Consider the circuit shown in Fig. P30.63. Let
> A current was sent through a helical coil spring. The spring contracted, as though it had been compressed. Why?
> 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?
> Two long, straight, parallel wires, 10.0 cm apart, carry equal 4.00-A currents in the same direction, as shown in Fig. E28.23. Find the magnitude and direction of the magnetic field at Fig. E28.23: (a). point P1, midway between the wires; (b). point
> The text discussed the magnetic field of an 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?
> 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?
> For the same magnetic field strength B, is the energy density greater in vacuum or in a magnetic material? Explain. Does Eq. (30.11) imply that for a long solenoid in which the current is I the energy stored is proportional to 1/m? And does this mean tha
> What features of atomic structure determine whether an element is diamagnetic or paramagnetic? Explain.
> If a magnet is suspended over a container of liquid air, it attracts droplets to its poles. The droplets contain only liquid oxygen; even though nitrogen is the primary constituent of air, it is not attracted to the magnet. Explain what this tells you ab
> Show that the units A ∙ m2 and J/T for the Bohr magneton are equivalent.
> In the circuit shown in Fig. Q28.13, when switch S is suddenly closed, the wire L is pulled toward the lower wire carrying current I. Which (a or b) is the positive terminal of the battery? How do you know? Fig. Q28.13: L
> When a capacitor, battery, and resistor are connected in series, does the resistor affect the maximum charge stored on the capacitor? Why or why not? What purpose does the resistor serve?
> For very large resistances it is easy to construct R-C circuits that have time constants of several seconds or minutes. How might this fact be used to measure very large resistances, those that are too large to measure by more conventional means?
> Verify that the time constant RC has units of time.
> A long, straight wire lies along the y-axis and carries a current I = 8.00 A in the -y-direction (Fig. E28.21). In addition to the magnetic field due to the current in the wire, a uniform magnetic field
> In a Hall-effect experiment, is it possible that no transverse potential difference will be observed? Under what circumstances might this happen?
> The emf of a flashlight battery is roughly constant with time, but its internal resistance increases with age and use. What sort of meter should be used to test the freshness of a battery?
> Identical light bulbs A, B, and C are connected as shown in Fig. Q26.16. When the switch S is closed, bulb C goes out. Explain why. What happens to the brightness of bulbs A and B? Explain. Fig. Q26.16: A B
> Two identical, closely wound, circular coils, each having self-inductance L, are placed next to each other, so that they are coaxial and almost touching. If they are connected in series, what is the self-inductance of the combination? What if they are co
> Could an accelerator be built in which all the forces on the particles, for steering and for increasing speed, are magnetic forces? Why or why not?
> The battery in the circuit shown in Fig. Q26.14 has no internal resistance. After you close the switch S, will the brightness of bulb B1 increase, decrease, or stay the same? Fig. Q26.14: B1 B2
> Is it possible to connect resistors together in a way that cannot be reduced to some combination of series and parallel combinations? If so, give examples. If not, state why not.
> 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?
> Magnetic field lines never have a beginning or an end. Use this to explain why it is reasonable for the field of an ideal toroidal solenoid to be confined entirely to its interior, while a straight solenoid must have some field outside.
> A loose, floppy loop of wire is carrying current I. The loop of wire is placed on a horizontal table in a uniform magnetic field
> Two long, straight wires, one above the other, are separated by a distance 2a and are parallel to the x-axis. Let the +y-axis be in the plane of the wires in the direction from the lower wire to the upper wire. Each wire carries current I in the +x-direc
> A light bulb is connected in the circuit shown in Fig. Q26.9. If we close the switch S, does the bulb’s brightness increase, decrease, or remain the same? Explain why. Fig. Q26.9: ww ww
> Two concentric, coplanar, circular loops of wire of different diameter carry currents in the same direction. Describe the nature of the force exerted on the inner loop by the outer loop and on the outer loop by the inner loop.
> A charged particle moves through a region of space with constant velocity (magnitude and direction). If the external magnetic field is zero in this region, can you conclude that the external electric field in the region is also zero? Explain. (By “extern
> 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?
> The tightly wound toroidal solenoid is one of the few configurations for which it is easy to calculate self-inductance. What features of the toroidal solenoid give it this simplicity?
> 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?
> The magnetic force on a moving charged particle is always perpendicular to the magnetic field
> Section 27.2 describes a procedure for finding the direction of the magnetic force using your right hand. If you use the same procedure, but with your left hand, will you get the correct direction for the force? Explain.
> Can a charged particle move through a magnetic field without experiencing any force? If so, how? If not, why not?
> In which 120-V light bulb does the filament have greater resistance: a 60-W bulb or a 120-W bulb? If the two bulbs are connected to a 120-V line in series, through which bulb will there be the greater voltage drop? What if they are connected in parallel?
> (a) How large a current would a very long, straight wire have to carry so that the magnetic field 2.00 cm from the wire is equal to 1.00 G (comparable to the earth’s northward-pointing magnetic field)? (b). If the wire is horizontal with the current run
> If all of the magnetic energy stored in this MRI magnet is converted to thermal energy, how much liquid helium will boil off? (a). 27 kg; (b). 38 kg; (c). 60 kg; (d). 110 kg.
> If part of the magnet develops resistance and liquid helium boils away, rendering more and more of the magnet nonsuperconducting, how will this quench affect the time for the current to drop to half of its initial value? (a). The time will be shorter be
> If a small part of this magnet loses its superconducting properties and the resistance of the magnet wire suddenly rises from 0 to a constant 0.005 Ω, how much time will it take for the current to decrease to half of its initial value? (a). 4.7 min; (b
> Consider the circuit shown in Fig. P30.71. Switch S is closed at time t = 0, causing a current i1 through the inductive branch and a current i2 through the capacitive branch. The initial charge on the capacitor is zero, and the charge at time t is q2.
