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1 How could you find out which strip of tape, the one pulled off the desk or the one pulled off the back of the other tape, is positively charged ? 7 List some insulators and conductors. Answer Answer Student answers will vary, but may include dry air, wood, plastic, glass, cloth, and deionized water as insulators; and metals, tap water, and your body as conductors. Rub a piece of hard plastic with wool. The plastic is charged negatively. It will repel the negatively charged strip of tape and attract the positively charged one. 8 2 Suppose you attach a long metal rod to a plastic handle so the rod is isolated. You touch a charged glass rod to one end of the metal rod. Describe the charges on the metal rod. Answer Metals contain free electrons; rubber has bound electrons. Answer The glass rod was positively charged. This charge spreads over the entire metal rod, charging it positively. 3 In the 1730s, Stephan Gray tried to see how far electrical charge could be conducted by metal rods. He hung metal rods by thin silk cords from the ceiling. When the rods were longer than 293 feet, the silk broke. Gray replaced the silk with stronger wires made of brass, but now the experiments failed. The metal rod would no longer transmit charge from one end to the other. Why? What property makes a metal a good conductor and rubber a good insulator? 9 Why does a woolen sock taken from a clothes dryer sometimes cling to other clothes? Answer It has been charged by the tumbling of the clothes and is attracted to the other clothing. 10 If you wipe a stereo record with a clean cloth, why does the record now attract dust? Answer Answer Brass is a conductor. The electric charge flowed into the ceiling instead of along the metal rod. 4 Suppose there was a third type of charge. What experiments could you suggest to explore its properties? Rubbing the record charges it. Neutral particles such as dust are attracted to a charged object. 11 How does the charge of an electron differ from the charge of a proton? Answer Answer If the new type is different from the other two types, then it should repel (or attract) both positively and negatively charged objects. 5 6 If you comb your hair on a dry day, the comb can become positively charged. Can your hair remain neutral? Explain. The charge of the proton is exactly the same size as the electron, but has the opposite sign. 12 If you scuff electrons from your feet while walking across a rug, are you now negatively charged or positively charged? Answer Answer No. By conservation of charge, your hair must become negatively charged. When you lose electrons, you become positively charged. The combined charge of all electrons in a nickel coin is hundreds of thousands of coulombs, a unit of electrical charge. Does that imply anything about the net charge on the coin? Explain. Answer No. Net charge is the difference between positive and negative charges. It can still be zero. 13 Using a charged rod and an electroscope, how can you find if an object is a conductor? Answer Use a known insulator to hold one end of the object against the electroscope. Touch the other end with the charged rod. If the electroscope indicates a charge, the object is a conductor. 14 Explain why an insulator that is charged can be discharged by passing it above a flame. 20 Answer Salt water drips slowly from a narrow dropper inside a negatively-charged metal ring, as seen in the figure. (a) Will the drops be charged? (b) If they are charged, are they positive or negative? The hot gases above the flame are a plasma, which acts as a conductor and pulls excess charges away from the insulator. 15 A charged rod is brought near a pile of tiny plastic spheres. Some of the spheres are attracted to the rod, but as soon as they touch the rod, they fly away in different directions. Explain . Answer The neutral spheres are initially attracted to the charged rod and all acquire the same charge as the rod when they touch it. subsequently, they are repelled from each other and from the rod. Answer (a) yes (b) The drops will be positive by induction. 16 A rod-shaped insulator is suspended so it can rotate. A negatively-charged comb held nearby attracts the rod. (a) Does this mean the rod is positively charged? Explain. (b) If the comb repelled the rod, what could you conclude, if anything, about the charge on the rod? 21 When a rubber rod is rubbed with wool, the rod becomes negatively charged. What can you conclude about the magnitude of the wool's charge after the rubbing process? Why? Answer Answer (a) No. Neutral objects are attracted by either charge. (b) It must be negative. Neutrals are never repelled . 17 Explain why a balloon that has been rubbed on a wool shirt sticks to the wall . magnitude of wool's charge equals magnitude of rod's charge; charge is conserved 22 Answer The balloon becomes charged by rubbing. It is attracted to the neutral wall because it separates the charges in the wall. If you stick a piece of transparent tape on your desk and then quickly pull it off, you will find that the tape is attracted to other areas of your desk that are not charged. Why does this happen? Answer The tape induces a surface charge on the desk, so the two are attracted to one another. 