Two 1.0 kg masses are 1.0 m apart on a frictionless table.

Problem 1CQ What is alike about charges when we say “two like charges”? Do they look, smell, or tasle the same?

Problem 1P A glass rod is charged to +5.0 nC by rubbing. a. Have electrons been removed from the rod or protons added? Explain. b. How many electrons have been removed or protons added?

Problem 2CQ Four lightweight balls A, B, C, and D are suspended by threads. Ball A has been touched by a plastic rod that was rubbed with wool. When the balls are brought close together, without touching, the following observations are made: ¦ Balls B, C, and D are attracted to ball A. ¦ Balls B and D have no effect on each other. ¦ Ball B is attracted to ball C. What are the charge states (positive, negative, or neutral) of balls A, B, C, and D? Explain.

Problem 2P A plastic rod is charged to -20 nC by rubbing. a. Have electrons been added to the rod or protons removed? Explain. b. How many electrons have been added or protons removed?

Problem 3CQ Plastic and glass rods that have been charged by rubbing with wool and silk, respectively, hang by threads. a. An object repels the plastic rod. Can you predict what it will do to the glass rod? If so, what? If not, why not? Explain. b. A different object attracts the plastic rod. Can you predict what it will do to the glass rod? If so, what? If not, why not? Explain.

Problem 3P Suppose you have 1.0 mol of gas. How many coulombs of positive charge are contained in the atomic nuclei of this gas?

Problem 4CQ a. Can an insulator be charged? If so, how would you charge an insulator? If not, why not? b. Can a conductor be charged? If so, how would you charge a conductor? If not, why not?

Problem 4P A plastic rod that has been charged to -15.0 nC touches a metal sphere. Afterward, the rod’s charge is -10.0 nC. a. What kind of charged particle was transferred between the rod and the sphere, and in which direction? That is, did it move from the rod to the sphere or from the sphere to the rod? b. How many charged particles were transferred?

Problem 5CQ When you take clothes out of the drier right after it stops, the clothes often stick to your hands and arms. Is your body charged? If so, how did it acquire a charge? If not, why does this happen?

Problem 5P A glass rod that has been charged to +12.0 nC touches a metal sphere. Afterward, the rod’s charge is +8.0 nC. a. What kind of charged particle was transferred between the rod and the sphere, and in which direction? That is, did it move from the rod to the sphere or from the sphere to the rod? b. How many charged particles were transferred?

Problem 6CQ A lightweight metal ball hangs by a thread. When a charged rod is held near, the ball moves toward the rod, touches the rod, then quickly “flies away” from the rod. Explain this behavior.

Problem 6P Two identical metal spheres A and B are in contact. Both are initially neutral. electrons are added to sphere A, then the two spheres are separated. Afterward, what are the charge of A and the charge of B?

Problem 8CQ Figure Q20.7 shows a positively charged rod held near, but not touching, a neutral metal sphere. a. Add plusses and minuses to the figure to show the charge distribution on the sphere. b. Does the sphere experience a net force? If so, in which direction? Explain.

Problem 8P If two identical conducting spheres are in contact, any excess charge will be evenly distributed between the two. Three identical metal spheres are labeled A, B, and C. Initially, A has charge q , B has charge -q/2, and C is uncharged. a. What is the final charge on each sphere if C is touched to B, removed, and then touched to A? b. Starting again from the initial conditions, what is the charge on each sphere if C is touched to A, removed, and then touched to B?

Problem 9CQ A plastic balloon that has been rubbed with wool will stick to a wall. a. Can you conclude that the wall is charged? If not, why not? If so, where does the charge come from? b. Draw a charge diagram showing how the balloon is held to the wall.

Problem 9P Two 1.0 kg masses are 1.0 m apart on a frictionless table. Each has +1.0 mC of charge. a. What is the magnitude of the electric force on one of the masses? b. What is the initial acceleration of each mass if they are released and allowed to move?

Problem 10CQ You are given two metal spheres on portable insulating stands, a glass rod, and a piece of silk. Explain how to give the spheres exactly equal but opposite charges.

Problem 10P Two small plastic spheres each have a mass of 2.0 g and a charge of —50.0 nC. They are placed 2.0 cm apart. a. What is the magnitude of the electric force between the spheres? ________________ b. By what factor is the electric force on a sphere larger than its weight?

