10–19 CFind the charge on the electron using these measurements. Get solution
38. Two charged spheres are 8.00 cm apart. They are moved closer to each other by enough that the force on each of them increases four times. How far apart are they now? Get solution
39. Two identically charged particles separated by a distance of 1.00 m repel each other with a force of 1.00 N. What is the magnitude of the charges? Get solution
40. How far apart must two electrons be placed on the Earth’s surface for there to be an electrostatic force between them equal to the weight of one of the electrons? Get solution
41. In solid sodium chloride (table salt), chloride ions have one more electron than they have protons, and sodium ions have one more proton than they have electrons. These ions are separated by about 0.28 nm. Calculate the electrostatic force between a sodium ion and a chloride ion. Get solution
42. In gaseous sodium chloride, chloride ions have one more electron than they have protons, and sodium ions have one more proton than they have electrons. These ions are separated by about 0.24 nm. Suppose a free electron is located 0.48 nm above the midpoint of the sodium chloride molecule. What are the magnitude and the direction of the electrostatic force the molecule exerts on it? Get solution
43. Calculate the magnitude of the electrostatic force the two up quarks inside a proton exert on each other if they are separated by a distance of 0.900 fm. Get solution
44. A –4.00-µC charge lies 20.0 cm to the right of a 2.00-µC charge on the x-axis. What is the force on the 2.00-µC charge? Get solution
45. Two initially uncharged identical metal spheres, 1 and 2, are connected by an insulating spring (unstretched length L0 = 1.00 m, spring constant κ = 25.0 N/m), as shown in the figure. Charges +q and –q are then placed on the spheres, and the spring contracts to length L = 0.635 m. Recall that the force exerted by a spring is Fs = k∆x, where ∆x is the change in the spring’s length from its equilibrium length. Determine the charge q. If the spring is coated with metal to make it conducting, what is the new length of the spring?... Get solution
46. A point charge +3q is located at the origin, and a point charge –q is located on the x-axis at D = 0.500 m. At what location on the x-axis will a third charge, q0, experience no net force from the other two charges? Get solution
47. Identical point charges Q are placed at each of the four corners of a rectangle measuring 2.00 m by 3.00 m. If Q = 32.0 µC, what is the magnitude of the electrostatic force on any one of the charges? Get solution
48. Charge q1 = 1.40·10–8 C is placed at the origin. Charges q2 = –1.80·10–8 C and q3 = 2.10·10–8 C are placed at points (0.180 m,0.000 m) and (0.000 m,0.240 m), respectively, as shown in the figure. Determine the net electrostatic force (magnitude and direction) on charge q3.... Get solution
49. A positive charge Q is on the y-axis at a distance a from the origin, and another positive charge q is on the x-axis at a distance b from the origin.a) For what value(s) of b is the x-component of the force on q a minimum?b) For what value(s) of b is the x-component of the force on q a maximum?... Get solution
50. Find the magnitude and direction of the electrostatic force acting on the electron in the figure.... Get solution
51. In a region of two-dimensional space, there are three fixed charges: +1.00 mC at (0,0), –2.00 mC at (17.0 mm,–5.00 mm), and +3.00 mC at (–2.00 mm,11.0 mm). What is the net force on the –2.00-mC charge? Get solution
52. Two cylindrical glass beads each of mass m = 10.0 mg are set on their flat ends on a horizontal insulating surface separated by a distance d = 2.00 cm. The coefficient of static friction between the beads and the surface is µs = 0.200. The beads are then given identical charges (magnitude and sign). What is the minimum charge needed to start the beads moving? Get solution
53. A small ball with a mass of 30.0 g and a charge of –0.200 µC is suspended from the ceiling by a string. The ball hangs at a distance of 5.00 cm above an insulating floor. If a second small ball with a mass of 50.0 g and a charge of 0.400 µC is rolled directly beneath the first ball, will the second ball leave the floor? What is the tension in the string when the second ball is directly beneath the first ball? Get solution
54. A +3.00-mC charge and a –4.00-mC charge are fixed in position and separated by 5.00 m.a) Where can a +7.00-mC charge be placed so that the net force on it is zero?b) Where can a –7.00-mC charge be placed so that the net force on it is zero? Get solution
55. Four point charges, q, are fixed to the four corners of a square that is 10.0 cm on a side. An electron is suspended above a point at which its weight is balanced by the electrostatic force due to the four electrons, at a distance of 15.0 nm above the center of the square. What is the magnitude of the fixed charges? Express the charge both in coulombs and as a multiple of the electron’s charge. Get solution
56. The figure shows a uniformly charged thin rod of length L that has total charge Q. Find an expression for the magnitude of the electrostatic force acting on an electron positioned on the axis of the rod at a distance d from the midpoint of the rod.... Get solution
