Discussion Questions Chapter 22 Q22-1 In a common design for a gyroscope, the flywheel and flywheel axis are enclosed in a light, spherical frame with the flywheel at the center of the frame. The gyroscope is then balanced on top of a pivot so that the flywheel is directly above the pivot. Does the gyroscope precess if it is released while the flywheel is spinning? Explain. Discussion Questions Chapter 22 Q22-2 The electric force between two charged particles becomes weaker with increasing distance. Suppose that instead the electric force were independent of distance. In this case, would a charged comb still cause a neutral insulator to become polarized as in Fig. 22-5? Why or why not? Would the neutral insulator still be attracted to the comb? Again, why or why not? Discussion Questions Chapter 22 Q22-3 Your clothing tends to cling together after going through the dryer. Why? Would you expect more or less cling if all your clothing is made of the same material (say, cotton) than if you dry different kinds of clothing together? Again, why? (You may want to experiment with your next load of laundry.) Discussion Questions Chapter 22 Q22-4 An uncharged metal sphere hangs from a nylon tread. When a positively charged glass rod is brought close to the metal sphere, the sphere is drawn toward the rod. But if the sphere touches the rod, it suddenly flies away from the rod. Explain why the sphere is first attracted, the repelled. Discussion Questions Chapter 22 Q22-5 The free electrons in a metal are gravitationally attracted toward the earth. Why then, don’t they all settle to the bottom of the conductor, like sediment setting to the bottom of a river? Discussion Questions Chapter 22 Q22-6 Some of the free electrons in a good conductor (such as a piece of copper) move at speeds of or more. Why don’t these electrons fly out of conductor completely? Discussion Questions Chapter 22 Q22-7 Good electrical conductors, such as metals, are typically good conductors of heat; electrical insulators, such as wood, are typically poor conductors of heat. Explain why there should be a relationship between electrical conduction and heat conduction in these materials. Discussion Questions Chapter 22 Q22-8 Defend the following statements: “If there were only one electrically charged particle in the entire universe, the concept of electric charge would be meaningless.” Discussion Questions Chapter 22 Q22-9 Two identical metal objects are mounted on insulating stands. Describe how you could place charges of opposite sign but exactly equal magnitude on the two objects. Discussion Questions Chapter 22 Q22-10 Plastic food wrap can be used to cover a container by stretching the material across the top and pressing the overhanging material against the sides. What makes it stick? (Hint: The answer involves the electric force.) Does the food wrap stick to itself with equal tenacity? Why or why not? Does it work with metallic containers? Again, why or why not? Discussion Questions Chapter 22 Q22-11 If you walk across a nylon rug and then touch a large metal object such as a doorknob, you may get a spark and a shock. Why does this tend to happen more on dry days than on humid days? Discussion Questions Chapter 22 Q22-12 The electric force between an electron and a proton, between two electrons, or between two protons is much stronger than the gravitational force between any of these pairs of particles. Yet even though the sun and planets contain electrons and protons, it is the gravitational force that holds the planets in their orbits around the sun. Explain this seeming contradiction. Discussion Questions Chapter 22 Q22-13 What similarities do electrical forces have to gravitational forces? What are the most significant differences? Discussion Questions Chapter 22 Q22-14 Atomic nuclei are made of protons and neutrons. This shows that there must be another kind of interaction in addition to gravitational and electric forces. Explain. Discussion Questions Chapter 22 Q22-15 Sufficiently strong electric fields can cause atoms to become positively ionized, that is, to lose one or more electrons. Explain how this can happen. What determines how strong the field must be to make this happen? Discussion Questions Chapter 22 Q22-16 When you pull transparent plastic tape off a roll and try to position it precisely on a piece of paper, the tape often jumps over and sticks where it is not wanted. Why? Discussion Questions Chapter 22 Q22-17 A particle with positive charge is held fixed at the origin. A second particle with positive charge is fired at the first particle, and follows a trajectory as shown in Fig. 22- 28. Is the angular momentum of the second particle constant? Why or why not? Discussion Questions Chapter 22 Q22-18 The air temperature and the velocity of the air have different values at different places in the earth’s atmosphere. Is the air