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Chapter 18 Conceptual Questions 795 18.3 Coulomb’s Law 15. Figure 18.44 shows an electric field extending over three...

Chapter 18 Conceptual Questions 795 18.3 Coulomb’s Law 15. Figure 18.44 shows an electric field extending over three regions, labeled I, II, and III. Answer the following 9. Figure 18.43 shows the charge distribution in a water questions. (a) Are there any isolated charges? If so, in molecule, which is called a polar molecule because it has what region and what are their signs? (b) Where is the an inherent separation of charge. Given water’s polar field strongest? (c) Where is it weakest? (d) Where is the character, explain what effect humidity has on removing field the most uniform? excess charge from objects. Figure 18.44 Figure 18.43 Schematic representation of the outer electron cloud of a neutral water molecule. The electrons spend more time near the oxygen than the hydrogens, giving a permanent 18.6 Electric Forces in Biology charge separation as shown. Water is thus a polar molecule. It 16. A cell membrane is a thin layer enveloping a cell. The is more easily affected by electrostatic forces than molecules thickness of the membrane is much less than the size of with uniform charge distributions. the cell. In a static situation the membrane has a charge distribution of C/m 2 on its inner surface 10. Using Figure 18.43, explain, in terms of Coulomb’s law, and 2 C/m on its outer surface. Draw a why a polar molecule (such as in Figure 18.43) is diagram of the cell and the surrounding cell membrane. attracted by both positive and negative charges. Include on this diagram the charge distribution and the 11. Given the polar character of water molecules, explain corresponding electric field. Is there any electric field how ions in the air form nucleation centers for rain inside the cell? Is there any electric field outside the cell? droplets. 18.7 Conductors and Electric Fields 18.4 Electric Field: Concept of a in Static Equilibrium Field Revisited 17. Is the object in Figure 18.45 a conductor or an insulator? 12. Why must the test charge in the definition of the Justify your answer. electric field be vanishingly small? 13. Are the direction and magnitude of the Coulomb force unique at a given point in space? What about the electric field? 18.5 Electric Field Lines: Multiple Charges 14. Compare and contrast the Coulomb force field and the electric field. To do this, make a list of five properties for the Coulomb force field analogous to the five properties listed for electric field lines. Compare each item in your list of Coulomb force field properties with those of the Figure 18.45 electric field—are they the same or different? (For 18. If the electric field lines in the figure above were example, electric field lines cannot cross. Is the same perpendicular to the object, would it necessarily be a true for Coulomb field lines?) conductor? Explain. 796 Chapter 18 Problems & Exercises 19. The discussion of the electric field between two parallel corners of a square and is located at its center. conducting plates, in this module states that edge 26. (a) Using the symmetry of the arrangement, show that effects are less important if the plates are close together. the electric field at the center of the square in Figure What does close mean? That is, is the actual plate 18.46 is zero if the charges on the four corners are separation crucial, or is the ratio of plate separation to exactly equal. (b) Show that this is also true for any plate area crucial? combination of charges in which and 20. Would the self-created electric field at the end of a 27. (a) What is the direction of the total Coulomb force on pointed conductor, such as a lightning rod, remove in Figure 18.46 if is negative, and both are positive or negative charge from the conductor? Would negative, and and both are positive? (b) What is the same sign charge be removed from a neutral the direction of the electric field at the center of the pointed conductor by the application of a similar square in this situation? externally created electric field? (The answers to both 28. Considering Figure 18.46, suppose that and questions have implications for charge transfer utilizing. First show that is in static equilibrium. (You points.) may neglect the gravitational force.) Then discuss 21. Why is a golfer with a metal club over her shoulder whether the equilibrium is stable or unstable, noting vulnerable to lightning in an open fairway? Would she be that this may depend on the signs of the charges and the any safer under a tree? direction of displacement of from the center of the 22. Can the belt of a Van de Graaff accelerator be a square. conductor? Explain. 