Chapter Assignment Solutions

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1 Chapter Assignment Solutions Table of Contents Page 558 #22, 24, 29, 31, 36, 37, 40, Lightning Worksheet (Transparency 20-4)... 4 Page 584 #42-46, 58-61, 66-69, 76-79, Chapter 20 Review Worksheet... 9 Chapter 21 Review Worksheet Page 558 #22, 24, 29, 31, 36, 37, 40, ) Complete the concept map below using the following terms: conduction, distance, elementary charge. 24) List some insulators and conductors. (20.1) Answers will vary. Some possibilities are listed below. Insulators: Dry air, wood, plastic, rubber, glass, cloth, deionized water Conductors: Metals, salt water, human bodies 29) How does the distance between two charges impact the force between them? If the distance is decreased while the charges remain the same, what happens to the force? (20.2) Electric force is inversely proportional to the distance squared. As distance decreases while charges remain the same, the force increases as the square of the distance.

2 31) How does the charge of an electron differ from the charge of a proton? How are they similar? The charge of an electron is negative, while the charge of a proton is positive. They both have the same magnitude, C. 36) As shown in Figure 20-13, Coulomb's Law and Newton's Law of Universal Gravitation appear to be similar. In what ways are the electric and gravitational forces similar? How are they different? Similar: Inverse-square dependence on distance Force proportional to product of a quantity (mass or charge) for two objects Different: Only one sign of mass, so gravitational force is always attractive Two signs of charge, so electric force can be either attractive or repulsive The constant for Coulomb's Law, K, is much greater than the universal gravitation constant, G, leading to much larger electric forces than gravitational forces for objects with a significant (non-negligible) net charge. 37) The constant, K, in Coulomb's equation is much larger than the constant, G, in the universal gravitation equation. Of what significance is this? The electric force is much larger than the gravitational force for objects that have a significant (nonnegligible) net charge. 40) Two charged bodies exert a force of N on each other. If they are moved so that they are onefourth as far apart, what force is exerted? F 1 1 r2 and F, so the force is 16 times the original force. ( 1 4 )2 F = 16(0.145 N) = 2.32 N 43) Lightning: A strong lightning bolt transfers about 25 C to Earth. How many electrons are transferred? 1 electron (25 C) ( C ) = electrons

3 44) Atoms: Two electrons in an atom are separated by m, the typical size of an atom. What is the electric force between them? F = Kq N m 1q 2 2 C r 2 = ) ( C)( C) ( m) 2 F = N, away from each other 45) A positive and a negative charge, each of magnitude C, are separated by a distance of 15 cm. Find the force on each of the particles. F = Kq N m 1q 2 2 C r 2 = ) ( C)( C) ( m) 2 F = N, towards each other 46) A force of N exists between a positive charge of C and a positive charge of C. What distance separates the charges? r = Kq 1q 2 F = F = Kq 1q 2 r 2 ( N m2 C 2 ) ( C)( C) N r = 0.30 m 47) Two identical positive charges exert a repulsive force of N when separated by a distance of m. Calculate the charge of each. F = Kq 1q 2 r 2 = Kq2 r 2 q = Fr2 K = ( N)( m) N m2 C 2 q = C

4 48) A positive charge of 3.0 μc is pulled on by two negative charges. As shown in Figure 20-14, one negative charge, 2.0 μc, is m to the west, and the other, 4.0 μc, is m to the east. What total force is exerted on the positive charge? F 1 = F 2 = N m2 C 2 ) ( C)( C) (0.050 m) 2 = 22 N west N m2 C 2 ) ( C)( C) (0.030 m) 2 = 120 N east F net = F 2 + F 1 = 120 N 22 N F net = 98 N, east Lightning Worksheet (Transparency 20-4) 1) What is the charge on the tree and ground before the cloud appears overhead? There is no net charge because the electrons and positive ions are evenly distributed. 2) How do charges tend to arrange themselves when they separate in clouds? The positive charges collect near the top of the cloud, and the negative charges collect near the bottom. 3) What causes the separation of charge in the tree and ground when the cloud moves overhead? The negative charges at the bottom of the cloud repel the negative charges in the tree and ground, leaving the surface with a net positive charge. This is induction. 4) How might a discharge occur within a single cloud? What would that do to the overall charge of the cloud? Negative charges near the bottom of a cloud might discharge toward positive regions near the top of the same cloud. The overall charge of the cloud would remain the same because no charges were transferred to or away from it. 5) How might a discharge occur between two clouds? What would that do to the overall charge of the two clouds? Negative charges near the bottom of a cloud might discharge toward positive regions near the top of a different cloud. The cloud from which the negative charges came is left with a net positive charge. The cloud to which the negative charges jumped would have a net negative charge. 6) Would it be likely that lightning would strike the same tree twice in a brief period of time? Why or why not? No. When the lightning strikes the tree the first time, it gives the tree an excess of negative charge. Until that charge can be dissipated, and/or induction from the cloud could again give the tree a positive charge, it is unlikely that a discharge would be attracted to it.