18 Name three methods to charge an object. Answer 23 conduction, friction, induction 19 The text describes Coulomb's method for obtaining two charged spheres, A and B, so that the charge on B was exactly half the charge on A. Suggest a way Coulomb could have placed a charge on sphere B that was exactly one third the charge on sphere A. Metals such as copper and silver can become charged by induction while plastic materials cannot. Explain why. Answer Because plastic, an insulator, does not easily conduct charge 24 Why is an electrostatic spray gun more efficient than an ordinary spray gun? Answer Answer More paint hits the object being painted due to an electrical attraction between the charged droplets and the oppositely charged object. After charging spheres A and B equally, sphere B is touched to two other equally sized balls that are touching each other. The charge on B will be divided equally among all three balls, leaving 1/3 the total charge on it. 25 How are conductors different from insulators? Answer Conductors transfer charge easily; insulators do not. 26 27 When a conductor is charged by induction, is the induced surface charge on the conductor the same or opposite the charge of the object inducing the surface charge? 32 Answer Answer opposite repulsion, because attraction can be the result of an induced surface charge, but repulsion only occurs when two objects each have a net charge Which activity does not produce the same results as the other three? (a) sliding over a plastic-covered automobile seat (b) walking across a woolen carpet (c) scraping food from a metal bowl with a metal spoon (d) brushing dry hair with a plastic comb 33 c the signs of the charges 34 If a suspended object is attracted to another object that is charged, can you conclude that the suspended object is charged? Answer No; if a charged object induces a surface charge on the suspended object, the two are attracted, but the suspended object has no net charge. 29 What determines the direction of the electric force between two charges? Answer Answer 28 Which effect proves more conclusively that an object is charged, attraction to or repulsion from another object? Explain. A metal can is placed on a wooden table. If a positively charged ball suspended by a thread is brought close to the can, the ball will swing toward the can, make contact, then move away. (a) Explain why this happens and predict whether the ball is likely to make contact a second time. (b) Sketch diagrams showing the charges on the ball and on the can at each phase. (c) How can you test whether your explanation is correct? (d) If your teacher approves of your plan, try testing your explanation. Answer The ball induces an opposite charge, some of which is transferred upon contact, repelling the ball. Student plans should include methods for measuring charge polarity. Explain from an atomic viewpoint why charge is usually transferred by electrons. Answer Protons are relatively fixed in the nucleus, whereas electrons can be transferred from one atom to another. 30 35 The figure shows five pairs of plates: A, B, and D are charged plastic plates and C is an electrically neutral copper plate. The electrostatic forces between the pairs of plates are shown for three of the pairs. For the remaining two pairs, do the plates repel or attract each other? Because of a higher moisture content, air is a better conductor of charge in the summer than in the winter. Would you expect the shocks from static electricity to be more severe in summer or winter? Explain your answer. Answer winter, because more charge can accumulate before electric discharge occurs Answer 31 A balloon is negatively charged by rubbing and then clings to a wall. Does this mean that the wall is positively charged? Answer No; the balloon clings because its charge induces a surface charge or the wall. C and D attract; B and D attract 36 A positively charged ball is brought close to an electrically neutral isolated conductor. The conductor is then grounded while the ball is kept close. Is the conductor charged positively, charged negatively, or neutral if (a) Is the conductor charged positively, charged negatively, or neutral if the ball is first taken away and then the ground connection is removed? (b) Is the conductor charged positively, charged negatively, or neutral if the ground connection is first removed and then the ball is taken away? 43 Answer 4.8 x 10-6 C 44 Answer (a) neutral; (b) negatively 37 Calculate the net charge on a substance consisting of a combination of 7.0 x 1013 protons and 4.0 x 1013 electrons. The figure shows three pairs of identical spheres that are to be touched together and then separated. The initial charges on them are indicated. (a) Rank the pairs according to the magnitude of the charge transferred during touching. (b) Rank the pairs according to the charge left on the positively charged sphere, greatest first. Explain how to charge a conductor negatively if you have only a positively-charged rod. Answer Answer Without touching the conductor, bring it close to, but not touching, the rod. Momentarily touch the side of the conductor farthest from the rod. The conductor will be charged by induction. 38 How many excess electrons are on a ball with a charge of -4.00 x 10-17 C? Answer 250 electrons 39 A strong lightning bolt transfers about 25 C to Earth. How many electrons are transferred? Answer (a) 3, 1, 2; (b) all tie 45 In figure a, two identical, electrically isolated conducting spheres A and B are separated by a (center-to-center) distance a that is large compared to the spheres. Sphere A has a positive charge of +Q, and sphere B is electrically neutral. Initially, there is no electrostatic force between the spheres. (Assume that there is no induced charge on the spheres because of their large separation.) (a) Suppose the spheres are connected for a moment by a conducting wire. The wire is thin enough so that any net charge on it is negligible. What is the electrostatic force between the spheres after the wire is removed? (b) Next, suppose sphere A is grounded momentarily, and then the ground connection is removed. What now is the electrostatic force between the spheres? 