29. If in Figure 18.46, under what conditions will 23. Are you relatively safe from lightning inside an there be no net Coulomb force on ? automobile? Give two reasons. 30. In regions of low humidity, one develops a special “grip” 24. Discuss pros and cons of a lightning rod being when opening car doors, or touching metal door knobs. grounded versus simply being attached to a building. This involves placing as much of the hand on the device 25. Using the symmetry of the arrangement, show that the as possible, not just the ends of one’s fingers. Discuss net Coulomb force on the charge at the center of the the induced charge and explain why this is done. square below (Figure 18.46) is zero if the charges on the 31. Tollbooth stations on roadways and bridges usually have four corners are exactly equal. a piece of wire stuck in the pavement before them that will touch a car as it approaches. Why is this done? 32. Suppose a woman carries an excess charge. To maintain her charged status can she be standing on ground wearing just any pair of shoes? How would you discharge her? What are the consequences if she simply walks away? Figure 18.46 Four point charges , , , and lie on the PROBLEMS & EXERCISES 18.1 Static Electricity and Charge: 3. To start a car engine, the car battery moves Conservation of Charge electrons through the starter motor. How many coulombs of charge were moved? 1. Common static electricity involves charges ranging from 4. A certain lightning bolt moves 40.0 C of charge. How nanocoulombs to microcoulombs. (a) How many many fundamental units of charge is this? electrons are needed to form a charge of (b) How many electrons must be removed from a neutral 18.2 Conductors and Insulators object to leave a net charge of ? 5. Suppose a speck of dust in an electrostatic precipitator 2. If electrons move through a pocket has protons in it and has a net charge of calculator during a full day’s operation, how many –5.00 nC (a very large charge for a small speck). How coulombs of charge moved through it? many electrons does it have? Access for free at openstax.org.  Chapter 18 Problems & Exercises 797 6. An amoeba has protons and a net charge of 18. (a) By what factor must you change the distance between 0.300 pC. (a) How many fewer electrons are there than two point charges to change the force between them by a protons? (b) If you paired them up, what fraction of the factor of 10? (b) Explain how the distance can either protons would have no electrons? increase or decrease by this factor and still cause a factor 7. A 50.0 g ball of copper has a net charge of. What of 10 change in the force. fraction of the copper’s electrons has been removed? 19. Suppose you have a total charge that you can split in (Each copper atom has 29 protons, and copper has an any manner. Once split, the separation distance is fixed. atomic mass of 63.5.) How do you split the charge to achieve the greatest 8. What net charge would you place on a 100 g piece of force? sulfur if you put an extra electron on 1 in of its 20. (a) Common transparent tape becomes charged when atoms? (Sulfur has an atomic mass of 32.1.) pulled from a dispenser. If one piece is placed above 9. How many coulombs of positive charge are there in 4.00 another, the repulsive force can be great enough to kg of plutonium, given its atomic mass is 244 and that support the top piece’s weight. Assuming equal point each plutonium atom has 94 protons? charges (only an approximation), calculate the magnitude of the charge if electrostatic force is great 18.3 Coulomb’s Law enough to support the weight of a 10.0 mg piece of tape 10. What is the repulsive force between two pith balls that held 1.00 cm above another. (b) Discuss whether the are 8.00 cm apart and have equal charges of – 30.0 nC? magnitude of this charge is consistent with what is 11. (a) How strong is the attractive force between a glass rod typical of static electricity. with a charge and a silk cloth with a 21. (a) Find the ratio of the electrostatic to gravitational charge, which are 12.0 cm apart, using the force between two electrons. (b) What is this ratio for approximation that they act like point charges? (b) two protons? (c) Why is the ratio different for electrons Discuss how the answer to this problem might be and protons? affected if the charges are distributed over some area 22. At what distance is the electrostatic force between two and do not act like point charges. protons equal to the weight of one proton? 12. Two point charges exert a 5.00 N force on each other. 