5 7) Lightning often strikes the highest object in the area. Lightning rods often are placed on top of tall buildings. What is their purpose? Lightning rods provide a safe conduit for the electricity from a lightning discharge to travel to the ground. A lightning rod has a wire running from it to a plate in the ground. Because the lightning rod is the highest point of the building, it is likely that a lightning discharge would strike it before striking the building. Having the lightning discharge travel through the lightning rod and wire to the plate in the ground is safer than having lightning randomly strike something that could easily be damaged by the heat, or having the discharge jump from object to object as it travels to the ground. 8) In what ways are lightning discharges similar to and different from the kind of shock you get when touching something metal after walking across a rug? A lightning discharge is orders of magnitude larger than the tiny discharge you feel from walking across a rug and then touching metal. However, they are produced in the same way. When you walk across the rug, you pick up negative charge, which moves over the surface of your body. When you bring a finger near a metal object, the negative charge in your finger induces a positive charge in the metal object, and a discharge occurs. Page 584 #42-46, 58-61, 66-69, 76-79, ) Complete the concept map below using the following terms: capacitance, field strength, J/C, work. 43) What are the two properties that a test charge must have? (21.1) The test charge must be small in magnitude relative to the charges producing the field, and it must be positive.

6 44) How is the direction of an electric field defined? (21.1) The direction of an electric field is the direction of the force on a positive charge placed inside the field. This is away from a positive object and towards a negative object. 45) What are electric field lines? (21.1) Lines that illustrate the force that a test charge would experience; a visual representation of the electric field. The closer the lines, the stronger the field (and resulting force). 46) How is the strength of an electric field indicated with electric field lines? (21.1) The closer together the lines are, the stronger the electric field (and resulting force on a test charge). 58) Figure shows three spheres with charges of equal magnitude, with their signs as shown. Spheres y and z are held in place, but sphere x is free to move. Initially, sphere x is equidistant from spheres y and z. Choose the path that sphere x will begin to follow. Assume that no other forces are acting on the spheres. Sphere x will initially follow path C. It will experience a force in the direction of D from sphere y, and an equal-magnitude force toward B from sphere z. The vector sum is towards C. 59) What is the unit of electric potential difference in terms of m, kg, s, and C? V = J kg m N m ( = C C = s 2 ) m = C kg m2 s 2 C 60) What do the electric field lines look like when the electric field has the same strength at all points in a region? They are parallel, equally spaced lines. 61) Millikan Oil-Drop Experiment: When doing a Millikan oil-drop experiment, it is best to work with drops that have small charges. Therefore, when the electric field is turned on, should you try to find drops that are moving rapidly or slowly? Explain. Slowly. The larger the charge, the stronger the force, and thus, the larger the (terminal) velocity. 66) What charge exists on a test charge that experiences a force of N at a point where the electric field intensity is N/C? E = F q q = F E = N N/C = C

7 67) A positive charge of C, shown in Figure 21-19, experiences a force of 0.30 N when it is located at a certain point. What is the electric field intensity at that point? E = F q = N/C in the same direction as the force 0.30 N C = N/C 68) A test charge experiences a force of 0.30 N on it when it is placed in an electric field intensity of N/C. What is the magnitude of the charge? E = F q q = F E = 0.30 N N/C = C 69) The electric field in the atmosphere is about 150 N/C downward. a) What is the direction of the force on a negatively charged particle? upward b) Find the electric force on an electron with charge C. E = F E q F E = qe = ( C)(150 N/C) = N N, upward c) Compare the force in part b with the force of gravity on the same electron (mass = kg). F g = mg = ( kg)(9.8 N/kg) = N N downward, more than one trillion times smaller than the magnitude of the electric force 76) If 120 J of work is performed to move 2.4 C of charge from the positive plate to the negative plate shown in Figure 21-21, what potential difference exists between the plates? ΔV = W q = 120 J 2.4 C = 50. V 77) How much work is done to transfer 0.15 C of charge through an electric potential difference of 9.0 V? ΔV = W q W = qδv = (0.15 C)(9.0 V) = 1.4 J