velocity a vector field? Why or why not? Is the air temperature a vector field? Again, why or why not? Discussion Questions Chapter 22 Q22-19 Suppose the charge shown in Fig. 22-22a is fixed in position. A small, positively charged particle is then placed at some point in the figure and released. Will the trajectory of the particle follow an electric field line? Why or why not? Suppose instead that the particle is placed at some point in Fig. 22-22b and released (the positive and negative charges shown in the figure are fixed in position). Will its trajectory follow an electric field line? Again, why or why not? Discussion Questions Chapter 22 Q22-20 The water molecule has a large dipole moment, while the benzene molecule has zero dipole moment. Use these facts to explain why ordinary table salt dissolves very easily in water, but dissolves poorly in benzene. Discussion Questions Chapter 23 Q23-1 A spherical Gaussian surface encloses a point charge . If the point charge is moved from the center of the sphere to a point away from the center, does the electric field at a point on the surface change? Does the total flux through the Gaussian surface change? Explain. Discussion Questions Chapter 23 Q23-2 A certain region of space bounded by an imaginary closed contains no charge. Is the electric field always zero everywhere on the surface? If not, under what circumstances is it zero on the surface? Discussion Questions Chapter 23 Q23-3 A rubber balloon has a single point charge in its interior. Does the electric flux through the balloon depend on whether or not it is fully inflated? Discussion Questions Chapter 23 Q23-4 Are Coulomb’s law and Gauss’s law completely equivalent? Are there any situations in electrostatics in which one is valid and the other is not? Explain your reasoning. Discussion Questions Chapter 23 Q23-5 In Fig. 23-13, suppose a third point charge were placed outside the yellow Gaussian surface C. Would this affect the electric flux through any of the surfaces A, B, C, or D in the figure? Why or why not? Discussion Questions Chapter 23 Q23-6 If the electric field of a point charge were proportional to instead of , would Gauss’s law still be valid? Explain your reasoning. Discussion Questions Chapter 23 Q23-7 A solid, right circular cylinder of radius and height has charge distributed uniformly throughout its volume. Can Gauss’s law be used to calculate the electric field at all points inside the cylinder? What about at all points outside the cylinder? Explain your reasoning. Discussion Questions Chapter 23 Q23-8 It was shown in the text that the electric field inside an empty cavity in a conductor is zero. Is this statement true no matter what the shape of the cavity? Why or why noot? Discussion Questions Chapter 23 Q23-9 The electric field is uniform throughout a certain region of space. A small conducting sphere that carries a net charge is then placed in this region. What is the electric field inside the sphere? Explain your reasoning. Discussion Questions Chapter 23 Q23-10 In a conductor, one or more electrons from each atom are free to roam throughout the volume of the conductor. Does this contradict the statement that any excess charge on a solid conductor must reside on its surface? Why or why not? Discussion Questions Chapter 23 Q23-11 Explain the following statement: “In a static situation, the electric field at the surface of a conductor can have no component parallel to the surface, because this would violate the condition that the charges on the surface are at rest.” Would this same statement be a valid one for the electric field at the surface of an insulator? Explain your answer, and the reason for any differences between the cases of a conductor and an insulator. Discussion Questions Chapter 23 Q23-12 The magnitude of at the surface of an irregularly shaped solid A conductor must be greatest in regions where the surface curves most sharply, such as point A in Fig. 23-27, and must be least in flat regions such as B. Explain why this must be so by considering how electric field lines must be arranged B near a conducting surface. How does the surface charge density compare at point A and B? Explain. Discussion Questions Chapter 23 Q23-13 A lightning rod is a pointed copper rod mounted on top of a building and welded to a heavy copper cable running down into the ground. Lightning rods are used to protect houses and barns from lightning; the lightning current runs through the copper rather than through the building. Why? Why should the end of the rod be pointed? Discussion Questions Chapter 23 Q23-14 A solid conductor has a cavity in its interior. Would the presence of a point charge inside the cavity affect the electric field outside the conductor? Why or why not? Would the presence of a point charge outside the conductor affect the electric field inside the cavity? Again why or why