57. A negative charge, –q, is fixed at the coordinate (0,0). It is exerting an attractive force on a positive charge, +q, that is initially at coordinate (x,0). As a result, the positive charge accelerates toward the negative charge. Use the binomial expansion (1+ x)n ≈ 1 + nx, for x δ x closer to the negative charge, the force that the negative charge exerts on it increases by ∆F = 2kq2 δ /x3. Get solution
59. Suppose the Earth and the Moon carried positive charges of equal magnitude. How large would the charge need to be to produce an electrostatic repulsion equal to 1.00% of the gravitational attraction between the two bodies? Get solution
60. The similarity of form of Newton’s law of gravitation and Coulomb’s Law caused some to speculate that the force of gravity is related to the electrostatic force. Suppose that gravitation is entirely electrical in nature— that an excess charge Q on the Earth and an equal and opposite excess charge –Q on the Moon are responsible for the gravitational force that causes the observed orbital motion of the Moon about the Earth. What is the required size of Q to reproduce the observed magnitude of the gravitational force? Get solution
61. In the Bohr model of the hydrogen atom, the electron moves around the one-proton nucleus on circular orbits of well-determined radii, given by rn = n2aB, where n = 1, 2, 3, ... is an integer that defines the orbit and aB = 5.29·10–11m is the radius of the first (minimum) orbit, called the Bohr radius. Calculate the force of electrostatic interaction between the electron and the proton in the hydrogen atom for the first four orbits. Compare the strength of this interaction to the gravitational interaction between the proton and the electron. Get solution
62. Some of the earliest atomic models held that the orbital velocity of an electron in an atom could be correlated with the radius of the atom. If the radius of the hydrogen atom is 5.29 · 10–11 m and the electrostatic force is responsible for the circular motion of the electron, what is the kinetic energy of this orbital electron? Get solution
63. For the atom described in Problem 21.62, what is the ratio of the gravitational force between electron and proton to the electrostatic force? How does this ratio change if the radius of the atom is doubled? Get solution
64. In general, astronomical objects are not exactly electrically neutral. Suppose the Earth and the Moon each carry a charge of –1.00·106 C (this is approximately correct; a more precise value is identified in Chapter 22).a) Compare the resulting electrostatic repulsion with the gravitational attraction between the Moon and the Earth. Look up any necessary data.b) What effects does this electrostatic force have on the size, shape, and stability of the Moon’s orbit around the Earth? Get solution
65. Eight 1.00-µC charges are arrayed along the y-axis located every 2.00 cm starting at y = 0 and extending to y = 14.0 cm. Find the force on the charge at y = 4.00 cm. Get solution
66. In a simplified Bohr model of the hydrogen atom, an electron is assumed to be traveling in a circular orbit of radius of about 5.29·10–11 m around a proton. Calculate the speed of the electron in that orbit. Get solution
67. The nucleus of a carbon-14 atom (mass = 14 amu) has diameter of 3.01 fm. It has 6 protons and a charge of +6e.a) What is the force on a proton located at 3.00 fm from the surface of this nucleus? Assume that the nucleus is a point charge.b) What is the proton’s acceleration? Get solution
68. Two charged objects experience a mutual repulsive force of 0.100 N. If the charge of one of the objects is reduced by half and the distance separating the objects is doubled, what is the new force? Get solution
69. A particle (charge = +19.0 µC) is located on the x-axis at x = –10.0 cm, and a second particle (charge = –57.0 µC) is placed on the x-axis at x = +20.0 cm. What is the magnitude of the total electrostatic force on a third particle (charge = –3.80 µC) placed at the origin (x = 0)? Get solution
70. Three point charges are positioned on the x-axis: +64.0 µC at x = 0.00 cm, +80.0 µC at x = 25.0 cm, and –160.0 µC at x = 50.0 cm. What is the magnitude of the electrostatic force acting on the +64.0–µC charge? Get solution
71. From collisions with cosmic rays and from the solar wind, the Earth has a net electric charge of approximately –6.8 · 105 C. Find the charge that must be given to a 1.0-g object for it to be electrostatically levitated close to the Earth’s surface. Get solution
72. Your sister wants to participate in the yearly science fair at her high school and asks you to suggest some exciting project. You suggest that she experiment with your recently created electron extractor to suspend her cat in the air. You tell her to buy a copper plate and bolt it to the ceiling in her room and then use your electron extractor to transfer electrons from the plate to the cat. If the cat weighs 7.00 kg and is suspended 2.00 m below the ceiling, how many electrons have to be extracted from the cat? Assume that the cat and the metal plate are point charges. Get solution
73. A 10.0-g mass is suspended 5.00 cm above a nonconducting flat plate, directly above an embedded charge of q (in coulombs). If the mass has the same charge, q, how much must q be so that the mass levitates (just floats, neither rising nor falling)? If the charge q is produced by adding electrons to the mass, by how much will the mass be changed? Get solution