1.6 x 1020 electrons 40 How many electrons would be required to have a total charge of 1.00 C on a sphere? Answer 6.25 x 1018 electrons 41 A typical lightning bolt has about 10.0 C of charge. How many excess electrons are in a typical lightning bolt? The charge of an electron is 1.6 x 10-19 C Answer 6.25 x 1019 electrons 42 A negatively charged balloon has 3.5 µC of charge. How many excess electrons are on this balloon? Answer 2.2 x 1013 electrons Answer 46 Benjamin Franklin once wrote that he had "erected an iron rod to draw the lightning down into my house, in order to make some experiment on it, with two bells to give notice when the rod should be electrify'd...." The chime had two small bells mounted side by side. One bell was connected to the iron rod for a charge; the other bell was attached to Earth. Between the two bells, a small metal ball was suspended on a silk thread so it could swing back and forth, striking the two bells. Explain why, when the one bell was charged, the ball would keep swinging, hitting first one bell then the other. 52 Answer -9.7 x 10-6C 53 Answer (The metal ball is neutral initially. It is attracted toward the charged bell. When it hits, it becomes charged. The ball is now repelled. It is now attracted to the uncharged bell. It hits this bell, becomes discharged, and starts up the process again. Two positive charges of 6.0 x 10-6 C are separated by 0.50 m. What force exists between the charges? Answer 1.296 N 54 47 A charge of 4.0 x 10-5 C is attracted by a second charge with a force of 350 N when the separation is 10.0 cm. Calculate the size of the second charge. Lightning usually occurs when a negative charge in a cloud is transported to Earth. If Earth is neutral, what provides the attractive force that pulls the electrons toward Earth? A negative charge of -2.0 x 10-4 C and a positive charge of 8.0 x 10-4 C are separated by 0.30 m. What is the force between the two charges? Answer Answer (The charge in the cloud repels electrons on Earth, causing a charge separation by induction. The side of Earth closest to the cloud is positive, resulting in an attractive force. 48 -1.6 x 104N 55 Explain what happens to the leaves of a positively-charged electroscope when rods with the following charges are nearby but not touching the electroscope. (a) positive (b) negative Answer Answer 3.0 x 10-6C 56 (a) The leaves will move farther apart. (b) The leaves will droop slightly. 49 A negative charge of -6.0 x 10-6 C exerts an attractive force of 65 N on a second charge 0.050 m away. What is the magnitude of the second charge? Object A has a charge + 1.8 x 10-6 C. Object B has a charge -1.0 x 10-6 C. They are 0.014 m apart. (a) What is the force on A? (b) What is the force on B? Answer If two identical charges, 1.000 C each, are separated by a distance of 1.00 km, what is the force between them? 83 N toward A; 83 N toward B Answer +9.0 x 103 N 50 57 Two point charges are separated by 10.0 cm. If one charge is +20.00 mC and the other is -6.00 mC, what is the force between them? A positive and a negative charge, each of magnitude 1.5 x 10-5 C, are separated by a distance of 15 cm. Find the force on each of the particles. Answer 90 N, toward the other charge Answer -1.1 x 108 N; the force is attractive. 51 Two identical point charges are 3.00 cm apart. Find the charge on each of them if the force of repulsion is 4.00 x 10-7N 58 Two negatively-charged bodies with -5.0 x 10-5 C are 0.20 m from each other. What force acts on each particle? Answer 5.6 x 102 N Answer +2.0 + 10-10C 59 A force of -4.4 x 103 N exists between a positive charge of 8.0 x 10 -4 C and a negative charge of -3.0 x 10-4 C. What distance separates the charges? 66 Answer 0.70 m 60 A small cork with an excess charge of +6 µC (1µ C = 10-6 C) is placed 0.12 m from another cork, which carries a charge of -4.3 µC. (a) What is the magnitude of the electric force between the corks? (b) Is theis force atractive or repulsive (c) How man excessive electrons are on te negative cork? (d) How many electrons has the postive cork lost? Answer Two identical positive charges exert a repulsive force of 6.4 x 10-9 N when separated by a distance of 3.8 x 10-10 m. Calculate the charge of each. (a) 16 N (b) attractive (c) 2.7 x 1013 electrons (d) 3.8 x 1013 electrons Answer 3.2 x 10-19C 67 61 What is the force between two equal positive charges of 2.0 x 10-4 C that are 2.0 m apart? Two electrostatic point charges of +60 µC and +50.0 µC exert a repulsive force on each other of 175 N. What is the distance between the two charges? Answer Answer 39.3 cm 89.9 N 68 62 Find the force between a positive charge of 1.0 microcoulombs and a positive charge of 2.0 microcoulombs when they are 0.030 m apart? (1 microcoulomb = 1 x 10-6 coulombs) Answer Answer 20 N 63 64 Two positive charges of 6.0 x 10-6 C are separated by 0.50 m. What force exists between the charges 3.2 x 10-8 C 69 Answer What must be the distance between point charge q1 = 26.0 µC and point charge q2 = -47 µC for the electrostatic force between them to have a magnitude of 5.70 N? 1.3 N Answer A negative charge of -2.0 x 10-4 C and a positive charge of 8.0 x 10-4 C are separated by 0.30 m. What is the force between the two charges? 