not? Discussion Questions Chapter 23 Q23-15 Some modern aircraft are made primarily of composite material that do not conduct electricity. The U.S. federal Aviation Administration requires that such aircraft have conducting wires imbedded in their surfaces to provide protection when flying near thunderstorms. Explain the physics behind this requirement. Discussion Questions Chapter 24 Q24-1 A student asked, “Since the electric potential is always proportional to potential energy, why bother with the concept of potential at all?” How would you respond? Discussion Questions Chapter 24 Q24-2 The potential (relative to a point at infinity) midway between two charges of equal magnitude and opposite sign is zero. Is it possible to bring a test charge from infinity to this midpoint in such a way that no work is done in any part of the displacement? If so, describe how it can be done. If it is not possible, explain why. Discussion Questions Chapter 24 Q24-3 Is it possible to have an arrangement of two point charges separated by a finite distance such that the electric potential energy of the arrangement is the same as if the two charges were infinitely far apart? Why or why not? What if there are three charges? Explain your reasoning. Discussion Questions Chapter 24 Q24-4 On a physics exam once given at a famous university, students were asked to calculate the potential energy of a particular distribution of point charges. One student did no calculations for this problem, but simply answered “The potential energy can have any value you want.” Although this was not the answer that the instructor had in mind when writing the problem, the student nonetheless received full credit for her answer. Why was this answer correct? Discussion Questions Chapter 24 Q24-5 If is zero everywhere along a certain path that leads from point A to point B, what is the potential difference between those two points? Does this mean that is zero everywhere along any path from A to B? Explain. Discussion Questions Chapter 24 Q24-6 If is zero throughout a certain region of space, is the potential necessarily also zero in this rejoin? Why or why not? If not, what can be said about the potential? Discussion Questions Chapter 24 Q24-7 If you carry out the integral of the electric field for a closed path like that shown in Fig. 24-29, the integral will always be equal to zero, independent of the shape of the path and independent of where charges may be located relative to the path. Explain why. Discussion Questions Chapter 24 Q24-8 The potential difference between the two terminals of an AA battery (used in flashlights and potable stereos) is . If two AA batteries are place end-to-end with the positive terminal of one battery touching the negative terminal of the other, what is the potential difference between the terminals at the exposed ends of the combination? What if the two positive terminals are touching each other? Explain your reasoning. Discussion Questions Chapter 24 Q24-9 It is easy to produce potential difference of several thousands volts between your body and the floor by scuffing your shoes across a nylon carpet. When you touch a metal doorknob, you get a mild shock. Yet contact with a power line of comparable voltage would probably be fatal. Why is there a difference? Discussion Questions Chapter 24 Q24-10 If the electric potential at a single point is known, can at that point be determined? If so, how? If not, why not? Discussion Questions Chapter 24 Q24-11 Because electric field lines and equipotential surfaces are always perpen- dicular, two equipotential surfaces can never cross; if they did, the direction of would be ambiguous at the crossing points. Yet two equipotential surfaces appear to cross at the center of Fig. 24-17c. Explain why there is no ambiguity about the direction of in this particular case. Discussion Questions Chapter 24 Q24-12 As you walk through a certain region of space, the potential at your position becomes more and more positive as you move from north to south. The potential doesn’t change when you move east, west, up, or down. Is there necessarily an electric field in this region? If so, what is its direction? Explain your reasoning. Suggest a way in which you could cause the potential to vary with position in the way described. Discussion Questions Chapter 24 Q24-13 Is potential gradient a scalar quantity or a vector quantity? How can you tell? Discussion Questions Chapter 24 Q24-14 A conducting sphere is to be charged by bring in positive charge a little at a time until the total charge is . the total work required for this process is alleged to be proportional to . Is this correct? Why or why not? Discussion Questions Chapter 24 Q24-15 Are there cases in electrostatics in which a conducting surface is not a equipotential surface? if so, give an example. If not, explain why not. Discussion Questions Chapter 