75. Three 5.00-g Styrofoam balls of radius 2.00 cm are coated with carbon black to make them conducting and then are tied to 1.00-m-long threads and suspended freely from a common point. Each ball is given the same charge, q. At equilibrium, the balls form an equilateral triangle with sides of length 25.0 cm in the horizontal plane. Determine q. Get solution
77. Two beads with charges q1 = q2 = +2.67 µC are on an insulating string that hangs straight down from the ceiling as shown in the figure. The lower bead is fixed in place on the end of the string and has a mass m1 = 0.280 kg. The second bead slides without friction on the string. At a distance d = 0.360 m between the centers of the beads, the force of the Earth’s gravity on m2 is balancedby the electrostatic force between the two beads. What is the mass, m2, of the second bead? (Hint: You can neglect the gravitational interaction between the two beads.)... Get solution
76. Two point charges lie on the x-axis. If one point charge is 6.00 µC and lies at the origin and the other is –2.00 µC and lies at 20.0 cm, at what position must a third charge be placed to be in equilibrium? Get solution
78. Find the net force on a +2.00-C charge at the origin of an xy-coordinate system if there is a +5.00-C charge at (3.00 m,0.00) and a –3.00-C charge at (0.00,4.00 m). Get solution
79. Two spheres, each of mass M = 2.33 g, are attached by pieces of string of length L = 45.0 cm to a common point. The strings initially hang straight down, with the spheres just touching one another. An equal amount of charge, q, is placed on each sphere. The resulting forces on the spheres cause each string to hang at an angle of θ = 10.0° from the vertical. Determine q, the amount of charge on each sphere. Get solution
80. A point charge q1 = 100. nC is at the origin of an xy-coordinate system, a point charge q2 = –80.0 nC is on the x-axis at x = 2.00 m, and a point charge q3 = –60.0 nC is on the y-axis at y = –2.00 m. Determine the net force (magnitude and direction) on q1. Get solution
81. A positive charge q1 = 1.00 µC is fixed at the origin, and a second charge q2 = –2.00 µC is fixed at x = 10.0 cm. Where along the x-axis should a third charge be positioned so that it experiences no force?... Get solution
82. A bead with charge q1 = 1.27 µC is fixed in place at the end of a wire that makes an angle of θ = 51.3° with the horizontal. A second bead with mass m2 = 3.77 g and a charge of 6.79 µC slides without friction on the wire. What is the distance d at which the force of the Earth’s gravity on m2 is balanced by the electrostatic force between the two beads? Neglect the gravitational interaction between the two beads.... Get solution
83. In the figure, the net electrostatic force on charge QA is zero. If QA = +1.00 nC, determine the magnitude of Q0.... Get solution
84. Two balls have the same mass, 0.9680 kg, and the same charge, 29.59 µC. They hang from the ceiling on strings of identical length, l, as shown in the figure. If the angle of the strings with respect to the vertical is 29.79°, what is the length of the strings? Get solution
85. Two balls have the same mass and the same charge, 15.71 µC. Th ey hang from the ceiling on strings of identical length, l = 1.223 m, as shown in the figure. The angle of the strings with respect to the vertical is 21.07°. What is the mass of each ball? Get solution
86. Two balls have the same mass, 0.9935 kg, and the same charge. They hang from the ceiling on strings of identical length, l = 1.235 m, as shown in the figure. The angle of the strings with respect to the vertical is 22.35°. What is the charge on each ball?... Get solution
87. As shown in the figure, point charge q1 is 3.979 µC and is located at x1 = –5.689 m, and point charge q2 is 8.669 μC and is located at x2 = 14.13 m. What is the x-oordinate of the point at which the net force on a point charge of 5.000 μC will be zero?... Get solution
88. As shown in the figure, point charge q1 is 4.325 µC and is located at x1, and point charge q2 is 7.757 µC and is located at x2 = 14.33 m. The x-coordinate of the point where the net force on a point charge of –3.000 µC is zero is 2.358 m. What is the value of x1? Get solution
89. As shown in the figure, point charge q1 is 4.671 µC and is located at x1 = –3.573 m, and point charge q2 is 6.845 µC and is located at x2. The x-coordinate of the point where the net force on a point charge of –1.000 µC is zero is 4.625 m. What is the value of x2? Get solution
1mcq. When a metal plate is given a positive charge, which of the following is taking place?a) Protons (positive charges) are transferred to the plate from another object.b) Electrons (negative charges) are transferred from the plate to another object.c) Electrons (negative charges) are transferred from the plate to another object, and protons (positive charges) are also transferred to the plate from another object.d) It depends on whether the object conveying the charge is a conductor or an insulator. Get solution
2cc. The hinged conductor moves away from the fixed conductor if a charge is applied to the electroscope, becausea) like charges repel each other.b) like charges attract each other.c) unlike charges attract each other.d) unlike charges repel each other. Get solution
2mcq. The force between a charge of 25 µC and a charge of –10 µC is 8.0 N. What is the separation between the two charges?a) 0.28 mb) 0.53 mc) 0.45 md) 0.15 m Get solution