1.39 m 70 Answer -15,964 N 65 Kalyan Ramji Sain, of India, had a mustache that measured 3.39 m from end to end in 1993. Suppose two charges, q and 3q, are placed 3.39 m apart. If the magnitude of the electric force between the charges is 2.4 x 10-6 N, what is the value of q? Two electrons in an atom are separated by 1.5 x 10-10 m, the typical size of an atom. What is the force between them? Answer The charges on the large metal sphere are repelled and move away from the small sphere, reducing the force. Answer 1.0 x 10-8 N Suppose you are testing Coulomb's law using a small, charged plastic sphere and a large, charged metal sphere. Both are charged positively. According to Coulomb's law, the force depends on 1/d2, where d is the distance between the centers of the spheres. As the two spheres get close together, the force is smaller than expected from Coulomb's law. Explain. 71 Two charges, q1, and q2, are separated by a distance, d, and exert a force on each other. What new force will exist if d is doubled? Answer F/4 72 73 Two identical point charges are separated by a distance of 3.0 cm and they repel each other with a force of 4.0 x 10-5 N. What is the new force if the distance between the point charges is doubled? 78 At the point of fission, a nucleus of 235U with 92 protons is divided into two smaller spheres, each with 46 protons and a radius of 5.9 x 10-15 m. What is the repulsive force pushing these two spheres apart? Answer Answer 1.0 x10-5 N 3.5 x 103 N An electric force of 2.5 x 10-4 N acts between two small equally-charged spheres which are 2.0 cm apart. Calculate the force acting between the spheres if the charge on one of the spheres is doubled and the spheres move to a 5.0-cm separation. 79 Suppose you separate the electrons and protons in 1.01 g of hydrogen and place the protons at Earth's North Pole and the electrons at Earth's South Pole. What is the magnitude of the electric force compressing Earth? The number of atoms in 1.01 g of hydrogen is 6.02 x 1023 atoms. Earth's diameter is 1.27 x 107 m. Answer Answer 7.9 x 10-5 N 5.17 x 105 N 74 Two charged bodies exert a force on each other of 16 millinewtons. What will be the force between the same two bodies if the distance between them is halved? 80 Answer 64 millinewtons or .064 newtons 75 In 1990, a French team flew a kite that was 1,034 m long. Imagine two charges, +2.0 nC and -2.8 nC, at opposite ends of the kite. (a) Calculate the magnitude of the electric force between them. b) If the separation of charges is doubled, what absolute value of equal and opposite charges would exert the same electric force? Answer A small sphere is given a charge of 20 microcoulombs and a second sphere of equal diameter located 10 cm away is given a charge of -5.0 microcoulombs. (a) What is the force of attraction between the charges? (b) The two spheres are now allowed to touch and again spaced 10 cm apart. What force now exists between them? (a) 4.7 x 10-14 N (b) 2.88 x 10-9 C 81 Answer (a) -89.87 N (b) 50.55 N What is the magnitude of the electrostatic force between a singly charged sodium ion (Nal, of charge +e) and an adjacent singly charged chlorine ion (Cl-, of charge -e) in a salt crystal if their separation is 2.82 x 10-10 m? Answer 76 The electric force between a negatively charged paint droplet and a positively charged automobile body is increased by a factor of two, but the charges on each remain constant. How has the distance between the two changed? (Assume that the charge on the automobile is located at a single point.) Answer 2.89 x 10-9 N 82 In the figure, particle 1 of charge +4e is above a floor by distance d1 = 2.00 mm and particle 2 of charge +6e is on the floor, at distance d2 = 6.00 mm horizontally from partcle 1. What is the x component of the electrostatic force on particle 2 due to particle 1? New distance = 1/√2 77 Answer the following questions: (a) How does the electric force between two charges change when the distance between them is doubled? (b) How does it change when the distance is halved? Answer (a) The force becomes 1/4 the initial value; (b) the force becomes 4 times the initial value. Answer +16e 83 Coulomb's law and Newton's Law of Universal Gravitation appear similar. In what ways are the electrical and gravitational forces similar? How are they different? 88 Answer Similar: inverse-square dependence on distance, force proportional to product of two masses or two charges. Different: only one sign of mass, so gravitational force is always attractive, while there are two signs of charge, so electrical force is either attractive or repulsive. 84 Two 10-10 kg meteorites are traveling in deep space 1000 km apart. Each has 1.00 C of positive charge. (a) Will their trajectories converge or diverge? (b) How would your answer change if the meteorites had greater masses? (c) What if they had greater charges? Answer The meteorites will diverge less with greater mass and more with greater charge. Coulombs Law and the Universal gravitational Law are very similar. (a) Calculate the repulsive Coulomb force between two protons of mass 1.67 x 0-24 g that are 4 x 10-15 m apart inside a nucleus. (b) Calculate the gravitational force of attraction between the two protons. (c) Why doesn't a force of such magnitude, acting on a proton cause the nucleus to fly apart? 89 Answer 90 Earth's mass is about 6.0 x 1024 kg, while the moon's mass is 7.3 x 1022 kg. What equal charges must be placed on Earth and the moon to make the net force between them zero? Answer 5.7 x 1013 C (a) 14.4 N (b) 1.17 x 10-35 N (c) How far apart must two protons be if the magnitude of the electrostatic force acting on either one due to the other is equal to the magnitude of the gravitational force on a proton at Earth's surface? Answer 85 The electron and proton of a hydrogen atom are separated on average by a distance of about 5.3 x 10-11 m. Find the magnitudes of the electric force and the gravitational force that each particle exerts on the other. 