23. A certain five cent coin contains 5.00 g of nickel. What What will the force become if the distance between them fraction of the nickel atoms’ electrons, removed and is increased by a factor of three? placed 1.00 m above it, would support the weight of this 13. Two point charges are brought closer together, coin? The atomic mass of nickel is 58.7, and each nickel increasing the force between them by a factor of 25. By atom contains 28 electrons and 28 protons. what factor was their separation decreased? 24. (a) Two point charges totaling exert a repulsive 14. How far apart must two point charges of 75.0 nC (typical force of 0.150 N on one another when separated by of static electricity) be to have a force of 1.00 N between 0.500 m. What is the charge on each? (b) What is the them? charge on each if the force is attractive? 15. If two equal charges each of 1 C each are separated in air 25. Point charges of and are placed by a distance of 1 km, what is the magnitude of the force 0.250 m apart. (a) Where can a third charge be placed so acting between them? You will see that even at a distance that the net force on it is zero? (b) What if both charges as large as 1 km, the repulsive force is substantial are positive? because 1 C is a very significant amount of charge. 26. Two point charges and are apart, and 16. A test charge of is placed halfway between a their total charge is. (a) If the force of repulsion charge of and another of separated by 10 between them is 0.075N, what are magnitudes of the cm. (a) What is the magnitude of the force on the test two charges? (b) If one charge attracts the other with a charge? (b) What is the direction of this force (away from force of 0.525N, what are the magnitudes of the two or toward the charge)? charges? Note that you may need to solve a quadratic 17. Bare free charges do not remain stationary when close equation to reach your answer. together. To illustrate this, calculate the acceleration of two isolated protons separated by 2.00 nm (a typical 18.4 Electric Field: Concept of a distance between gas atoms). Explicitly show how you Field Revisited follow the steps in the Problem-Solving Strategy for 27. What is the magnitude and direction of an electric field electrostatics. that exerts a upward force on a charge? 798 Chapter 18 Problems & Exercises 28. What is the magnitude and direction of the force 18.7 Conductors and Electric Fields exerted on a charge by a 250 N/C electric field in Static Equilibrium that points due east? 37. Sketch the electric field lines in the vicinity of the 29. Calculate the magnitude of the electric field 2.00 m conductor in Figure 18.48 given the field was originally from a point charge of 5.00 mC (such as found on the uniform and parallel to the object’s long axis. Is the terminal of a Van de Graaff). resulting field small near the long side of the object? 30. (a) What magnitude point charge creates a 10,000 N/C electric field at a distance of 0.250 m? (b) How large is the field at 10.0 m? 31. Calculate the initial (from rest) acceleration of a proton in a electric field (such as created by a research Van de Graaff). Explicitly show how you follow Figure 18.48 the steps in the Problem-Solving Strategy for electrostatics. 38. Sketch the electric field lines in the vicinity of the 32. (a) Find the magnitude and direction of an electric field conductor in Figure 18.49 given the field was originally that exerts a westward force on an uniform and parallel to the object’s long axis. Is the electron. (b) What magnitude and direction force does resulting field small near the long side of the object? this field exert on a proton? 18.5 Electric Field Lines: Multiple Charges 33. (a) Sketch the electric field lines near a point charge. (b) Do the same for a point charge. Figure 18.49 34. Sketch the electric field lines a long distance from the charge distributions shown in Figure 18.26 (a) and (b) 39. Sketch the electric field between the two conducting 35. Figure 18.47 shows the electric field lines near two plates shown in Figure 18.50, given the top plate is charges and. What is the ratio of their positive and an equal amount of negative charge is on magnitudes? (b) Sketch the electric field lines a long the bottom plate. Be certain to indicate the distribution distance from the charges shown in the figure. of charge on the plates. Figure 18.50 Figure 18.47 The electric field near two charges. 36. Sketch the electric field lines in the vicinity of two opposite charges, where the negative charge is three times greater in magnitude than the positive. (See Figure 18.47 for a similar situation). Access for free at openstax.org.  