3cc. You place two charges a distance r apart. Then you double each charge and double the distance between the charges. How does the force between the two charges change?a) The new force is twice as large.b) The new force is half as large.c) The new force is four times larger.d) The new force is four times smaller.e) The new force is the same. Get solution
3mcq. A charge Q1 is positioned on the x-axis at x = a. Where should a charge Q2 = –4Q1 be placed to produce a net electrostatic force of zero on a third charge, Q3 = Q1, located at the origin?a) at the originb) at x = 2ac) at x = –2ad) at x = –a Get solution
4cc. What do the forces acting on the charge q3 in Figure 21.15 indicate about the signs of the three charges?a) All three charges must be positive.b) All three charges must be negative.c) Charge q3 must be zero.d) Charges q1 and q2 must have opposite signs.e) Charges q1 and q2 must have the same sign, and q3 must have the opposite sign.Figure 21.15 The forces exerted on charge 3 by charge 1 and charge 2.... Get solution
4mcq. Which one of these systems has the most negative charge?a) 2 electronsb) 3 electrons and 1 protonc) 5 electrons and 5 protonsd) N electrons and N – 3 protonse) 1 electron Get solution
5cc. Assuming that the lengths of the vectors in Figure 21.15 are proportional to the magnitudes of the forces they represent, what do they indicate about the magnitudes of the charges q1 and q2? (Hint: The distance between x1 and x2 is the same as the distance between x2 and x3.)a) |q1 q2|b) |q1 = q2|c) |q1 > q2|d) The answer cannot be determined from the information given in the figure.Figure 21.15 The forces exerted on charge 3 by charge 1 and charge 2.... Get solution
5mcq. Two point charges are fixed on the x-axis: q1 = 6.0 µC is located at the origin, O, with x1 = 0.0 cm, and q2 = –3.0 µC is located at point A, with x2 = 8.0 cm. Where should a third charge, q3, be placed on the x-axis so that the total electrostatic force acting on it is zero?a) 19 cmb) 27 cmc) 0.0 cmd) 8.0 cme) –19 cm... Get solution
6cc. Three charges are arranged on a straight line as shown in the figure. What is the direction of the electrostatic force on the middle charge?...a) ...b) ...c) ...d) ...e) There is no force on that charge. Get solution
6mcq. Which of the following situations produces the largest net force on the charge Q?a) Charge Q = 1 C is 1 m from a charge of –2 C.b) Charge Q = 1 C is 0.5 m from a charge of –1 C.c) Charge Q = 1 C is halfway between a charge of –1 C and a charge of 1 C that are 2 m apart.d) Charge Q = 1 C is halfway between two charges of –2 C that are 2 m apart.e) Charge Q = 1 C is a distance of 2 m from a charge of –4 C. Get solution
7cc. Three charges are arranged on a straight line as shown in the figure. What is the direction of the electrostatic force on the right charge? (Note that the left charge is double what it was in Concept Check 21.6.)a) ...b) ...c) ...d) ...e) There is no force on that charge. Get solution
7mcq. Two protons placed near one another with no other objects close by woulda) accelerate away from each other.b) remain motionless.c) accelerate toward each other.d) be pulled together at constant speed.e) move away from each other at constant speed. Get solution
8cc. Consider three charges placed along the x-axis, as shown in the figure....The values of the charges are q1 = –8.10 μC, q2 = 2.16 μC, and q3 = 2.16 pC. The distance between q1 and q2 is d1 = 1.71 m. The distance between q1 and q3 is d2 = 2.62 m. What is the magnitude of the total electrostatic force exerted on q3 by q1 and q2?a) 2.77 · 10–8 Nb) 7.92 · 10–6 Nc) 1.44 · 10–5 Nd) 2.22 · 10–4 Ne) 6.71 · 10–2 N Get solution
8mcq. Two lightweight metal spheres are suspended near each other from insulating threads. One sphere has a net charge; the other sphere has no net charge. The spheres willa) attract each other.b) exert no net electrostatic force on each other.c) repel each other.d) do any of these things depending on the sign of the net charge on the one sphere. Get solution
9cc. Three charges are arranged at the corners of a square as shown in the figure. What is the direction of the electrostatic force on the lower-right charge?...a) ...b) ...c) ...d) ...e) There is no force on that charge. Get solution
9mcq. A metal plate is connected by a conductor to a ground through a switch. The switch is initially closed. A charge +Q is brought close to the plate without touching it, and then the switch is opened. After the switch is opened, the charge +Q is removed. What is the charge on the plate then?a) The plate is uncharged.b) The plate is positively charged.c) The plate is negatively charged.d) The plate could be either positively or negatively charged, depending on the charge it had before +Q was brought near.... Get solution
10cc. Four charges are arranged at the corners of a square as shown in the figure. What is the direction of the electrostatic force on the lower-right charge?...a) ...b) ...c) ...d) ...e) There is no force on that charge. Get solution
10mcq. You bring a negatively charged rubber rod close to a grounded conductor without touching it. Then you disconnect the ground. What is the sign of the charge on the conductor after you remove the charged rod?a) negativeb) positivec) no charged) cannot be determined from the information given Get solution