Problem 11CQ A honeybee acquires a positive electric charge as it flies through the air. This charge causes pollen grains to be attracted to the bee. Explain, using words and diagrams, how a neutral, conducting pollen grain will be attracted to a positively charged bee.

Problem 11P A small plastic sphere with a charge of -5.0 nC is near another small plastic sphere with a charge of -12 nC. If the spheres repel one another with a force of magnitude , what is the distance between the spheres?

Problem 12CQ A metal rod A and a metal sphere B, on insulating stands, touch each other as shown in Figure Q20.11 . They are originally neutral. A positively charged rod is brought near (but not touching) the far end of A. While the charged rod is still close, A and B are separated. The charged rod is then withdrawn. Is the sphere then positively charged, negatively charged, or neutral? Explain.

Problem 12P A small metal bead, labeled A, has a charge of 25 nC. It is touched to metal bead B, initially neutral, so that the two beads share the 25 nC charge, but not necessarily equally. When the two beads are then placed 5.0 cm apart, the force between them is on the beads?

Problem 13CQ Each part of Figure Q20.12 shows two points near two charges. Compare the electric field strengths at these two points. Is ?

Problem 13P A small glass bead has been charged to +20 nC. A tiny ball bearing 1.0 cm above the bead feels a 0.018 N downward electric force. What is the charge on the ball bearing?

Problem 14CQ Iontophoresis is a noninvasive process that transports drugs through the skin without needles. In the photo, the red electrode is positive and the black electrode is negative. The electric field between the electrodes will drive the negatively charged molecules of an anesthetic through the skin. Should the drug be placed at the red or the black electrode? Explain.

Problem 14P What are the magnitude and direction of the electric force on charge A in Figure P20.14 ?

Problem 15CQ Rank in order, from largest to smallest, noting any ties, the electric field strengths E1 to E4 at points 1 to 4 in Figure 15.

Problem 15P In Figure P20.15 , charge experiences no net electric force. What is ?

Problem 16CQ A 10 nC charge sits at a point in space where the magnitude of the electric field is 1200 N/C. What will the magnitude of the field be if the 10 nC charge is replaced by a 20 nC charge?

Problem 16P Object A, which has been charged to +10 nC, is at the origin. Object B, which has been charged to -20 nC, is at (x, y) = (0.0 cm, 2.0 cm). What are the magnitude and direction of the electric force on each object?

Problem 17P A small glass bead has been charged to +20 nC. What are the magnitude and direction of the acceleration of (a) a proton and (b) an electron that is 1.0 cm from the center of the bead?

Problem 17CQ When DNA breaks into fragments in a cell, electrostatic forces y actually inhibit repair. Explain why this happens,

Problem 18CQ A hollow soda straw is uniformly charged, as shown in Figure Q20.15. What is the electric field at the center (inside) of the straw? Explain.

Problem 18P What magnitude charge creates a 1.0 N/C electric field at a point 1.0 m away?

Problem 19CQ A small positive charge q experiences a force of magnitude when placed at point 1 in Figure Q20.18. In terms of : a. What is the magnitude of the force on charge q at point 3? b. What is the magnitude of the force on a charge 3q at point 1? c. What is the magnitude of the force on a charge 2q at point 2? d. What is the magnitude of the force on a charge -2q at point 2?

Problem 19P What are the strength and direction of the electric field 2.0 cm from a small glass bead that has been charged to +6.0 nC?

Problem 20CQ A typical commercial airplane is struck by lightning about once per year. When this happens, the external metal skin of the airplane might be burned, but the people and equipment inside the aircraft experience no ill effects. Explain why this is so.

Problem 20P A 30 nC charge experiences a 0.035 N electric force. What is the magnitude of electric field at the position of this charge?

Problem 21CQ Microbes such as bacteria have small positive charges when in solution. Public health agencies are exploring a new way to measure the presence of small numbers of microbes in drinking water by using electric forces to concentrate the microbes. Water is sent between the two oppositely charged electrodes of a parallel-plate capacitor. Any microbes in the water will collect on one of the electrodes. a. On which electrode will the microbes collect? b. How could the microbes be easily removed from the electrodes for analysis?

Problem 21P What are the strength and direction of the electric field 1.0 mm from (a) a proton and (b) an electron?