Chapter 18 Problems & Exercises 799 40. Sketch the electric field lines in the vicinity of the 45. Using the symmetry of the arrangement, determine the charged insulator in Figure 18.51 noting its nonuniform direction of the force on in the figure below, given that charge distribution. and. (b) Calculate the magnitude of the force on the charge , given that the square is 10.0 cm on a side and. Figure 18.51 A charged insulating rod such as might be used in a classroom demonstration. Figure 18.53 41. What is the force on the charge located at in Figure 18.52(a) given that ? 46. (a) Using the symmetry of the arrangement, determine the direction of the electric field at the center of the square in Figure 18.53, given that and. (b) Calculate the magnitude of the electric field at the location of , given that the square is 5.00 cm on a side. 47. Find the electric field at the location of in Figure 18.53 Figure 18.52 (a) Point charges located at 3.00, 8.00, and given that , 11.0 cm along the x-axis. (b) Point charges located at 1.00, , and the square is 20.0 cm on a side. 5.00, 8.00, and 14.0 cm along the x-axis. 48. Find the total Coulomb force on the charge in Figure 18.53, given that , , 42. (a) Find the total electric field at in Figure , , and 18.52(b) given that. (b) Find the total. The square is 50.0 cm on a side. electric field at in Figure 18.52(b). (c) If 49. (a) Find the electric field at the location of in Figure the charges are allowed to move and eventually be 18.54, given that and brought to rest by friction, what will the final charge. (b) What is the force on , given that configuration be? (That is, will there be a single charge, ? double charge, etc., and what will its value(s) be?) 43. (a) Find the electric field at in Figure 18.52(a), given that. (b) At what position between 3.00 and 8.00 cm is the total electric field the same as that for alone? (c) Can the electric field be zero anywhere between 0.00 and 8.00 cm? (d) At very large positive or negative values of x, the electric field approaches zero in both (a) and (b). In which does it most rapidly approach zero and why? (e) At what position to the right of 11.0 cm is the total electric field zero, other than at infinity? (Hint: A graphing calculator can yield considerable insight in this problem.) Figure 18.54 Point charges located at the corners of an 44. (a) Find the total Coulomb force on a charge of 2.00 nC equilateral triangle 25.0 cm on a side. located at in Figure 18.52 (b), given that. (b) Find the x-position at which the electric field is zero in Figure 18.52 (b). 800 Chapter 18 Problems & Exercises 50. (a) Find the electric field at the center of the triangular 53. A simple and common technique for accelerating configuration of charges in Figure 18.54, given that electrons is shown in Figure 18.55, where there is a , , and. uniform electric field between two plates. Electrons are (b) Is there any combination of charges, other than released, usually from a hot filament, near the negative , that will produce a zero strength plate, and there is a small hole in the positive plate that electric field at the center of the triangular allows the electrons to continue moving. (a) Calculate configuration? the acceleration of the electron if the field strength is. (b) Explain why the electron will not 18.8 Applications of Electrostatics be pulled back to the positive plate once it moves 51. (a) What is the electric field 5.00 m from the center of through the hole. the terminal of a Van de Graaff with a 3.00 mC charge, noting that the field is equivalent to that of a point charge at the center of the terminal? (b) At this distance, what force does the field exert on a charge on the Van de Graaff’s belt? 52. (a) What is the direction and magnitude of an electric field that supports the weight of a free electron near the surface of Earth? (b) Discuss what the small value for this field implies regarding the relative strength of the gravitational and electrostatic forces. Figure 18.55 Parallel conducting plates with opposite charges on them create a relatively uniform electric field used to accelerate electrons to the right. Those that go through the hole can be used to make a TV or computer screen glow or to produce X-rays. 54. Earth has a net charge that produces an electric field of approximately 150 N/C downward at its surface. (a) What is the magnitude and sign of the excess charge, noting the electric field of a conducting sphere is equivalent to a point charge at its center? (b) What acceleration will the field produce on a free electron near Earth’s surface? (c) What mass object with a single extra electron will have its weight supported by this field? 55. Point charges of and are placed 0.500 m apart. (a) At what point along the line between them is the electric field zero? (b) What is the electric field halfway between them? 56. What can you say about two charges and , if the electric field one-fourth of the way from to is zero? Access for free at openstax.org.