11cc. The proton’s mass is ~2000 times larger than the electron’s mass. Therefore, the ratio Fe/Fg for two protons is ______________ the value calculated in Example 21.4 for two electrons.a) ~4 million times smaller thanb) ~2000 times smaller thanc) the same asd) ~2000 times larger thane) ~4 million times larger thanExample 21.4Forces between Electrons...... Get solution
11mcq. When a rubber rod is rubbed with rabbit fur, the rod becomesa) negatively charged.b) positively charged.c) neutral.d) either negatively charged or positively charged, depending on whether the fur is always moved in the same direction or is moved back and forth. Get solution
12mcq. When a glass rod is rubbed with a polyester scarf, the rod becomesa) negatively charged.b) positively charged.c) neutral.d) either negatively charged or positively charged, depending on whether the scarf is always moved in the same direction or is moved back and forth. Get solution
13mcq. Consider an electron with mass m and charge –e moving in a circular orbit with radius r around a fixed proton with mass M and charge +e. The electron is held in orbit by the electrostatic force between itself and the proton. Which one of the following expressions for the speed of the electron is correct?a) ...b) ...c) ...d) ...e) ... Get solution
14mcq. Consider an electron with mass m and charge –e located a distance r from a fixed proton with mass M and charge +e. The electron is released from rest. Which one of the following expressions for the magnitude of the initial acceleration of the electron is correct?a) ...b) ...c) ...d) ...e) ... Get solution
15cq. If two charged particles (the charge on each is Q) are separated by a distance d, there is a force F between them. What is the force if the magnitude of each charge is doubled and the distance between them changes to 2d? Get solution
16cq. Suppose the Sun and the Earth were each given an equal amount of charge of the same sign, just sufficient to cancel their gravitational attraction. How many times the charge on an electron would that charge be? Is this number a large fraction of the number of charges of either sign in the Earth? Get solution
17cq. It is apparent that the electrostatic force is extremely strong, compared to gravity. In fact, the electrostatic force is the basic force governing phenomena in daily life—the tension in a string, the normal forces between surfaces, friction, chemical reactions, and so forth—except weight. Why then did it take so long for scientists to understand this force? Newton came up with his gravitational law long before electricity was even crudely understood. Get solution
18cq. Occasionally, people who gain static charge by shuffling their feet on the carpet will have their hair stand on end. Why does this happen? Get solution
19cq. Two positive charges, each equal to Q, are placed a distance 2d apart. A third charge, –0.2Q, is placed exactly halfway between the two positive charges and is displaced a distance x ˂˂ d (that is, x is much smaller than d) perpendicular to the line connecting the positive charges. What is the force on this charge? For x ˂˂ d, how can you approximate the motion of the negative charge? Get solution
20cq. Why does a garment taken out of a clothes dryer sometimes cling to your body when you wear it? Get solution
21cq. Two charged spheres are initially a distance d apart. The magnitude of the force on each sphere is F. They are moved closer to each other such that the magnitude of the force on each of them is 9F. By what factor has the distance between the two spheres changed? Get solution
22cq. How is it possible for one electrically neutral atom to exert an electrostatic force on another electrically neutral atom? Get solution
23cq. The scientists who first contributed to the understanding of the electrostatic force in the 18th century were well aware of Newton’s law of gravitation. How could they deduce that the force they were studying was not a variant or some manifestation of the gravitational force? Get solution
24cq. Two charged particles move solely under the influence of the electrostatic forces between them. What shapes can their trajectories have? Get solution
25cq. Rubbing a balloon causes it to become negatively charged. The balloon then tends to cling to the wall of a room. For this to happen, must the wall be positively charged? Get solution
26cq. Two electric charges are placed on a line, as shown in the figure. Is it possible to place a charged particle (that is free to move) anywhere on the line between the two charges and have it not move?... Get solution
27cq. Two electric charges are placed on a line as shown in the figure. Where on the line can a third charge be placed so that the force on that charge is zero? Does the sign or the magnitude of the third charge make any difference to the answer?... Get solution
29cq. When you exit a car and the humidity is low, you often experience a shock from static electricity created by sliding across the seat. How can you discharge yourself without experiencing a painful shock? Why is it dangerous to get back into your car while fueling your car? Get solution
30. How many electrons are required to yield a total charge of 1.00 C? Get solution
32. Another unit of charge is the electrostatic unit (esu). It is defined as follows: Two point charges, each of 1 esu and separated by 1 cm, exert a force of exactly 1 dyne on each other: 1 dyne = 1 g cm/s2 = 1 · 10–5 N.a) Determine the relationship between the esu and the coulomb.b) Determine the relationship between the esu and the elementary charge. Get solution
