A 2.0-mm-diameter copper ball is charged to +50 nC. What fraction of its electrons have

Four lightweight balls A, B, C, andD are suspended by threads. Ball A has been touched by a plastic rod that was mbbed 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.

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 wi ll 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.

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

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? Tf so, how did it acquire a charge? Tf not, why does this happen?

The positive charge in Figure Q20.5 is +Q. What is the negative charge if the electric field at the dot is zero?

As shown in Figure Q20.6, metal sphere A 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.

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 Metal distribution on the sphere. b. Does the sphere experience a net force? If so, in which direction? Explain.

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

You are given two metal spheres on portable insulating stands, a glass rod, and a piece of silk. Explain how to give the spheres exac1ly equal but opposite charges.

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.

A metal rod A and a metal sphere B, on insulati ng stands, touch each other as shown in Figure Q20. I I. 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 Bare separated. The charged rod is then withdrawn. Is the sphere then positively charged, negatively charged, or neutral? Explain.

Each part of Figure Q20. l 2 shows two points near two charges. Compare the electric field strengths 1 and 2 at these two points. Is 1 > 2, 1 = 2 , or 1 < E2?

Iontophoresis is a noninvasive process that transports drugs through the skin wi thout needles. In the photo, the red electrode is posi tive and the black electrode is negative. The electric field between the e lectrodes 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.

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 IO nC charge is replaced by a 20 nC charge?

A hollow soda straw is uniformly charged, as shown in Figure Q20. I 5. What is the electric field at the center (inside) of the straw? Explain.

A positively charged particle is in the center of a parallel-plate capacitor that has charge Q on its plates. Suppose the distance between the plates is doubled, with the charged particle remaining in t)le center. Does the force on this particle increase, decrease, or stay tJie same? Explai n.

Two charged particles are separated by 10 cm. Suppose the charge on each particle is doubled. By what factor does the electric force betweeu the particles change?

A small positive charge q experiences a force of magnitade Fr when r/ placed at point I in Figure Q20. 18. Jn terms of Fr: a. What is the magnitude of the FIGURE 020.18 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?

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.

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 wi ll 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?

a. Ts there a point between a 10 nC charge and a 20 nC charge at which the electric fie ld 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.

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 I 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 I. 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.

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?

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?

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?

A glass bead charged to + 3.5 nC exerts an 8.0 X 10-4 N repulsive electric force on a plastic bead 2.9 cm away. What is the charge on the plastic bead? A. + 2.1 nC B. + 7.4nC C. + 21 nC D. + 740 nC

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? A. 3.3 X 103 N/C B. 5.7 X 103 N/C C. 2.2 x 105 N/C D. 3.8 x 105 N/C

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?

A positive charge is brought near to a dipole, as shown in Figure Q20.29. If the dipole is free to rotate, it A. Begins to rotate in a clockwise direction. B. Begins to rotate in a counterclockwise direction. C. Remains stationary.

Two identical closely spaced circ ular disks form a parallelplate capacitor. Transfen-ing 1.5 x 109 electrons from one disk to the other causes the electric field strength between them to be 1.0 x 105 N/C. What are the diameters of the disks?

A parallel-plate capacitor is constructed of two horizontal 12.0-cm-diameter circular plates. A 1.0 g plastic bead, wi th a charge of - 6.0 nC, is suspended between the two plates by the force of the e lectric field between them. a. Which plate, the upper or the lower, is positi vely charged? b. What is the charge on the positive plate?

Stonn 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 ea1th's surface, as we can explain with a simple model. The top metal plate in Figure P20.32 has uniformly disttibuted 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 fie ld. Where is the field strongest? c. Explain why it is more dangerous to be on top of a hill or mountain during a lightning s torm than on level ground.

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.

One kind of e-book display consists of millions of very small INT spheres that float in a thin fluid layer between two conducting, transparent plates. Each sphere is black on one side and white on the other, and possesses an electric dipole moment directed from the white side to the black. When an electric fie ld is applied between the plates, the spheres rotate so that their dipole moment lines up with the field. Depending on the fi eld's direction, either the black or the white sides of the spheres can be made visible. The dipole moment of the spheres can be modeled as two opposite charges of magnitude 3.5 X 10- 15 C, separated by a distance of 100 m. What is the maximum possible torque on a sphere if the electric field between the transparent plates is 4.0 x I 05 NIC?