24 Q24-16 A conducting sphere is placed between two charged parallel plates such as those shown in Fig. 24-1. does the electric field inside the sphere depend on precisely where between the plates the sphere is placed? What about the electric potential inside the sphere? Do the answers to these questions depend on whether or not there is a net charge on the sphere? Explain your reasoning. Discussion Questions Chapter 24 Q24-17 A conductor that carries a net charge has a hollow, empty cavity in its interior. Does the potential vary from point to point within the material of the conductor? What about within the cavity? How does the potential inside the cavity compare to the potential within the material of the conductor? Discussion Questions Chapter 24 Q24-18 A high-voltage dc power line falls on a car, so the entire metal body of the car is at a potential of with respect to the ground. What happens to the occupants a) when they are sitting in the car? b) When they step pout of the car? Explain your reasoning. Discussion Questions Chapter 25 Q25-1 Equation (25-2) shows that the capacitance of a parallel-plate capacitor becomes larger as the plate separation decreases. However, there is a practical limit to how small can be made, which places limits on how large can be. Explain what sets the limit on . Discussion Questions Chapter 25 Q25-2 A solid slab of metal is placed between the plates of a capacitor without touching either plate. Does the capacitance increase, decrease, or stay the same? Explain your reasoning. Discussion Questions Chapter 25 Q25-3 Suppose the two plates of a capacitor have different areas. When the capacitor is charged by connecting it to a battery, do the charges on the two plates have equal magnitude, or may they be different? Explain your reasoning. Discussion Questions Chapter 25 Q25-4 At the Fermi National Accelerator Laboratory (Fermilab) in Illinois, protons are accelerated around a ring in radius to speeds that approach that of light. The energy for this is stored in capacitors the size of a house. When these capacitors are being charged, they make a very loud creaking sound. What is the origin of this sound? Discussion Questions Chapter 25 Q25-5 In the parallel-plate capacitor of Fig. 25-2, suppose the plates are pulled apart so that the separation is much larger than the size of the plates. a) Is it still accurate to say that the electric field between the plates is uniform? Why or why not? b) In the situation shown in Fig. 25-2, the potential difference between the plates is . If the plates are pulled apart as described above, is more or less than this formula would say? Explain your reasoning. c) With the plates pulled apart as described above, is the capacitance more than, less than, or the same as that given by Eq. (25-27)? Explain your reasoning. Discussion Questions Chapter 25 Q25-6 A parallel-plate capacitor is charged by being connected to a battery and is kept connected to the battery. The separation between the plates is then doubled. How does the electric field change? The charge on the plates? The total energy? Explain your reasoning. Discussion Questions Chapter 25 Q25-7 A parallel-plate capacitor is charged by being connected to a battery and is then disconnected from the battery. The separation between the plates is then doubled. How does the electric field change? The potential difference? The total energy? Explain your reasoning. Discussion Questions Chapter 25 Q25-8 According to the text, we can consider the energy in a charged capacitor to be located in the field between the plates. But suppose there is a vacuum between the plates; can there be energy in a vacuum? Why or why not? What form could this energy take? Discussion Questions Chapter 25 Q25-9 The charged plates of a capacitor attract each other, so to pull the plates farther apart requires work by some external force. What becomes of the energy added by this work? Explain your reasoning. Discussion Questions Chapter 25 Q25-10 The two plates of a capacitor are given charges . The capacitor is then dis- connected from the charging device so that the charges on the plates can’t change, and the capacitor is immersed in a tank of oil. Does the electric field between the plates increase, decrease, or stay the same? Explain your reasoning. How may this field be measured? Discussion Questions Chapter 25 Q25-11 As shown in Table 25-1, water has a very large dielectric constant . Why do you think water is not commonly used as a dielectric in capacitors? Discussion Questions Chapter 25 Q25-12 Is dielectric strength the same thing as dielectric constant? Explain any differences between the two quantities. Is there a simple relationship between dielectric strength and dielectric constant? Discussion Questions Chapter 25 Q25-13 A capacitor made of aluminum foil strips separated by Mylar film was subjected to