FIGURE P22.52 shows three charges and the net force on

What is electric charge?

How do charges behave?

What are conductors and insulators?

What is Coulombs law?

What is an electric field?

Why are electric charges important?

In Experiment 12, touching one metal sphere with a charged plastic rod caused a second metal sphere to become charged with the same type of charge as the rod. Use the postulates of the charge model to explain this

To determine if an object has glass charge, you need to a. See if the object attracts a charged plastic rod. b. See if the object repels a charged glass rod. c. Do both a and b. d. Do either a or b.

Rank in order, from most positive to most negative, the charges qa to qe of these five systems

Many electricity demonstrations are carried out with the help of an electroscope like the one shown in FIGURE 22.7. Touching the sphere at the top of an electroscope with a charged plastic rod causes the leaves to fly apart and remain hanging at an angle. Use charge diagrams to explain why

An electroscope is positively charged by touching it with a positive glass rod. The electroscope leaves spread apart and the glass rod is removed. Then a negatively charged plastic rod is brought close to the top of the electroscope, but it doesnt touch. What happens to the leaves? a. The leaves get closer together. b. The leaves spread farther apart. c. One leaf moves higher, the other lower. d. The leaves dont move.

A small plastic sphere charged to -10 nC is held 1.0 cm above a small glass bead at rest on a table. The bead has a mass of 15 mg and a charge of +10 nC. Will the glass bead leap up to the plastic sphere?

Two positively charged particles q1 and q2 = 3q1 are 10.0 cm apart on the x-axis. Where (other than at infinity) could a third charge q3 be placed so as to experience no net force?

Charged spheres A and B exert repulsive forces on each other. qA = 4qB. Which statement is true? a. FA on B 7 FB on A b. FA on B = FB on A c. FA on B 6 FB on A

Three charged particles with q1 = -50 nC, q2 = +50 nC, and q3 = +30 nC are placed on the corners of the 5.0 cm * 10.0 cm rectangle shown in FIGURE 22.18. What is the net force on charge q3 due to the other two charges? Give your answer both in component form and as a magnitude and direction

An electron is placed at the position marked by the dot. The force on the electron is a. Zero. b. To the right. c. To the left. d. Theres not enough information to tell.

Every cell in your body is electrically active in various ways. For example, nerve propagation occurs when large electric fields in the cell membranes of neurons cause ions to move through the cell walls. The field strength in a typical cell membrane is 1.0 * 107 N/C. What is the magnitude of the electric force on a singly charged calcium ion?

Rank in order, from largest to smallest, the electric field strengths Ea to Ed at points a to d. r q a r 2q b 2r q c 2r 2q d

A -1.0 nC charged particle is located at the origin. Points 1, 2, and 3 have (x, y) coordinates (1 cm, 0 cm), (0 cm, 1 cm), and (1 cm, 1 cm), respectively. Determine the electric field E u at these points, then show the vectors on an electric field diagram.

The electron in a hydrogen atom orbits the proton at a radius of 0.053 nm. a. What is the protons electric field strength at the position of the electron? b. What is the magnitude of the electric force on the electron?

A horizontal electric field causes the charged ball in FIGURE 22.29 to hang at a 15 angle, as shown. The spring is plastic, so it doesnt discharge the ball, and in its equilibrium position the spring extends only to the vertical dashed line. What is the electric field strength?

Can an insulator be charged? If so, how would you charge an insulator? If not, why not?

Can a conductor be charged? If so, how would you charge a conductor? If not, why not?

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 (glass, plastic, or neutral) of balls A, B, C, and D? Explain

Charged plastic and glass rods 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? 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?

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.

A plastic balloon that has been rubbed with wool will stick to a wall. Can you conclude that the wall is charged? If so, where does the charge come from? If not, why does the balloon stick?

Suppose there exists a third type of charge in addition to the two types weve called glass and plastic. Call this third type X charge. What experiment or series of experiments would you use to test whether an object has X charge? State clearly how each possible outcome of the experiments is to be interpreted.

The two oppositely charged metal spheres in FIGURE Q22.8 have equal quantities of charge. They are brought into contact with a neutral metal rod. What is the final charge state of each sphere and of the rod? Use both charge diagrams and words to explain.