33. A current of 5.00 mA is enough to make your muscles twitch. Calculate how many electrons flow through your skin if you are exposed to such a current for 10.0 s. Get solution
35. The Earth is constantly being bombarded by cosmic rays, which consist mostly of protons. These protons are incident on the Earth’s atmosphere from all directions at a rate of 1245. protons per square meter per second. Assuming that the depth of Earth’s atmosphere is 120.0 km, what is the total charge incident on the atmosphere in 5.000 min? Assume that the radius of the surface of the Earth is 6378. km. Get solution
36. Performing an experiment similar to Millikan’s oil drop experiment, a student measures these charge magnitudes:3.26 · 10–19 C6.39 · 10–19 C5.09 · 10–19 C4.66 · 10–19 C1.53 · 10–19 CFind the charge on the electron using these measurements. Get solution
38. Two charged spheres are 8.00 cm apart. They are moved closer to each other by enough that the force on each of them increases four times. How far apart are they now? Get solution
39. Two identically charged particles separated by a distance of 1.00 m repel each other with a force of 1.00 N. What is the magnitude of the charges? Get solution
40. How far apart must two electrons be placed on the Earth’s surface for there to be an electrostatic force between them equal to the weight of one of the electrons? Get solution
41. In solid sodium chloride (table salt), chloride ions have one more electron than they have protons, and sodium ions have one more proton than they have electrons. These ions are separated by about 0.28 nm. Calculate the electrostatic force between a sodium ion and a chloride ion. Get solution
42. In gaseous sodium chloride, chloride ions have one more electron than they have protons, and sodium ions have one more proton than they have electrons. These ions are separated by about 0.24 nm. Suppose a free electron is located 0.48 nm above the midpoint of the sodium chloride molecule. What are the magnitude and the direction of the electrostatic force the molecule exerts on it? Get solution
43. Calculate the magnitude of the electrostatic force the two up quarks inside a proton exert on each other if they are separated by a distance of 0.900 fm. Get solution
44. A –4.00-µC charge lies 20.0 cm to the right of a 2.00-µC charge on the x-axis. What is the force on the 2.00-µC charge? Get solution
45. Two initially uncharged identical metal spheres, 1 and 2, are connected by an insulating spring (unstretched length L0 = 1.00 m, spring constant κ = 25.0 N/m), as shown in the figure. Charges +q and –q are then placed on the spheres, and the spring contracts to length L = 0.635 m. Recall that the force exerted by a spring is Fs = k∆x, where ∆x is the change in the spring’s length from its equilibrium length. Determine the charge q. If the spring is coated with metal to make it conducting, what is the new length of the spring?... Get solution
46. A point charge +3q is located at the origin, and a point charge –q is located on the x-axis at D = 0.500 m. At what location on the x-axis will a third charge, q0, experience no net force from the other two charges? Get solution
47. Identical point charges Q are placed at each of the four corners of a rectangle measuring 2.00 m by 3.00 m. If Q = 32.0 µC, what is the magnitude of the electrostatic force on any one of the charges? Get solution
48. Charge q1 = 1.40·10–8 C is placed at the origin. Charges q2 = –1.80·10–8 C and q3 = 2.10·10–8 C are placed at points (0.180 m,0.000 m) and (0.000 m,0.240 m), respectively, as shown in the figure. Determine the net electrostatic force (magnitude and direction) on charge q3.... Get solution
49. A positive charge Q is on the y-axis at a distance a from the origin, and another positive charge q is on the x-axis at a distance b from the origin.a) For what value(s) of b is the x-component of the force on q a minimum?b) For what value(s) of b is the x-component of the force on q a maximum?... Get solution
50. Find the magnitude and direction of the electrostatic force acting on the electron in the figure.... Get solution
51. In a region of two-dimensional space, there are three fixed charges: +1.00 mC at (0,0), –2.00 mC at (17.0 mm,–5.00 mm), and +3.00 mC at (–2.00 mm,11.0 mm). What is the net force on the –2.00-mC charge? Get solution
52. Two cylindrical glass beads each of mass m = 10.0 mg are set on their flat ends on a horizontal insulating surface separated by a distance d = 2.00 cm. The coefficient of static friction between the beads and the surface is µs = 0.200. The beads are then given identical charges (magnitude and sign). What is the minimum charge needed to start the beads moving? Get solution
53. A small ball with a mass of 30.0 g and a charge of –0.200 µC is suspended from the ceiling by a string. The ball hangs at a distance of 5.00 cm above an insulating floor. If a second small ball with a mass of 50.0 g and a charge of 0.400 µC is rolled directly beneath the first ball, will the second ball leave the floor? What is the tension in the string when the second ball is directly beneath the first ball? Get solution