Problem 22CQ a. Is there a point between a 10 nC charge and a 20 nC charge at which the electric field is zero? If so, which charge is this point closer to? If not, why not? b. Repeat part a for the case of a 10 nC charge and a ?20 nC charge.

Problem 22P A +10 nC charge is located at the origin. a. What are the strengths of the electric fields at the positions (x, y) = (5.0 cm, 0.0 cm), (-5.0 cm, 5.0 cm), and (-5.0 cm, -5.0 cm)? b. Draw a field diagram showing the electric field vectors at these points.

Problem 23MCQ Two lightweight, electrically neutral conducting balls hang from threads. Choose the diagram in Figure Q20.22 that shows how the balls hang after: a. Both are touched by a negatively charged rod. b. Ball 1 is touched by a negatively charged rod and ball 2 is touched by a positively charged rod. c. Both are touched by a negatively charged rod but ball 2 picks up more charge than ball 1. d. Only ball 1 is touched by a negatively charged rod. Note that parts a through d are independent; these are not actions taken in sequence.

Problem 23P A -10 nC charge is located at the origin. a. What are the strengths of the electric fields at the positions (x, y) = (0.0 cm, 5.0 cm), (-5.0 cm, -5.0 cm), and (-5.0 cm, 5.0 cm)? b. Draw a field diagram showing the electric field vectors at these points.

Problem 24MCQ All the charges in Figure Q20.23 have the same magnitude. In which case does the electric field at the dot have the largest magnitude?

Problem 24P What are the strength and direction of the electric field at the position indicated by the dot in Figure P20.24 ? Specify the direction as an angle above or below horizontal.

Problem 25MCQ All the charges in Figure Q20.24 have the same magnitude. In which case does the electric field at the dot have the largest magnitude?

Problem 25P What are the strength and direction of the electric field at the position indicated by the dot in Figure P20.25? Specify the direction as an angle above or below horizontal.

Problem 26MCQ All the charges in Figure Q20.25 have the same magnitude. In which case does the electric field at the dot have the largest magnitude?

Problem 26P What are the strength and direction of an electric field that will balance the weight of a 1.0 g plastic sphere that has been charged to ?3.0 nC?

Problem 27MCQ A glass bead charged to +3.5 nC exerts an repulsive electric force on a plastic bead 2.9 cm away. What is the charge on the plastic bead? A. +2.1 Nc B. +7.4 nC C. +21 nC D. +740 nC

Problem 27P What are the strength and direction of an electric field that will balance the weight of (a) a proton and (b) an electron?

Problem 28MCQ A +7.5 nC point charge and a -2.0 nC point charge are 3.0 cm apart. What is the electric field strength at the midpoint between the two charges?

Problem 28P A 0.10 g plastic bead is charged by the addition of excess electrons. What electric field (strength and direction) will cause the bead to hang suspended in the air?

Problem 29MCQ Three point charges are arranged as shown in Figure Q20.28. Which arrow best represents the direction of the electric field vector at the position of the dot?

Problem 29P A parallel-plate capacitor is constructed of two square plates, size L × L, separated by distance d. The plates are given charge ±Q. What is the ratio of the final electric field strength to the initial electric field strength if: a. Q is doubled? b. L is doubled? c. d is doubled?

Problem 30MCQ A rod has positive charge +q at one end and negative charge ?q at the other, forming a dipole. The dipole is placed in a nonuniform electric field represented by the field lines in Figure 30. Which arrow best indicates the direction of the net electric force on the dipole? FIGURE 30

Problem 30P A parallel-plate capacitor is formed from two 4.0 cm × 4.0 cm electrodes spaced 2.0 mm apart. The electric field strength inside the capacitor is . What is the charge (in nC) on each electrode?

Problem 32P Storm clouds may build up large negative charges near their bottom edges. The earth is a good conductor, so the charge on the cloud attracts an equal and opposite charge on the earth under the cloud. The electric field strength near the earth depends on the shape of the earth’s surface, as we can explain with a simple model. The top metal plate in Figure P20.32 has uniformly distributed negative charge. The bottom metal plate, which has a high point, has an equal and opposite charge that is free to move. a. Sketch the two plates and the region between them, showing the distribution of positive charge on the bottom plate. b. Complete your diagram by sketching electric field lines between the two plates. Be sure to note the direction of the field. Where is the field strongest? c. Explain why it is more dangerous to be on top of a hill or mountain during a lightning storm than on level ground.