Metal sphere A in FIGURE Q22.9 has 4 units of negative charge and metal sphere B has 2 units of positive charge. The two spheres are brought into contact. What is the final charge state of each sphere? Explain.

A negatively charged electroscope has separated leaves. a. Suppose you bring a negatively charged rod close to the top of the electroscope, but not touching. How will the leaves respond? Use both charge diagrams and words to explain. b. How will the leaves respond if you bring a positively charged rod close to the top of the electroscope, but not touching? Use both charge diagrams and words to explain

Metal spheres A and B in FIGURE Q22.11 are initially neutral and are touching. A positively charged rod is brought near A, but not touching. Is A now positive, negative, or neutral? Use both charge diagrams and words to explain.

If you bring your finger near a lightweight, negatively charged hanging ball, the ball swings over toward your finger as shown in FIGURE Q22.12. Use charge diagrams and words to explain this observation

Reproduce FIGURE Q22.13 on your paper. Then draw a dot (or dots) on the figure to show the position (or positions) where an electron would experience no net force

Charges A and B in FIGURE Q22.14 are equal. Each charge exerts a force on the other of magnitude F. Suppose the charge of B is increased by a factor of 4, but everything else is unchanged. In terms of F, (a) what is the magnitude of the force on A, and (b) what is the magnitude of the force on B?

The electric force on a charged particle in an electric field is F. What will be the force if the particles charge is tripled and the electric field strength is halved?

A glass rod is charged to +8.0 nC by rubbing. a. Have electrons been removed from the rod or protons added? b. How many electrons have been removed or protons added?

A plastic rod is charged to -12 nC by rubbing. a. Have electrons been added to the rod or protons removed? b. How many electrons have been added or protons removed?

A plastic rod that has been charged to -15 nC touches a metal sphere. Afterward, the rods charge is -10 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?

A glass rod that has been charged to +12 nC touches a metal sphere. Afterward, the rods 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?

What is the total charge of all the electrons in 1.0 L of liquid water?

What mass of aluminum has a total nuclear charge of 1.0 C? Aluminum has atomic number 13

A chemical reaction takes place among 3 molecular ions that have each lost 2 electrons, 2 molecular ions that have each gained 3 electrons, and 1 molecular ion that has gained 2 electrons. The products of the reaction are two neutral molecules and multiple molecular ions that each have a charge of magnitude e. How many molecular ions are produced, and are they charged positively or negatively?

A linear accelerator uses alternating electric fields to accelerate electrons to close to the speed of light. A small number of the electrons collide with a target, but a large majority pass through the target and impact a beam dump at the end of the accelerator. In one experiment the beam dump measured charge accumulating at a rate of -2.0 nC/s. How many electrons traveled down the accelerator during the 2.0 h run?

Figure 22.8 showed how an electroscope becomes negatively charged. The leaves will also repel each other if you touch the electroscope with a positively charged glass rod. Use a series of charge diagrams to explain what happens and why the leaves repel each other.

Two neutral metal spheres on wood stands are touching. A negatively charged rod is held directly above the top of the left sphere, not quite touching it. While the rod is there, the right sphere is moved so that the spheres no longer touch. Then the rod is withdrawn. Afterward, what is the charge state of each sphere? Use charge diagrams to explain your answer

You have two neutral metal spheres on wood stands. Devise a procedure for charging the spheres so that they will have like charges of exactly equal magnitude. Use charge diagrams to explain your procedure

You have two neutral metal spheres on wood stands. Devise a procedure for charging the spheres so that they will have opposite charges of exactly equal magnitude. Use charge diagrams to explain your procedure.

Two 1.0 kg masses are 1.0 m apart (center to center) on a frictionless table. Each has +10 mC of charge. a. What is the magnitude of the electric force on one of the masses? b. What is the initial acceleration of this mass if it is released and allowed to move?

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 (center to center). a. What is the magnitude of the electric force on each sphere? b. By what factor is the electric force on a sphere larger than its weight?

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

Two protons are 2.0 fm apart. 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?

What is the net electric force on charge A in FIGURE EX22.17?

What is the net electric force on charge B in FIGURE EX22.18?

What is the force F u on the 1.0 nC charge in Figure EX22.19? Give your answer as a magnitude and a direction.