11.9 cm 91 Answer Felectric = -8.2 x 10-8 N Fg = 3.6 x 10-49 N 86 Answer the following questions: (a) What are some similarities between the electric force and the gravitational force? (b) What are some differences between the two? Answer (a) 5.7 x 1013 C; (b) cancels out; (c) 6.0 x 105 kg Answer both are field forces, both are inverse square laws; electric forces are attractive or repulsive while gravitational forces are always attractive, electric force is significantly stronger than gravitational force 87 Answer the following questions. (a) What equal positive charges would have to be placed on Earth and on the Moon to neutralize their gravitational attraction? (b) Why don't you need to know the lunar distance to solve this problem? (c) How many kilograms of hydrogen ions (that is, protons) would be needed to provide the positive charge calculated in (a)? 92 The moon (m = 7.36 x 1022 kg) is bound to Earth (m = 5.98 x 1024 kg) by gravity. The moon is 3.82 x 108 m from the earth. If, instead, the force of attraction were the result of each having a charge of the same magnitude but opposite in sign, find the quantity of charge that would have to be placed on each to produce the required force. The nucleus in an iron atom has a radius of about 4.0 x 10-15 m and contains 26 protons. (a) What is the magnitude of the repulsive electrostatic force between two of the protons that are separated by 4.0 x 10-15 m? (b) What is the magnitude of the gravitational force between those same two protons? Answer (a) 14.38 N (b) 1.17 x 10-39 N Answer 5.72 x 1013 C 93 A positive charge of 3.0 x 10-6 C is pulled on by two negative charges. One, -2.0 x 10-5 C, is 0.050 m to the north and the other, -4.0 x 10-6 C, is 0.030 m to the south. What total force is exerted on the positive charge? Answer 96 N, North 94 Three particles are placed in a line. The left particle has a charge of -67 x 10-6 C, the middle, +45 x 10-6C,and the right, -83 x 10-6 C. The middle particle is 72 cm from each of the others. (a) Find the net force on the middle particle. (b) Find the net force on the right particle. 99 In 1994, a group of British and Canadian athletes performed a rope slide off the top of Mount Gibraltar, in Canada. The speed of the sliders at times exceeded 160 km/h. The total length of the slide was 1,747 m. Suppose several sliders are located on the rope as shown. Due to friction, they acquire the electric charges shown. Find the magnitude and direction of the resultant electric force acting on the athlete at the far right of the diagram. Answer (a) 12.5 N, right (b) 40.7 N, left 95 A charge Q1 = +10 x 10-9 C on the x axis at x = 0, and a second charge Q2 = +3 x 10-9 C is on the x axis at x = 5 m. A third charge Q3 = -10 x 10-9 C is placed on the x axis at x = 15 m. Calculate the magnitude and direction of the force on Q2. Answer 13.7 x 10-9 N toward the right 96 Three charges, each of +80 x 10-6 C, are equally spaced along a straight line, successive charges being 6 m apart. (a) Calculate the force on one of the end charges. (b) Calculate the force on the central charge. Answer 3.2 x 10-13 N, up the rope 100 Answer (a) 2.00 N away from the center (b) 0 newtons on the center charge. 97 Three charges are located on the x-axis. A 5.0 µC charge is located at x = 0. 0 cm, a 1. 5 µC charge is located at x = 3.0 cm, and a -3.0 µC charge is located at x = 5.0 cm. Find the resultant force on the 5.0 µC charge. Answer (a) leftward; (b) llleftward; (c) lleftward Answer 21 N, along the negative x-axis 98 In 1919 in Germany, a train of eight kites was flown 9,740 m above the ground. This distance is 892 m higher than Mount Everest. Consider the arrangement of charges located at the various heights shown below. If q1 = 2.80 mC, q2 = -6.40 mC, and q3 = 48.0 mC, find the magnitude and direction of the resultant electric force acting on q1. The figure shows two protons (symbol p) and one electron (symbol e) on an axis. (a) What is the direction of the electrostatic force on the central proton due to the electron? (b) What is the direction of the electrostatic force on the central proton due to the other proton? (c) What is the direction of the net electrostatic force on the central proton? 101 In the figure, four particles are fixed along an x axis, separated by distances d = 2.00 cm. The charges are q1 = +2e, q2 = -e, q3 = +e , and q4 = +4e, with e = 1.60 x 10-19 C. (a) In unit-vector notation, what is the net electrostatic force on particle 1 due to the other particles? (b) In unit-vector notation, what is the net electrostatic force on particle 2 due to the other particles? Answer (a) (3.52 x 10-25 N)ˆi ; (b) 0 Answer 0.189 N downward 102 The figure shows four situations in which five charged particles are evenly spaced along an axis. The charge values are indicated except for the central particle, which has the same charge in all four situations. Rank the situations according to the magnitude of the net electrostatic force on the central particle, greatest first. 106 Equal charges of +15 x 10-6 C are placed at the four corners of a square 0.3 m on a side. Calculate the magnitude and direction of the force on one of the charges. Answer 43.1 N outward along the diagonal 107 Equal masses of 15 x 106 kg are placed at the four corners of a square 3 m on a side. Calculate the magnitude and direction of the force on one of the masses. Answer 3206 N Answer 3, 1, & 2 same, 4 (zero) 103 Three particles are placed on a straight line. The left particle has a charge of +4.6 x l0-6 C, the middle particle has a charge of -2.3 x l0-6 C, and the right particle has a charge of -2.3 x l0-6 C. (a) The left particle is 12 cm from the middle particle and the right particle is 24 cm from the middle particle. Find the force on the middle particle. (b) The left particle is now moved directly above the middle particle, still 12 cm away. Find the force on the middle particle. 