Problem 31P Two identical closely spaced circular disks form a parallelplate capacitor. Transferring electrons from one disk to the other causes the electric field strength between them to be . What are the diameters of the disks?

Problem 33P A neutral conducting sphere is between two parallel charged plates, as shown in Figure P20.33. Sketch the electric field lines in the region between the plates. Be sure to include the effect of the conducting sphere.

Problem 34P Two small plastic spheres, one charged to 17 nC and the other to ?17nC, are connected by a 25-mm-long insuladng rod. Suppose this dipole is placed in a uniform electric field with strength 7.4 × 105 N/C. What is the maximum possible torque on the dipole?

Problem 35P A protein molecule in an electrophoresis gel has a negative charge. The exact charge depends on the pH of the solution, but 30 excess electrons is typical. What is the magnitude of the electric force on a protein with this charge in a 1500 N/C electric field?

Problem 36P Large electric fields in cell membranes cause ions to move through the cell wall, as we will explore in Chapter 23. The field strength in a typical membrane is . What is the magnitude of the force on a calcium ion with charge +e?

Problem 37P Molecules of carbon monoxide are permanent electric dipoles due to unequal sharing of electrons between the carbon and oxygen atoms. Figure P20.37 shows the distance and charges. Suppose a carbon monoxide molecule with a horizontal axis is in a vertical electric field of strength 15,000 N/C. a. What is the magnitude of the net force on the molecule? b. What is the magnitude of the torque on the molecule?

Problem 38GP A 2.0-mm-diameter copper ball is charged to +50 nC. What fraction of its electrons have been removed? The density of copper is .

Problem 39GP Pennies today are copper-covered zinc, but older pennies are 3.1 g of solid copper. What are the total positive charge and total negative charge in a solid copper penny that is electrically neutral? The density of copper is .

Problem 40GP Two protons are 2.0 fm apart. (1 fm = 1 femtometer = .) a. What is the magnitude of the electric force on one proton due to the other proton? b. What is the magnitude of the gravitational force on one proton due to the other proton? c. What is the ratio of the electric force to the gravitational force?

Problem 41GP The nucleus of a atom (an isotope of the element xenon with mass 125 u) is 6.0 fm in diameter. It has 54 protons and charge q = +54e. (1 fm = 1 femtometer= .) a. What is the electric force on a proton 2.0 fm from the surface of the nucleus? b. What is the proton’s acceleration? Hint: Treat the spherical nucleus as a point charge.

Problem 42GP Two equally charged, 1.00 g spheres are placed with 2.00 cm between their centers. When released, each begins to accelerate at . What is the magnitude of the charge on each sphere?

Problem 43GP Objects A and B are both positively charged. Both have a mass of 100 g, but A has twice the charge of B. When A and B are placed with 10 cm between their centers, B experiences an electric force of 0.45 N. a. How large is the force on A? b. What are the charges ?

Problem 44GP An electric dipole is formed from ±1.0 nC point charges spaced 2.0 mm apart. The dipole is centered at the origin, oriented along the y-axis. What is the electric field strength at the points (a) (x, y) = (10 mm, 0 mm) and (b) (x, y) = (0 mm, 10 mm)?

Problem 45GP What are the strength and direction of the electric field at the position indicated by the dot in Figure P20.45? Specify the direction as an angle above or below horizontal.

Problem 46GP What are the strength and direction of the electric field at the position indicated by the dot in Figure P20.46? Specify the direction as an angle above or below horizontal.

Problem 47GP What is the force on the 1.0 nC charge in Figure P20.47? Give your answer as a magnitude and a direction.

What is the force on the 1.0 nC charge in Figure P20.48? Give your answer as a magnitude and a direction. FIGURE P20.48

Problem 49GP What is the magnitude of the force on the 1.0 nC charge in the middle of Figure P20.49 due to the four other charges?

Problem 50GP What are the magnitude and direction of the force on the 1.0 Nc charge in the middle of Figure P20.50 due to the four other charges?

Problem 51GP What are the magnitude and direction of the force on the 1.0 nC charge at the bottom of Figure P20.51?