What is the force F u on the 1.0 nC charge in FIGURE EX22.20? Give your answer as a magnitude and a direction.

Object A, which has been charged to +4.0 nC, is at the origin. Object B, which has been charged to -8.0 nC, is at 1x, y2 = 10.0 cm, 2.0 cm2. Determine the electric force on each object. Write each force vector in component form.

A small plastic bead has been charged to -15 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?

A 2.0 g plastic bead charged to -4.0 nC and a 4.0 g glass bead charged to +8.0 nC are 2.0 cm apart and free to move. What are the accelerations of (a) the plastic bead and (b) the glass bead?

Two positive point charges q and 4q are at x = 0 and x = L, respectively, and free to move. A third charge is placed so that the entire three-charge system is in static equilibrium. What are the magnitude, sign, and x-coordinate of the third charge?

A massless spring is attached to a support at one end and has a 2.0 mC charge glued to the other end. A -4.0 mC charge is slowly brought near. The spring has stretched 1.2 cm when the charges are 2.6 cm apart. What is the spring constant of the spring?

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

The electric field at a point in space is E u = 1400 i n + 100j n2 N/C. a. What is the electric force on a proton at this point? Give your answer in component form. b. What is the electric force on an electron at this point? Give your answer in component form. c. What is the magnitude of the protons acceleration? d. What is the magnitude of the electrons acceleration?

What are the strength and direction of the electric field 4.0 cm from a small plastic bead that has been charged to -8.0 nC?

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

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?

The electric field 2.0 cm from a small object points away from the object with a strength of 270,000 N/C. What is the objects charge?

A +12 nC charge is located at the origin. a. What are the electric fields at the positions 1x, y2 = 15.0 cm, 0 cm2, (-5.0 cm, 5.0 cm), and 1-5.0 cm,-5.0 cm2? Write each electric field vector in component form. b. Draw a field diagram showing the electric field vectors at these points.

A 12 nC charge is located at 1x, y2 = 11.0 cm, 0 cm2. What are the electric fields at the positions 1x, y2 = 15.0 cm, 0 cm2, 1-5.0 cm, 0 cm2, and 10 cm, 5.0 cm2? Write each electric field vector in component form.

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

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?

Two 1.0 g spheres are charged equally and placed 2.0 cm apart. When released, they begin to accelerate at 150 m/s2 . What is the magnitude of the charge on each sphere?

The nucleus of a 125 Xe 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. a. What is the electric force on a proton 2.0 fm from the surface of the nucleus? b. What is the protons acceleration? Hint: Treat the spherical nucleus as a point charge

A Van de Graaff generator is a device that accumulates electrons on a large metal sphere until the large amount of charge causes sparks. As youll learn in Chapter 23, the electric field of a charged sphere is exactly the same as if the charge were a point charge at the center of the sphere. Suppose that a 25-cmdiameter sphere has accumulated 1.0 * 1013 extra electrons and that a small ball 50 cm from the edge of the sphere feels the force F u = 19.2 * 10-4 N, away from sphere2. What is the charge on the ball?

A smart phone charger delivers charge to the phone, in the form of electrons, at a rate of 0.75 C/s. How many electrons are delivered to the phone during 30 min of charging?

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 10 cm apart, B experiences an electric force of 0.45 N. a. What is the charge on A? b. If the objects are released, what is the initial acceleration of A?

What is the force F u on the -10 nC charge in FIGURE P22.41? Give your answer as a magnitude and an angle measured cw or ccw (specify which) from the +x@axis.

What is the force F u on the -10 nC charge in FIGURE P22.42? Give your answer as a magnitude and an angle measured cw or ccw (specify which) from the +x@axis

What is the force F u on the 5.0 nC charge in FIGURE P22.43? Give your answer as a magnitude and an angle measured cw or ccw (specify which) from the +x@axis.

What is the force F u on the 1.0 nC charge in the middle of FIGURE P22.44 due to the four other charges? Give your answer in component form.

What is the force F u on the 1.0 nC charge at the bottom in FIGURE P22.45? Give your answer in component form.

What is the force F u on the 1.0 nC charge at the bottom in FIGURE P22.46? Give your answer in component form

A +2.0 nC charge is at the origin and a -4.0 nC charge is at x = 1.0 cm. a. At what x-coordinate could you place a proton so that it would experience no net force? b. Would the net force be zero for an electron placed at the same position? Explain.