108 Equal charges of +8 x 10-6 C are placed at the three corners of an equilateral triangle 2 m on a side. Calculate the magnitude and direction of the force on one of the charges. Answer .249 N away from the triangle, perpendicular to the opposite base. 109 Consider three point charges at the corners of a triangle, as shown in the figure, where q1 = 6.00 x 109 C, q2 = -2.00 x 109 C, and q3 = 5.00 x 109 C. Find the magnitude and direction of the resultant force on q3. Answer Hard (a) 7.42 N when Horizontal (b) 7.2° to the left or vertical6.6 N 104 Two charges, q1, and q2, are at rest near a positive test charge, q, of 7.2 x 10-6 C. The first charge, q1, is a positive charge of 3.6 x 10-6 C, located 0.025 m away from q at 350; q2 is a negative charge of -6.6 x 10-6 C, located 0.068 m away at 1250. (a) Determine the magnitude of each of the forces acting on q. (b) Sketch a force diagram. (c) Graphically determine the resultant force acting on q. Answer Answer (a) 3.7 x 102 N,away (b) 92 N, toward (c) Refer to Problems and Solutions Manual for diagram. 105 A triangle ABC, marked out on a flat surface, has sides of the following lengths: AB = 4 m, BC = 5 m, and AC = 3 m. At the corners are the following charges: -40 x 10-6 C at A, -160 x 10-6 C at B, and +90 x 10-6 C at (C) What are the magnitude and direction of the net force on the charge at A? Answer 5.09 N, 45 degrees from AC, 135 degrees from AB 7.16 x 1027 N θ = 65.20 110 Four equal charges of 1.5,uC are placed at the corners of a square with 5.0 cm sides. (a) Find the net force on a fifth charge placed in the center of the square if the new charge is -1.5 µC (b) Find the net force on a fifth charge placed in the center of the square if the new charge is +3.0 µC Answer (a) -1.5 µC (b) +3.0 µC 111 Four charged particles are placed so that each particle is at the corner of a square. The sides of the square are 15 cm. The charge at the upper left corner is +3.0 µC, the charge at the upper right corner is -6.0 µC, the charge at the lower left corner is -2.4 µC, and the charge at the lower right corner is -9.0 µC. (a) What is the net electric force on the +3.0 µC charge? (b) What is the net electric force on the -6.0 µC charge? (c) What is the net electric force on the -9.0 µC charge? 115 Answer Answer (a) 13.0 N, 3 V below the positive x-axis (b) 25 N, 780 above the negative x-axis (c) 18 N, 750 below the positive x-axis 112 to the left 116 Three charges lie along the x-axis. One positive charge, q1 = 15 µC, is at x= 2.0 m, and another positive charge, q2 = 6.0 µC, is at the origin. At what point on the x-axis must a negative charge, q3, be placed so that the resultant force on it is zero? Answer Three charges lie along the x-axis. One positive charge, q1 = 15 µC, is at x= 2.0 m, and another positive charge, q2 = 6.0 µC, is at the origin. At what point on the x-axis must a negative charge, q3, be placed so that the resultant force on it is zero? Three positive point charges of 3.0 nC, 6.0 nC, and 2.0 nC, respectively, are arranged in a triangle, as shown in the figure below. Find the magnitude and direction of the electric force on the 6.0 nC charge. Answer p = 0.80 m from q2. 113 In which direction will the electric force from the two equal positive charges pull the negative charge shown in the figure below? 9.73 x 10-8 N 11.50 below the positive x-axis 117 In 1993, a chocolate chip cookie was baked in Arcadia, California. It contained about three million chips and was 10.7 m long and 8.7 m wide. Suppose four charges are placed in the corners of that cookie as follows: q1 = -12.0 nC at the lower left corner, q2 = 5.6 nC at the upper left corner, q3 = 2.8 nC at the upper right corner, and q4 = 8.4 nC at the lower right corner. (a) Draw a picture of the rectangular cooke (b) Find the magnitude and direction of the resultant electric force acting on q1. Answer Answer .77 m from q2 114 A +2.2 x 10-9 C charge is on the x-axis at x = 1. 5 m, a +5.4 x 10-9 C charge is on the x-axis at x = 2.0 m, and a + 3.5 x 10-9 C charge is at the origin. Find the net force on the charge at the origin. Answer 7.3 x 10-8 N along the negative x-axis (a) Picture (b) 12.7 x 10-89N 44.6 0 above the positive x-axis 118 119 In 1988, a giant firework was exploded at the Lake Toya festival, in Japan. The shell had a mass of about 700 kg and produced a fireball 1.2 km in diameter. Consider a circle with this diameter. Suppose four charges are placed on the circle's perimeter so that the lines between them form a square with sides parallel to the x- or y-axes. The charges have the following strengths and locations: q1 = 16.0 mC at the upper left "corner," q2 = 2.4 mC at the upper right corner, q3 = -3.2 mC at the lower right corner, and q4 = -4.0 mC at the lower left corner. Find the magnitude and direction of the resultant electric force acting on q1. (Hint: Find the distances between the charges first.) 123 In the figure, particle 1 of charge +1.0 μC and particle 2 of charge -3.0 μC are held at separation L = 10.0 cm on an x axis. Assume particle 3 of unknown charge q3 is to be located such that the net electrostatic force on it from particles 1 and 2 is zero. (a) What must be the x coordinates of particle 3? (b) What must be the y coordinates of particle 3? Answer Answer 1.0 N 770 below the negative x axis (a) 14 cm; (b) 0 In 1955, a water bore that was 2,231 m deep was drilled in Montana. Consider two charges, q2 = 1.60 mC and q1, separated by a distance equal to the depth of the well. If a third charge, q3 1.998 mC is placed 888 m from q2 and is between q2 and q1, this third charge will be in equilibrium. What is the value of q1? 