Problem 52GP A 5,0 nC point charge sits at x = 0, At the same time, a 4500 N/C uniform electric field (created by distant source charges) points in the positive -v-direction. At what point along the x-axis, if any, would (a) a proton and (b) an electron experience no net force?

Problem 53GP The net force on the 1.0 nC charge in Figure P20.53 is zero. What is q?

Problem 54GP Two particles have positive charges q and Q. A third charged particle is placed halfway between them. What must this particle’s charge be so that the net force on charge Q is zero?

Problem 55GP Figure 55 shows four charges at the corners of a square of side L. Assume q and O are positive. a. Draw a diagram showing the three forces on charge q due to the other charges. Give your vectors the correct relative lengths. ________________ b. Find an expression for the magnitude of the net force on q. FIGURE 55

Problem 56GP Suppose the magnitude of the proton charge differs from that of the electron charge by a mere 1 part in 109. a. What would he the force between two 2.0-mm-diaraeter copper spheres 1.0 cm apart? Assume that each copper atom has an equal number of electrons and protons. The density of copper is 8900 kg/m3 ________________ b. Would this amount of force be detectable? What can you conclude from the fact that no such forces arc observed?

Problem 57GP In a simple model of the hydrogen atom, the electron moves in a circular orbit of radius 0.053 nm around a stationary proton. How many revolutions per second does the electron make? Hint: What must be true for a force that causes circular motion?

Problem 58GP A 0.10 g honeybee acquires a charge of +23 pC while flying. a. The electric field near the surface of the earth is typically 100 N/C, directed downward. What is the ratio of the electric force on the bee to the bee’s weight? b. What electric field strength and direction would allow the bee to hang suspended in the air?

Problem 59GP A +10 nC charge is located at (x, y) = (0 cm, 10 cm) and a -5.0 nC charge is located at (x, y) = (5.0 cm, 0 cm). Where would a -10 nC charge need to be located in order that the electric field at the origin be zero?

Problem 60GP Two 2.0-cm-diameter disks face each other, 1.0 mm apart. They are charged to ±10 nC. a. What is the electric field strength between the disks? b. A proton is shot from the negative disk toward the positive disk. What launch speed must the proton have to just barely reach the positive disk?

The electron gun in a television tube uses a uniform electric field to accelerate electrons from rest to 5.0 x 107 m/s in a distance of 1.2cm. What is the electric field strength?

Problem 62GP A 0.020 g plastic bead hangs from a lightweight thread. Another bead is fixed in position beneath the point where the thread is tied. If both beads have charge q, the moveable bead swings out to the position shown in Figure P20.62. What is q?

Problem 63GP You have a lightweight spring whose unstretched length is 4.0 cm. You’re curious to see if you can use this spring to measure charge. First, you attach one end of the spring to the ceiling and hang a 1.0 g mass from it. This stretches the spring to a length of 5,0 cm. You then attach two small plastic beads to the opposite ends of the spring, lay the spring on a frictionless table, and give each plastic bead the same charge. This stretches the spring to a length of 4.5 cm. What is the magnitude of the charge (in nC) on each bead?

Problem 64GP Two 3.0 g spheres on 1.0-m-long threads repel each other after being equally charged, as shown in Figure P20.64. What is the charge q?

Problem 66GP An electric field causes the 2.0 g ball in Figure P20.66 to hang at an angle. What is ??

Problem 65GP An electric field causes the 5.0 g ball in Figure P20.65 to hang at a 20° angle. What is the charge on the ball?

Problem 67GP A small charged bead has a mass of 1.0 g. It is held in a uniform electric field .When the bead is released, it accelerates upward with an acceleration of . What is the charge on the bead?

Problem 68GP A bead with a mass of 0.050 g and a charge of 15 nC is free to slide on a vertical rod. At the base of the rod is a fixed 10 nC charge. In equilibrium, at what height above the fixed charge does the bead rest?

Problem 69GP A small bead with a positive charge q is free to slide on a horizontal wire of length 4.0 cm. At the left end of the wire is a fixed charge q, and at the right end is a fixed charge 4q. How far from the left end of the wire does the bead come to rest?

Problem 70GP In Problems you are given the equation used to solve a problem. For each of these, a. Write a realistic problem for which this is the correct equation. b. Finish the solution of the problem.