The net force on the 1.0 nC charge in FIGURE P22.48 is zero. What is q?

Charge q2 in FIGURE P22.49 is in equilibrium. What is q1?

A positive point charge Q is located at x = a and a negative point charge -Q is at x = -a. A positive charge q can be placed anywhere on the y-axis. Find an expression for 1Fnet 2x, the xcomponent of the net force on q

FIGURE P22.51 shows four charges at the corners of a square of side L. What is the magnitude of the net force on q?

FIGURE P22.52 shows three charges and the net force on charge -q. Charge Q is some multiple a of q. What is a?

Suppose the magnitude of the proton charge differs from the magnitude of the electron charge by a mere 1 part in 109 . a. What would be the force between two 2.0-mm-diameter copper spheres 1.0 cm apart? Assume that each copper atom has an equal number of electrons and protons. b. Would this amount of force be detectable? What can you conclude from the fact that no such forces are observed?

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?

You have two small, 2.0 g balls that have been given equal but opposite charges, but you dont know the magnitude of the charge. To find out, you place the balls distance d apart on a slippery horizontal surface, release them, and use a motion detector to measure the initial acceleration of one of the balls toward the other. After repeating this for several different separation distances, your data are as follows: Distance (cm) Acceleration (m/s2 ) 2.0 0.74 3.0 0.30 4.0 0.19 5.0 0.10 Use an appropriate graph of the data to determine the magnitude of the charge.

A 2.0 g metal cube and a 4.0 g metal cube are 6.0 cm apart, measured between their centers, on a horizontal surface. For both, the coefficient of static friction is 0.65. Both cubes, initially neutral, are charged at a rate of 7.0 nC/s. How long after charging begins does one cube begin to slide away? Which cube moves first?

Space explorers discover an 8.7 * 1017 kg asteroid that happens to have a positive charge of 4400 C. They would like to place their 3.3 * 105 kg spaceship in orbit around the asteroid. Interestingly, the solar wind has given their spaceship a charge of 1.2 C. What speed must their spaceship have to achieve a 7500-km-diameter circular orbit?

Two equal point charges 2.5 cm apart, both initially neutral, are being charged at the rate of 5.0 nC/s. At what rate (N/s) is the force between them increasing 1.0 s after charging begins?

rce between them increasing 1.0 s after charging begins? 59. || You have a lightweight spring whose unstretched length is 4.0 cm. 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?

An electric dipole consists of two opposite charges {q separated by a small distance s. The product p = qs is called the dipole moment. FIGURE P22.60 shows an electric dipole perpendicular to an electric field E u . Find an expression in terms of p and E for the magnitude of the torque that the electric field exerts on the dipole.

You sometimes create a spark when you touch a doorknob after shuffling your feet on a carpet. Why? The air always has a few free electrons that have been kicked out of atoms by cosmic rays. If an electric field is present, a free electron is accelerated until it collides with an air molecule. Most such collisions are elastic, so the electron collides, accelerates, collides, accelerates, and so on, gradually gaining speed. But if the electrons kinetic energy just before a collision is 2.0 * 10-18 J or more, it has sufficient energy to kick an electron out of the molecule it hits. Where there was one free electron, now there are two! Each of these can then accelerate,hit a molecule, and kick out another electron. Then there will be four free electrons. In other words, as FIGURE P22.61 shows, a sufficiently strong electric field causes a chain reaction of electron production. This is called a breakdown of the air. The current of moving electrons is what gives you the shock, and a spark is generated when the electrons recombine with the positive ions and give off excess energy as a burst of light. a. The average distance between ionizing collisions is 2.0 mm. (The electrons mean free path is less than this, but most collisions are elastic collisions in which the electron bounces with no loss of energy.) What acceleration must an electron have to gain 2.0 * 10-18 J of kinetic energy in this distance? b. What force must act on an electron to give it the acceleration found in part a? c. What strength electric field will exert this much force on an electron? This is the breakdown field strength. Note: The measured breakdown field strength is a little less than your calculated value because our model of the process is a bit too simple. Even so, your calculated value is close. d. Suppose a free electron in air is 1.0 cm away from a point charge. What minimum charge is needed to cause a breakdown and create a spark as the electron moves toward the point charge?