124 In the figure, six charged particles surround particle 7 at radial distances of either d = 1.0 cm or 2d, as drawn. The charges are q1 = +2e, q2 = +4e, q3 = +e, q4 = +4e, q5 = +2e, q6 = +8e, q7 = +6e, with e = 1.60 x 10-19 C. What is the magnitude of the net electrostatic force on particle 7? Answer 366 mC 120 Hans Langseth's beard measured 5.33 m in 1927. Consider two charges, q1 = 2.5 nC and q2 = 8.0 nC, separated by the length of Langseth's beard. How far from q1 should a third charge of 1.0 nC be placed so that no force is exerted on the third charge? Answer Answer 0 1.9 m 125 121 In more than 30 years, Albert Klein, of California, drove 2.5 x 106 km in one automobile. Consider two charges, q1 = 2.0 C and q2 = 6.0 C, separated by Klein's total driving distance. A third charge, q3 = 4.0 C, is placed on the line connecting q1 and q2. How far from q1 should q3 be placed for q3 to be in equilibrium? The figure shows four identical conducting spheres that are actually well separated from one another. Sphere W (with an initial charge of zero) is touched to sphere A and then they are separated. Next, sphere W is touched to sphere B (with an initial charge of -32e) and then they are separated. Finally, sphere W is touched to sphere C (with an initial charge of +48e), and then they are separated. The final charge on sphere W is +18e. What was the initial charge on sphere A? Answer 9.3 x 108 m 122 A charge of +2.00 x 10-9C is placed at theorigin, and another charge of +4 x 10-9 C is placed at x = 1.5 m. find the point between these two charges where a charge of +3.00 x 10-9C should be paced so that the net electric force on it is zero. Answer (a) (0.829 N)ˆi ; (b) (-0.621 N)ˆj Answer x = 0.64 m 126 In the figure, three identical conducting spheres form an equilateral triangle of side length d = 20.0 cm. The sphere radii are much smaller than d, and the sphere charges are qA = -2.00 nC, qB = -4.00 nC, and qC = +8.00 nC. (a) What is the magnitude of the electrostatic force between spheres A and C? The following steps are then taken: A and B are connected by a thin wire and then disconnected; B is grounded by the wire, and the wire is then removed; B and C are connected by the wire and then disconnected. (b) What now is the magnitude of the electrostatic force between spheres A and C? (c) What now is the magnitude of the electrostatic force between spheres B and C? 128 In the figure, a central particle of charge -q is surrounded by two circular rings of charged particles. What are the magnitude and direction of the net electrostatic force on the central particle due to the other particles? (Hint: Consideration of symmetry can greatly reduce the amount of work required here.) Answer 2kq2/r2 , up the page Answer (a) 3.60 µN; (b) 2.70 µN; (c) 3.60 µN 127 The figure shows two charged particles on an axis. The charges are free to move. However, a third charged particle can be placed at a certain point such that all three particles are then in equilibrium. (a) Is that point to the left of the first two particles, to their right, or between them? (b) Should the third particle be positively or negatively charged? (c) Is the equilibrium stable or unstable? 129 In the figure, a central particle of charge -2q is surrounded by a square array of charged particles, separated by either distance d or d/2 along the perimeter of the square. What are the magnitude and direction of the net electrostatic force on the central particle due to the other particles? (Hint: Consideration of symmetry can greatly reduce the amount of work required here.) Answer (a) between; (b) positively charged; (c) unstable Answer 6kq2/d2 , leftward 24q2/d2 130 The figure shows four arrangements of charged particles. Rank the arrangements according to the magnitude of the net electrostatic force on the particle with charge +Q, greatest first. 135 Two small spheres each having a mass of 0.10 g are suspended from the same point on silk threads 20 cm long. When given equal charges, they repel each other, coming to rest 24 cm apart. Find the charge on each sphere? Answer 6.86 x 10-8 C 136 An electron is released above the Earth's surface. A second electron directly below it exerts just enough of an electric force on the first electron to cancel the gravitational force on it. Find the distance between the two electrons. Answer 5.07 m Answer a and d tie, then b and c tie 137 131 A charge q1 of -6.00 x 10-9 C and a charge q2 of -3.00 x 10-9 C are separated by a distance of 60.0 cm. Where could a third charge be placed so that the net electric force on it is zero? Answer Answer 35.2 cm from q1 (24.8 cm from q2) 132 Three point charges lie along the y-axis. A charge of q1 = -9.0 µC is at y = 6.0 m, and a charge of q2 = -8.0 µC is at y= -4.0 m. The net electric force on the third charge is zero. Where is this charge located? Two small metallic spheres, each with a mass of 0.20 g, are suspended as pendulums by light strings from a common point. They are given the same electric charge, and the two come to equilibrium when each string is at an angle of 5.00 with the vertical. If the string is 30.0 cm long, what is the magnitude of the charge on each sphere? 