excessive voltage, and the resulting dielectric breakdown melted holes in the Mylar. After this the capacitance was found to be about the same as before, but the breakdown voltage was much less. Why? Discussion Questions Chapter 28 Q28-1 Can a charged particle move through a magnetic field without experiencing any force? If so, how? If not, why not? Discussion Questions Chapter 28 Q28-2 At any point in space, the electric field is defined to be in the direction of the electric force on a positively charged particle at that point. Why don’t we similarly define the magnetic field to be in the direction of the magnetic force on a moving positively charged particle? Discussion Questions Chapter 28 Q28-3 f an electron beam in a cathode-ray tube travels in a straight line, can you be sure that there is no magnetic field present? Why or why not? Discussion Questions Chapter 28 Q28-4 The magnetic force on a moving charged particle is always perpendicular to the magnetic field. Is the trajectory of a moving charged particle always perpendicular to the magnetic field lines? Explain your reasoning. Discussion Questions Chapter 28 Q28-5 A charged particle is fired into a cubical region of space where there is a uniform magnetic field. Outside this region, there is no magnetic field. Is it possible that the particle will remain inside the cubical region? Why or why not? Discussion Questions Chapter 28 Q28-6 If the magnetic force does no work on a charged particle, how can it have any effect on the particle’s motion? Are there other examples of forces that do no work but have a significant effect on a particle’s motion? Discussion Questions Chapter 28 Q28-7 A compass in New York points about west of true north; in California, it points about east of true north. Magnetic declination also varies with time. What are some possible explanations for magnetic declination? Discussion Questions Chapter 28 Q28-8 Could the electron beam in an oscilloscope tube (cathode-ray tube) be used as a compass? How? What advantages and disadvantages would it have in comparison with a conventional compass? Discussion Questions Chapter 28 Q28-9 How might a loop of wire carrying a current be used as a compass? Could such a compass distinguish between north and south? Why or why not? Discussion Questions Chapter 28 Q28-10 How could the direction of a magnetic field be determined by making only qualitative observations of the magnetic force on a straight wire carrying a current? Discussion Questions Chapter 28 Q28-11 Does a magnetic field exert forces on the electrons within atoms? Why or why not? What observable effect might such interactions have on the behavior of the atom? Discussion Questions Chapter 28 Q28-12 A loose, floppy loop of wire is carrying current . The loop of wire is placed on a horizontal table in a uniform magnetic filed perpendicular to the plane of the table. This cases the loop of wire to expand into a circular shape while still lying on the table. In a diagram, show all possible orientations of the current and magnetic field that could cause this to occur. Explain your reasoning. Discussion Questions Chapter 28 Q28-13 Equation (28-19) for the force on a current-carrying wire, , was derived using the assumption that the cross-section area of the wire is constant along its length. Is this equation still valid if the cross-section area varies along the wire’s length? Why or why not? Discussion Questions Chapter 28 Q28-14 A student claims that if lightning strikes a metal flagpole, the force exerted by the earth’s magnetic field on the current in the pole can be large enough to bend it. Typical lightning currents are of the order of to . Is the student’s opinion justified? Explain your reasoning. Discussion Questions Chapter 28 Q28-15 A student tried to make an electromagnetic compass by suspending a coil or wire from a tread (with the plane of the coil vertical) and passing a current through it. She expected the coil to align itself perpendicular to the horizontal components of the earth’s magnetic field; instead, the coil went into what appeared to be angular simple harmonic motion, oscillating back and forth around the expected direction. What was happening? Was the motion truly simple harmonic? Discussion Questions Chapter 28 Q28-16 How could a compass be used for a quantitative determination of the magnitude and direction of the magnetic field a t a point? Discussion Questions Chapter 28 Q28-17 An ordinary loudspeaker such as that shown in Fig. 28-24 should be placed next to a computer monitor or TV screen. Why not? Discussion Questions Chapter 29 Q29-1 A topic of current interest in physics research is the search (thus far unsuccessful) for an isolated magnetic pole, or magnetic monopole. If such an entity were found, how could it be recognized? What would its properties be? Discussion Questions Chapter 29 Q29-2 Streams of charged