8 78) An electron is moved through an electric potential difference of 450 V. How much work is done on the electron? ΔV = W q W = qδv = ( C)(450 V) = J 79) A 12-V battery does 1200 J of work transferring charge. How much charge is transferred? ΔV = W q q = W ΔV = 1200 J 12 V = C 84) The oil drop shown in Figure is negatively charged and weighs N. The drop is suspended in an electric field intensity of N/C. 1) What is the charge on the drop? E = F q q = F E = N N/C = C 2) How many excess electrons does it carry? ( electron C) ( C ) = 5 electrons 85) What is the charge on a 15.0-pF capacitor when it is connected across a 45.0-V source? C = q ΔV q = CΔV = ( F)(45.0 V) = C 86) A force of N is required to move a charge of 37 μc a distance of 25 cm in a uniform electric field, as in Figure What is the size of the electric potential difference between the two points? ΔV = W q = FΔx q = (0.065 N)(0.25 m) C = V

9 Chapter 20 Review Worksheet Vocabulary Review 1) An object is said to be neutral if all positive charges in the object are balanced by a negative charge, leaving no net charge. 2) Coulomb s Law states that the magnitude of the force between two charges is inversely proportional to the square of the distance between them. 3) Applying a charge by touching a charged object to a neutral object is conduction. 4) Electrostatics is the study of electric charges that are not moving. 5) The Coulomb is the SI unit of charge. 6) An electric conductor allows charge to easily move through it. 7) Separating the charges in an object without touching it is called induction. 8) Materials through which electric charges do not easily move are electrical insulators. Multiple Choice 9) Coulomb s constant, K, measured in N m 2 /C 2, is equal to c. 9.0x ) The charge on an electron, measured in C, is equal to a. 1.60x ) The force F E, between two charges, with the square of the distance between the centers of the two charged objects. b. varies indirectly (means the same as varies inversely) 12) Objects with the charge attract each other b. opposite Free Response 13) What is the repulsive force between two electrons that are 1.0x10-10 m apart? F E = Kq N m 1q 2 2 C r 2 = ) ( C)( C) ( m) 2 F E = N 14) What is the force between a charge of +2.1 µc and a charge of -3.7 µc that are 6.4 cm apart? Is it an attractive force or a repulsive force? F E = Kq N m 1q 2 2 C r 2 = ) ( C)( C) ( m) 2

10 F E = 17 N, attractive 15) A 52 µc blue sphere experiences a 2.9x10-4 N force towards a maize sphere that is 2.7 cm away. What is the charge of the maize sphere? F E = Kq 1q 2 r 2 q 2 = F Er 2 Kq 1 = ( N)( m) 2 ( N m2 C 2 ) ( C) q 2 = C 16) How far apart must a 12 µc charge and a 7.2 µc charge be if the force between them is 1.0 mn? F E = Kq 1q 2 r 2 r = Kq N m 1q = (9.0 ) (12 C C)( C) F E N r = 28 m Chapter 21 Review Worksheet Vocabulary Review 1) Capacitance is the ratio of an object s stored charge to its electric potential difference, measured in Farads. 2) One Joule per Coulomb is equal to one Volt. 3) The lines providing a picture of the size and strength of the field around a charged object are called electric field lines. 4) When the electric potential between two or more points is zero, they are said to be at equipotential. 5) The work done moving a test charge between two points in an electric field divided by the magnitude of the test charge is equal to the electric potential difference. 6) A capacitor stores charge and has a constant capacitance. 7) The electric field intensity is a vector quantity that relates the force exerted on a charge to the size of a charge. 8) Electric field lines are pointed towards negative charges and away from positive charges. 9) A Farad is equal to a Coulomb per Volt.

11 Multiple Choice 10) Only electric potential can be measured. c. differences in 11) As an electric field becomes stronger, the field lines should be drawn. a. closer together 12) The magnitude of the force on a charge in an electric field depends on. d. both the size of the charge and the magnitude of the field Free Response 13) A negative charge of 0.14 µc experiences a force of 1.2 N east. What is the magnitude and direction of the electric field at this location? E = F E q = 1.2 N east C E = N C west 14) What charge would experience a 1.2 mn force when in a uniform electric field of 4.4x10 6 N/C? E = F E q q = F E E = N N/C = C 15) Two plates of a capacitor are 12 cm apart and have an electric field of 350 N/C. What is the electric potential difference between the plates? ΔV = E Δx = (350 N/C)(0.12 m) = 42 V 16) How much work is done in moving a positive charge of 5.1 µc from the negative plate to the positive plate of the capacitor in problem 15? ΔV = W q W = qδv = ( C)(42 V) = J 17) What is the capacitance of a sphere that is charged to 2.2 µc and has an electric potential difference of 240 V? C = q ΔV = C = F 240 V