54. A +3.00-mC charge and a –4.00-mC charge are fixed in position and separated by 5.00 m.a) Where can a +7.00-mC charge be placed so that the net force on it is zero?b) Where can a –7.00-mC charge be placed so that the net force on it is zero? Get solution
55. Four point charges, q, are fixed to the four corners of a square that is 10.0 cm on a side. An electron is suspended above a point at which its weight is balanced by the electrostatic force due to the four electrons, at a distance of 15.0 nm above the center of the square. What is the magnitude of the fixed charges? Express the charge both in coulombs and as a multiple of the electron’s charge. Get solution
56. The figure shows a uniformly charged thin rod of length L that has total charge Q. Find an expression for the magnitude of the electrostatic force acting on an electron positioned on the axis of the rod at a distance d from the midpoint of the rod.... Get solution
57. A negative charge, –q, is fixed at the coordinate (0,0). It is exerting an attractive force on a positive charge, +q, that is initially at coordinate (x,0). As a result, the positive charge accelerates toward the negative charge. Use the binomial expansion (1+ x)n ≈ 1 + nx, for x δ x closer to the negative charge, the force that the negative charge exerts on it increases by ∆F = 2kq2 δ /x3. Get solution
59. Suppose the Earth and the Moon carried positive charges of equal magnitude. How large would the charge need to be to produce an electrostatic repulsion equal to 1.00% of the gravitational attraction between the two bodies? Get solution
60. The similarity of form of Newton’s law of gravitation and Coulomb’s Law caused some to speculate that the force of gravity is related to the electrostatic force. Suppose that gravitation is entirely electrical in nature— that an excess charge Q on the Earth and an equal and opposite excess charge –Q on the Moon are responsible for the gravitational force that causes the observed orbital motion of the Moon about the Earth. What is the required size of Q to reproduce the observed magnitude of the gravitational force? Get solution
61. In the Bohr model of the hydrogen atom, the electron moves around the one-proton nucleus on circular orbits of well-determined radii, given by rn = n2aB, where n = 1, 2, 3, ... is an integer that defines the orbit and aB = 5.29·10–11m is the radius of the first (minimum) orbit, called the Bohr radius. Calculate the force of electrostatic interaction between the electron and the proton in the hydrogen atom for the first four orbits. Compare the strength of this interaction to the gravitational interaction between the proton and the electron. Get solution
62. Some of the earliest atomic models held that the orbital velocity of an electron in an atom could be correlated with the radius of the atom. If the radius of the hydrogen atom is 5.29 · 10–11 m and the electrostatic force is responsible for the circular motion of the electron, what is the kinetic energy of this orbital electron? Get solution
63. For the atom described in Problem 21.62, what is the ratio of the gravitational force between electron and proton to the electrostatic force? How does this ratio change if the radius of the atom is doubled? Get solution
64. In general, astronomical objects are not exactly electrically neutral. Suppose the Earth and the Moon each carry a charge of –1.00·106 C (this is approximately correct; a more precise value is identified in Chapter 22).a) Compare the resulting electrostatic repulsion with the gravitational attraction between the Moon and the Earth. Look up any necessary data.b) What effects does this electrostatic force have on the size, shape, and stability of the Moon’s orbit around the Earth? Get solution
65. Eight 1.00-µC charges are arrayed along the y-axis located every 2.00 cm starting at y = 0 and extending to y = 14.0 cm. Find the force on the charge at y = 4.00 cm. Get solution
66. In a simplified Bohr model of the hydrogen atom, an electron is assumed to be traveling in a circular orbit of radius of about 5.29·10–11 m around a proton. Calculate the speed of the electron in that orbit. Get solution
67. The nucleus of a carbon-14 atom (mass = 14 amu) has diameter of 3.01 fm. It has 6 protons and a charge of +6e.a) What is the force on a proton located at 3.00 fm from the surface of this nucleus? Assume that the nucleus is a point charge.b) What is the proton’s acceleration? Get solution
68. Two charged objects experience a mutual repulsive force of 0.100 N. If the charge of one of the objects is reduced by half and the distance separating the objects is doubled, what is the new force? Get solution
69. A particle (charge = +19.0 µC) is located on the x-axis at x = –10.0 cm, and a second particle (charge = –57.0 µC) is placed on the x-axis at x = +20.0 cm. What is the magnitude of the total electrostatic force on a third particle (charge = –3.80 µC) placed at the origin (x = 0)? Get solution
70. Three point charges are positioned on the x-axis: +64.0 µC at x = 0.00 cm, +80.0 µC at x = 25.0 cm, and –160.0 µC at x = 50.0 cm. What is the magnitude of the electrostatic force acting on the +64.0–µC charge? Get solution
71. From collisions with cosmic rays and from the solar wind, the Earth has a net electric charge of approximately –6.8 · 105 C. Find the charge that must be given to a 1.0-g object for it to be electrostatically levitated close to the Earth’s surface. Get solution