Two 5.0 g point charges on 1.0-m-long threads repel each other after being charged to +100 nC, as shown in FIGURE P22.62. What is the angle u? You can assume that u is a small angle.

What are the electric fields at points 1, 2, and 3 in FIGURE P22.63? Give your answer in component form.

What are the electric fields at points 1, 2, and 3 in FIGURE P22.64? Give your answer in component form.

A 10.0 nC charge is located at position 1x, y2 = 11.0 cm, 2.0 cm2. At what 1x, y2 position(s) is the electric field a. -225,000 ni N/C? b. 1161,000 ni + 80,500j n2 N/C? c. 121,600 ni - 28,800j n2 N/C?

Three 1.0 nC charges are placed as shown in FIGURE P22.66. Each of these charges creates an electric field E u at a point 3.0 cm in front of the middle charge. a. What are the three fields E u 1, E u 2, and E u 3 created by the three charges? Write your answer for each as a vector in component form. b. Do you think that electric fields obey a principle of superposition? That is, is there a net field at this point given by E u net = E u 1 + E u 2 + E u 3? Use what you learned in this chapter and previously in our study of forces to argue why this is or is not true. c. If it is true, what is E u net ?

An electric field E u = 100,000 i n N/C causes the 5.0 g point charge in FIGURE P22.67 to hang at a 20 angle. What is the charge on the ball?

An electric field E u = 200,000 i n N/C causes the point charge in FIGURE P25.68 to hang at an angle. What is u?

In Problems 69 through 72 you are given the equation(s) used to solve a problem. For each of these, a. Write a realistic problem for which this is the correct equation(s). b. Finish the solution of the problem.19.0 * 109 Nm2 /C2 2 * N * 11.60 * 10-19 C2 11.0 * 10-6 m22 = 1.5 * 106 N/C

In Problems 69 through 72 you are given the equation(s) used to solve a problem. For each of these, a. Write a realistic problem for which this is the correct equation(s). b. Finish the solution of the problem.19.0 * 109 Nm2 /C2 2q2 10.0150 m22 = 0.020 N

In Problems 69 through 72 you are given the equation(s) used to solve a problem. For each of these, a. Write a realistic problem for which this is the correct equation(s). b. Finish the solution of the problem.19.0 * 109 Nm2 /C2 2115 * 10-9 C2 r2 = 54,000 N/C

In Problems 69 through 72 you are given the equation(s) used to solve a problem. For each of these, a. Write a realistic problem for which this is the correct equation(s). b. Finish the solution of the problem.aFx = 2 * 19.0 * 109 Nm2 /C2 211.0 * 10-9 C2q 110.020 m2/sin 3022 * cos 30 = 5.0 * 10-5 N aFy = 0 N

Two 3.0 g point charges on 1.0-m-long threads repel each other after being equally charged, as shown in FIGURE CP22.73. What is the magnitude of the charge q?

Three 3.0 g balls are tied to 80-cm-long threads and hung from a single fixed point. Each of the balls is given the same charge q. At equilibrium, the three balls form an equilateral triangle in a horizontal plane with 20 cm sides. What is q?

The identical small spheres shown in FIGURE CP22.75 are charged to +100 nC and -100 nC. They hang as shown in a 100,000 N/C electric field. What is the mass of each sphere?

The force on the -1.0 nC charge is as shown in FIGURE CP22.76. What is the magnitude of this force?

In Section 22.3 we claimed that a charged object exerts a net attractive force on an electric dipole. Lets investigate this. FIGURE CP22.77 shows a permanent electric dipole consisting of charges +q and -q separated by the fixed distance s. Charge +Q is distance r from the center of the dipole. Well assume, as is usually the case in practice, that s V r. a. Write an expression for the net force exerted on the dipole by charge +Q. b. Is this force toward +Q or away from +Q? Explain. c. Use the binomial approximation 11 + x2-n 1 - nx if x V 1 to show that your expression from part a can be written Fnet = 2KqQs/r3 . d. How can an electric force have an inverse-cube dependence? Doesnt Coulombs law say that the electric force depends on the inverse square of the distance? Explain