7.17 x 10-9 C 138 The most accurate balance can measure objects with masses as small as 1.0 x 10-11 kg, which is less than the mass of the ink in the period at the end of this sentence. Suppose a mass this small is suspended by electric repulsion over a charge of -4.0 nC. How many extra electrons must be placed on the mass so that it will float 2.0 cm directly over the -4.0 nC charge? Answer Answer y = 0.8 m from the zero point or 5.1 from one end 6.8 x 103 electrons 133 Two Ping-Pong balls painted with aluminum paint are suspended from the same point by threads 50 cm long. The mass of each ball is 20 g. When equal charges are given to the two balls, they come to rest in an equilibrium position in which their centers are 60 cm apart. Calculate the charge on each ball. 139 In 1959, Alf Dean caught a 1,208 kg white shark with a fishing rod. Consider a 1,208 kg block hung from a cable. Suppose the mass has an extra charge of 4.80 nC. By what percent would the electric force increase the tension of the cable (compared to the situation with the mass only) if an equal and opposite charge is placed 20.0 cm directly underneath the block? Answer Answer 2.42 x 10-6 C 4.7 x 10-8 percent 134 Two small spheres each having a mass of 0.050 g are suspended by silk threads from the same point. When given equal charges, they separate, the threads make an angle of 10 degrees with each other. What is the force of repulsion acting on each sphere? 140 The CN Tower, in Toronto, Canada, is 553 m tall. Suppose two balls, each with a mass of 5.00 kg and a charge of 40.0 mC, are placed at the top and bottom of the tower, respectively. The ball at the top is then dropped. At what height is the acceleration on the ball zero? Answer 4.3 x 10-5 N Answer 542 141 In 1995, a single diamond was sold for more than 16 million. It was not the largest diamond in the world, but its mass was an impressive 20.0 g. Consider such a diamond resting on a horizontal surface. It is known that if the diamond is given a charge of 2.0 µC and a charge of at least -8.0 µC is placed on that surface at a distance of 1.7 m from it, then the diamond will barely keep from sliding. Calculate the coefficient of static friction between the diamond and the surface. 146 Answer 147 Answer 0.25 142 Answer (a) 2.3 x 10-9 m/s2 (b) 2.3 x 10-28 N The parasitic wasp Carapractus cinctus has a mass of 5.0 x 10-6 kg, which makes it one of the smallest insects in the world. If two such wasps are given equal and opposite charges with an absolute value of 2.0 x 10-15 C and are placed 1.00 m from each other on a horizontal smooth surface, what extra horizontal force must be applied to each wasp to keep it from sliding? Take into account both gravitational and electric forces between the wasps. Answer 145 2.0 x 10-6 C 148 A DNA molecule (deoxyribonucleic acid) is 2.17 mm long. The ends of the molecule become singly ionized so that there is an increase of 1.00 percent upon becoming charged. Find the effective spring constant of the molecule. Answer 2.25 x 10-9 N/m An electron is in a vacuum near Earth's surface and located at y = 0 on a vertical y axis. At what value of y should a second electron be placed such that its electrostatic force on the first electron balances the gravitational force on the first electron? Two particles are fixed on anx axis. Particle 1 of charge 40 μC is located at x = -2.0 cm; particle 2 of charge Q is located at x = 3.0 cm. Particle 3 of charge magnitude 20 μC is released from rest on the y axis at y = 2.0 cm. (a) What is the value of Q if the initial acceleration of particle 3 is in the positive direction of the x axis? (b) What is the value of Q if the initial acceleration of particle 3 is in the positive direction of the y axis? Answer Answer -5.1 m (a) -83 µC; (b) l55 µC 3.77 x 10-20 N 144 Three identical point charges, each of mass m = 0.10 kg, hang from three strings, as shown in the figure below. If L = 30.0 cm. and θ = 450, what is the value of θ? Mycoplasma is the smallest living organism known. Its mass has an estimated value of 1.0 x 10-16 g. (a) If two specimens of this organism are placed 1.0 m apart and one electron is placed on each, what is their initial acceleration due to the electric force? (b) If the medium through which the Allycoplasma move exerts a resistive force on the organisms, how large must that force be to balance the force of electrostatic repulsion? Answer 143 Four objects of equal mass and equal charge are placed at the corners of a square with 4 meter sides. A charge of 12 x 10-5C are placed on each object. What is the mass of each object if the Gravitational Force on each object is equal to the electrostatic force. A small plastic sphere coated with a thin metalized surface has mass 0.05 g and carries a charge of +8 x 10-9 C. It is suspended by a light insulating thread at a point 3 cm below the center of a small fixed conducting sphere carrying -5 x 10-9 C. The thread is cut. (a) What is the electrostatic force upward? (b) What is the net force? (b) What is the observed acceleration? Answer (a) (b) 1 x10-4 N (c) 2 m/s2 downward 149 150 The figure shows an arrangement of four charged particles, with angle θ = 30.00 and distance d = 2.00 cm. Particle 2 has charge q2 = +8.00 x 10-19 C; particles 3 and 4 have charges q3 = q4 = -1.60 x 10-19 C. (a) What is distance D between the origin and particle 2 if the net electrostatic force on particle 1 due to the other particles is zero? (b) If particles 3 and 4 were moved closer to the x axis but maintained their symmetry about that axis, would the required value of D be greater than, less than, or the same as in part (a)? Answer (a) 1.92 cm; (b) less than 151 In the figure, all four particles are fixed in the xy plane, and q1 = -3.20 x 10-19 C, q2 = +3.20 x 10-19 C, q3 = +6.40 x 10 -19 C, q4 = +3.20 x 10-19 Q, θ, = 35.00, d1 = 3.00 cm, and d2 = d3= 2.00 cm. (a) What is the magnitude of the net electrostatic force on particle 4 due to the other three particles? (b) What is the direction of the net electrostatic force on particle 4 due to the other three particles? Answer (a) 6.16 x 10-24 N; (b) 2080