72. Your sister wants to participate in the yearly science fair at her high school and asks you to suggest some exciting project. You suggest that she experiment with your recently created electron extractor to suspend her cat in the air. You tell her to buy a copper plate and bolt it to the ceiling in her room and then use your electron extractor to transfer electrons from the plate to the cat. If the cat weighs 7.00 kg and is suspended 2.00 m below the ceiling, how many electrons have to be extracted from the cat? Assume that the cat and the metal plate are point charges. Get solution
73. A 10.0-g mass is suspended 5.00 cm above a nonconducting flat plate, directly above an embedded charge of q (in coulombs). If the mass has the same charge, q, how much must q be so that the mass levitates (just floats, neither rising nor falling)? If the charge q is produced by adding electrons to the mass, by how much will the mass be changed? Get solution
75. Three 5.00-g Styrofoam balls of radius 2.00 cm are coated with carbon black to make them conducting and then are tied to 1.00-m-long threads and suspended freely from a common point. Each ball is given the same charge, q. At equilibrium, the balls form an equilateral triangle with sides of length 25.0 cm in the horizontal plane. Determine q. Get solution
77. Two beads with charges q1 = q2 = +2.67 µC are on an insulating string that hangs straight down from the ceiling as shown in the figure. The lower bead is fixed in place on the end of the string and has a mass m1 = 0.280 kg. The second bead slides without friction on the string. At a distance d = 0.360 m between the centers of the beads, the force of the Earth’s gravity on m2 is balancedby the electrostatic force between the two beads. What is the mass, m2, of the second bead? (Hint: You can neglect the gravitational interaction between the two beads.)... Get solution
76. Two point charges lie on the x-axis. If one point charge is 6.00 µC and lies at the origin and the other is –2.00 µC and lies at 20.0 cm, at what position must a third charge be placed to be in equilibrium? Get solution
78. Find the net force on a +2.00-C charge at the origin of an xy-coordinate system if there is a +5.00-C charge at (3.00 m,0.00) and a –3.00-C charge at (0.00,4.00 m). Get solution
79. Two spheres, each of mass M = 2.33 g, are attached by pieces of string of length L = 45.0 cm to a common point. The strings initially hang straight down, with the spheres just touching one another. An equal amount of charge, q, is placed on each sphere. The resulting forces on the spheres cause each string to hang at an angle of θ = 10.0° from the vertical. Determine q, the amount of charge on each sphere. Get solution
80. A point charge q1 = 100. nC is at the origin of an xy-coordinate system, a point charge q2 = –80.0 nC is on the x-axis at x = 2.00 m, and a point charge q3 = –60.0 nC is on the y-axis at y = –2.00 m. Determine the net force (magnitude and direction) on q1. Get solution
81. A positive charge q1 = 1.00 µC is fixed at the origin, and a second charge q2 = –2.00 µC is fixed at x = 10.0 cm. Where along the x-axis should a third charge be positioned so that it experiences no force?... Get solution
82. A bead with charge q1 = 1.27 µC is fixed in place at the end of a wire that makes an angle of θ = 51.3° with the horizontal. A second bead with mass m2 = 3.77 g and a charge of 6.79 µC slides without friction on the wire. What is the distance d at which the force of the Earth’s gravity on m2 is balanced by the electrostatic force between the two beads? Neglect the gravitational interaction between the two beads.... Get solution
83. In the figure, the net electrostatic force on charge QA is zero. If QA = +1.00 nC, determine the magnitude of Q0.... Get solution
84. Two balls have the same mass, 0.9680 kg, and the same charge, 29.59 µC. They hang from the ceiling on strings of identical length, l, as shown in the figure. If the angle of the strings with respect to the vertical is 29.79°, what is the length of the strings? Get solution
85. Two balls have the same mass and the same charge, 15.71 µC. Th ey hang from the ceiling on strings of identical length, l = 1.223 m, as shown in the figure. The angle of the strings with respect to the vertical is 21.07°. What is the mass of each ball? Get solution
86. Two balls have the same mass, 0.9935 kg, and the same charge. They hang from the ceiling on strings of identical length, l = 1.235 m, as shown in the figure. The angle of the strings with respect to the vertical is 22.35°. What is the charge on each ball?... Get solution
87. As shown in the figure, point charge q1 is 3.979 µC and is located at x1 = –5.689 m, and point charge q2 is 8.669 μC and is located at x2 = 14.13 m. What is the x-oordinate of the point at which the net force on a point charge of 5.000 μC will be zero?... Get solution
88. As shown in the figure, point charge q1 is 4.325 µC and is located at x1, and point charge q2 is 7.757 µC and is located at x2 = 14.33 m. The x-coordinate of the point where the net force on a point charge of –3.000 µC is zero is 2.358 m. What is the value of x1? Get solution
89. As shown in the figure, point charge q1 is 4.671 µC and is located at x1 = –3.573 m, and point charge q2 is 6.845 µC and is located at x2. The x-coordinate of the point where the net force on a point charge of –1.000 µC is zero is 4.625 m. What is the value of x2? Get solution