particles emitted from the sun during periods of solar activity create a disturbance in the earth’s magnetic field. How does this happen? Discussion Questions Chapter 29 Q29-3 The text discussed the magnetic field of infinitely long, straight conductor carrying a current. Of course, there is no such thing as an infinitely long anything. How do you decide whether a particular wire is long enough to be considered infinite? Discussion Questions Chapter 29 Q29-4 Two parallel conductors carrying current in the same direction attract each other. If they are permitted to move toward each other, the forces of attraction do work. Where does the energy come from? Does this contradict the assertion in Chapter 28 that magnetic forces on moving charges do no work? Explain. Discussion Questions Chapter 29 Q29-5 Pairs of conductors carrying current into or out of the power-supply components of electronic equipment are sometimes twisted together to reduce magnetic field effects. Why does this help? Discussion Questions Chapter 29 Q29-6 Suppose you have three long, parallel wires, arranged so that in cross section they are at the corners of an equilateral triangle. Is there any way to arrange the currents so that all three wires attract each other? So that all three wires repel each other? Explain. Discussion Questions Chapter 29 Q29-7 In deriving the force on one of the long current-carrying conductors in Section 29-5, why did we use the magnetic field due to only one of the conductors? That is, why didn’t we use the total magnetic field due to both conductors? Discussion Questions Chapter 29 Q29-8 Considering the magnetic field of a circular loop of wire, would you expect the field to be greatest at the center, or is it greater at some points in the plane of the loop but off-center? Explain. Discussion Questions Chapter 29 Q29-9 Two concentric coplanar circular loops of wire, of different diameter, carry currents in the same direction. Describe the nature of the forces exerted on the inner loop and on the outer loop. Discussion Questions Chapter 29 Q29-10 A current was sent through a helical coil spring. The spring contracted, as though it had been compressed. Why? Discussion Questions Chapter 29 Q29-11 What are the relative advantages and disadvantages of Ampere’s law and the law of Biot and Savart for practical calculations of magnetic field? Discussion Questions Chapter 29 Q29-12 Magnetic field lines never have a beginning or an end. Use this to explain why it is reasonable for the field of a toroidal solenoid to be confined entirely to its interior, while a straight solenoid must have some field outside. Discussion Questions Chapter 30 Q30-1 A sheet of copper is placed between the poles of an electromagnet with the magnetic field perpendicular to the sheet. When it is pulled out, a considerable force is required, and the force required increases with speed. Explain. Discussion Questions Chapter 30 Q30-2 In Fig. 30-7, if the angular speed of the loop is doubled, then the frequency with which the induced current changes direction doubles, and the maximum emf also doubles. Why? Does the torque required to turn the loop change? Explain. Discussion Questions Chapter 30 Q30-3 Two circular loops lie side by side in the same plane. One is connected to a source that supplies an increasing current, the other is a simple closed ring. Is the induced current in the in the same direction as that in the loop connected to the source, or opposite? What if the current in the first loop is decreasing? Explain. Discussion Questions Chapter 30 Q30-4 A farmer claimed that the high-voltage transmission lines running parallel to his fence induced dangerous large voltages on the fence. Is this within the realm of possibility? Explain. Discussion Questions Chapter 30 Q30-5 A long, straight conductor passes through the center of a metal ring, perpendicular to its plane. If the current in the conductor increases, is a current induced in the ring? Explain. Discussion Questions Chapter 30 Q30-6 A student asserted that if a permanent magnet is dropped down a vertical copper pipe, it eventually reaches a terminal velocity even if there is no air resistance. Why should this be? Or should it? Discussion Questions Chapter 30 Q30-7 When a conductor moves through a magnetic field, the magnetic forces on the charges in the conductor cause an emf. But if this phenomenon is viewed in a frame of reference moving with the conductor, there is no motion yet there is still an emf. How is this paradox resolved? Discussion Questions Chapter 30 Q30-8 Consider the moving rod in Fig. 30-13. If the charge of charge carriers within the rod were negative rather than positive, how would this affect the directions of the electric and magnetic forces on these charge carriers? Would this affect the sign of the potential difference or the sign of the motional emf? Explain.