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

Large electric fields in cell membranes cause ions to move through the cell wall, as we will explore in Chapter 23. The field stre ngth in a typical membrane is 1.0 X 107 N/C. What is the magnitude of the force on a calcium ion with charge +e?

Molecules of carbon monoxide are permanent electric dipoles due to unequal sharing of electrons between the carbon and oxygen atoms 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?

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 8900 kg/m3.

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 8900 kglm3 .

Two protons are 2.0 fm apart. ( 1 fm = 1 femtometer = 1 x 10-15 m.) 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 e lectric force to the gravitational force?

The nucleus of a 125Xe atom (an isotope of the element xenon with mass 125 u) is 6.0 fm in diameter. It has 54 proto ns and charge q = +54e. (1 fm = I femtometer= I x 10-15 m.) 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.

Two equally charged, 1.00 g spheres are placed with 2.00 cm between their centers. When released, each begins to accelerate at 225 m/s2 . What is the magnitude of the charge on each sphere?

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 I 0 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 qA and qB?

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, IO mm)?

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.

What are the strength and direction of the electric fi eld at the position indicated by the dot in Figure P20.46? Speci fy the direction as an angle above or below horizontal

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.

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?

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?

What are the magnitude and direction of the force on the 1.0 nC charge at the bottom of Figure P20.5 l?

As shown in Figure P20.52, a 5.0 nC charge sits at x = 0 in a uni form 4500 N/C electric field directed to the right. At what point along the x-axis would (a) a proton and (b) an electron experience no net force?

The net force on the l.O nC charge in Figure P20.53 is zero. What is q?

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 cnarge Q is zero?

Figure P20.55 shows four charges at the corners of a square of side L. Whamagnitude and sign of charge Q will make the force on charge q zero?

Model a pollen grain as a sphere INT of carbon 0. 10 mm in diameter. Tf two such grains, spaced 1.0 m apart, were somehow stripped of all their electrons, leaving only the protons, what would be the force between them?Compare this force to the weight of an aircraft carrier, which is about 9 x 108 N. The density of carbon is 2300 kg/m3 .

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 c ircular motion?

A +10 g honeybee acquires a charge of +23 pC while flying. a. The electric field near the surface of the earth is typically I 00 NIC, 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?

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

Two 2.0-cm-diameter disks face each other, 1.0 mm apart. They are charged to I 0 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 I 07 mis in a distance of L.2 cm. What is the electric field strength?

0.020 g plastic bead hangs from a INT 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 swi ngs out to the position shown in Figure P20.62. What is q?

A 4 .0 mg bead with a charge of 5.0 cm 2.5 nC rests on a table. A second bead, with a charge of - 5.6 nC, is directly above the first bead and is slowly lowered toward it. What is the closest the centers of the two beads can be brought together before the lower bead is Ii fted off the table?

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?

An electric field E = ( I 00,000 N/C, right) causes the 5.0 g ball in Figure P20.65 to hang at a 20 angle. What is the charge on the ball?

An electric field E = (200,000 N/C, right) causes the 2.0 g INT ball in Figure P20.66 to hang at an angle. What is IJ?

A small charged bead has a mass of 1.0 g. It is held in a uniform electric field E = (200,000 N/C, up).When the bead is released, it accelerates upward with an acceleration of 20 m/s2 . What is the charge on the bead?

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 I 0 nC charge. In equilibrium, at what height above the fixed charge does the bead rest?

A small bead with a positive c harge q is free to slide on a INT horizontal wire of length 4.0 cm. At the le ft end of the wire is a fixed charge q, and at the right end is a fi xed charge 4q. How far from the left end of the wire does the bead come to rest?

A parallel-plate capacitor consists of two plates, each with an area of 28 cm2 , separated by 3.0 mm. The charge on the capacitor is 8.3 nC. A proton is released from rest next to the positive plate. How long does it take for the proton to reach the negative plate?

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.

Which of the following describes the charges on the droplets that end up in the fi ve 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

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.

Another way to sort the droplets would be to give each droplet the same charge, then vary the e lectric 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.