Problem 71GP In Problems you are given the equation used to solve a problem. For each of these, a. Write a realistic problem for which this is the correct equation. b. Finish the solution of the problem.

Problem 72GP Flow Cytometry Flow cytometry, illustrated in Figure P20.71, is a technique used to sort cells by type. The cells are placed in a conducting saline solution which is then forced from a nozzle. The stream breaks up into small droplets, each containing one cell. A metal collar surrounds the stream right at the point where the droplets separate from the stream. Charging the collar polarizes the conducting liquid, causing the droplets to become charged as they break off from the stream. A laser beam probes the solution just upstream from the charging collar, looking for the presence of certain types of cells. All droplets containing one particular type of cell are given the same charge by the charging collar. Droplets with other desired types of cells receive a different charge, and droplets with no desired cell receive no charge. The charged droplets then pass between two parallel charged electrodes where they receive a horizontal force that directs them into different collection tubes, depending on their charge. If the charging collar has a positive charge, the net charge on a droplet separating from the stream will be A. Positive. B. Negative. C. Neutral. D. The charge will depend on the type of cell.

Problem 73GP Flow Cytometry Flow cytometry, illustrated in Figure P20.71, is a technique used to sort cells by type. The cells are placed in a conducting saline solution which is then forced from a nozzle. The stream breaks up into small droplets, each containing one cell. A metal collar surrounds the stream right at the point where the droplets separate from the stream. Charging the collar polarizes the conducting liquid, causing the droplets to become charged as they break off from the stream. A laser beam probes the solution just upstream from the charging collar, looking for the presence of certain types of cells. All droplets containing one particular type of cell are given the same charge by the charging collar. Droplets with other desired types of cells receive a different charge, and droplets with no desired cell receive no charge. The charged droplets then pass between two parallel charged electrodes where they receive a horizontal force that directs them into different collection tubes, depending on their charge. Which of the following describes the charges on the droplets that end up in the five tubes, moving from left to right? A. +2q, +q, 0, -q, -2q B. +q, +2q, 0, -2q, -q C. -q, -2q, 0, +2q, +q D. -2q, -q, 0, +q, +2q

Problem 74GP Flow Cytometry Flow cytometry, illustrated in Figure P20.71, is a technique used to sort cells by type. The cells are placed in a conducting saline solution which is then forced from a nozzle. The stream breaks up into small droplets, each containing one cell. A metal collar surrounds the stream right at the point where the droplets separate from the stream. Charging the collar polarizes the conducting liquid, causing the droplets to become charged as they break off from the stream. A laser beam probes the solution just upstream from the charging collar, looking for the presence of certain types of cells. All droplets containing one particular type of cell are given the same charge by the charging collar. Droplets with other desired types of cells receive a different charge, and droplets with no desired cell receive no charge. The charged droplets then pass between two parallel charged electrodes where they receive a horizontal force that directs them into different collection tubes, depending on their charge. Because the droplets are conductors, a droplet’s positive and negative charges will separate while the droplet is in the region between the deflection plates. Suppose a neutral droplet passes between the plates. The droplet’s dipole moment will point A. Up. B. Down. C. Left. D. Right.

Problem 75GP Flow Cytometry Flow cytometry, illustrated in Figure P20.71, is a technique used to sort cells by type. The cells are placed in a conducting saline solution which is then forced from a nozzle. The stream breaks up into small droplets, each containing one cell. A metal collar surrounds the stream right at the point where the droplets separate from the stream. Charging the collar polarizes the conducting liquid, causing the droplets to become charged as they break off from the stream. A laser beam probes the solution just upstream from the charging collar, looking for the presence of certain types of cells. All droplets containing one particular type of cell are given the same charge by the charging collar. Droplets with other desired types of cells receive a different charge, and droplets with no desired cell receive no charge. The charged droplets then pass between two parallel charged electrodes where they receive a horizontal force that directs them into different collection tubes, depending on their charge. Another way to sort the droplets would be to give each droplet the same charge, then vary the electric field between the deflection plates. For the apparatus as sketched, this technique will not work because A. Several droplets are between the plates at one time, and they would all feel the same force. B. The cells in the solution have net charges that would affect the droplet charge. C. A droplet with a net charge would always experience a net force between the plates. D. The droplets would all repel each other, and this force would dominate the deflecting force.