> To investigate the properties of a large industrial solenoid, you connect the solenoid and a resistor in series with a battery. Switches allow the battery to be replaced by a short circuit across the solenoid and resistor. Therefore Fig. 30.11 applies, w
> The current in a resistanceless inductor is caused to vary with time as shown in the graph of Fig. Q30.10. Figure Q30.10: (a). Sketch the pattern that would be observed on the screen of an oscilloscope connected to the terminals of the inductor. (The
> In the circuit shown in Fig. Q26.4, three identical light bulbs are connected to a flashlight battery. How do the brightnesses of the bulbs compare? Which light bulb has the greatest current passing through it? Which light bulb has the greatest potential
> You are studying a solenoid of unknown resistance and inductance. You connect it in series with a 50.0 Ω resistor, a 25.0-V battery that has negligible internal resistance, and a switch. Using an ideal voltmeter, you measure and digit
> During a summer internship as an electronics technician, you are asked to measure the self-inductance L of a solenoid. You connect the solenoid in series with a 10.0-Ω resistor, a battery that has negligible internal resistance, and a
> In the circuit shown in Fig. P30.66, neither the battery nor the inductors have any appreciable resistance, the capacitors are initially uncharged, and the switch S has been in position 1 for a very long time. Fig. P30.66: (a). What is the current in
> Certain bacteria (such as Aquaspirillum magnetotacticum) tend to swim toward the earth’s geographic north pole because they contain tiny particles, called magnetosomes, that are sensitive to a magnetic field. If a transmission line carrying 100 A is laid
> In the circuit shown in Fig. P30.65, switch S is closed at time t = 0. Fig. P30.65: (a). Find the reading of each meter just after S is closed. (b). What does each meter read long after S is closed? 40.0 N 5.0 Ω 10.0 2 15.0 N 20.0 mH 10.0 mH 25.
> After the current in the circuit of Fig. P30.63 has reached its final, steady value with switch S1 closed and S2 open, switch S2 is closed, thus short-circuiting the inductor. (Switch S1 remains closed. See Problem 30.63 for numerical values of the circu
> In the circuit shown in Fig. P30.61,
> In the circuit shown in Fig. P30.60, switch S1 has been closed for a long enough time so that the current reads a steady 3.50 A. Suddenly, switch S2 is closed and S1 is opened at the same instant. Figure P30.60: (a). What is the maximum charge that t
> In the circuit shown in Fig. P30.59, switch S is closed at time t = 0 with no charge initially on the capacitor. Fig. P30.59: (a). Find the reading of each ammeter and each voltmeter just after S is closed. (b). Find the reading of each meter after
> In the circuit shown in Fig. P30.58, find the reading in each ammeter and voltmeter Figure P30.58: (a). just after switch S is closed and (b). after S has been closed a very long time. (A3 100.0 0 15.0 mH (V2 (A2) 50.0 2 50.0 V 75.0 N V3 (A) 000
> A metal rectangle is close to a long, straight, current-carrying wire, with two of its sides parallel to the wire. If the current in the long wire is decreasing, is the rectangle repelled by or attracted to the wire? Explain why this result is consistent
> In the circuit shown in Fig. P30.57, the switch S has been open for a long time and is suddenly closed. Neither the battery nor the inductors have any appreciable resistance. What do the ammeter and the voltmeter read Fig. P30.57: (a). just after S is
> A 6.40-nF capacitor is charged to 24.0 V and then disconnected from the battery in the circuit and connected in series with a coil that has L = 0.0660 H and negligible resistance. After the circuit has been completed, there are current oscillations. (a)
> Two parallel wires are 5.00 cm apart and carry currents in opposite directions, as shown in Fig. E28.12. Find the magnitude and direction of the magnetic field at point P due to two 1.50-mm segments of wire that are opposite each other and each 8.00 cm f
> Consider the circuit shown in Fig. Q26.12. What happens to the brightnesses of the bulbs when the switch S is closed if the battery Fig. Q26.12: (a). has no internal resistance and (b). has nonnegligible internal resistance? Explain why. ww S. +
> A 7.00-µF capacitor is initially charged to a potential of 16.0 V. It is then connected in series with a 3.75-mH inductor. (a). What is the total energy stored in this circuit? (b). What is the maximum current in the inductor? What is the charge on the
> An inductor with inductance L = 0.200 H and negligible resistance is connected to a battery, a switch S, and two resistors, R1 = 8.00 Ω and R2 = 6.00 Ω (Fig. P30.52). The battery has emf 48.0 V and negligible inter
> An inductor with inductance L = 0.300 H and negligible resistance is connected to a battery, a switch S, and two resistors, R1 = 12.0 and R2 = 16.0 (Fig. P30.50). The battery has emf 96.0 V and negligible internal resistance. S is closed at t = 0. Fi
> Consider the circuit in Fig. 30.11 with both switches open. At t = 0 switch S1 is closed while switch S2 is left open. Fig. 30.11: (a). Use Eq. (30.14) to derive an equation for the rate PR at which electrical energy is being consumed in the resistor
> Consider the coaxial cable of Problem 30.46. The conductors carry equal currents i in opposite directions. Problem 30.46: A small solid conductor with radius a is supported by insulating, nonmagnetic disks on the axis of a thin-walled tube with inner
> Which graph in Fig. P29.74 best represents the time t dependence of the current i induced in the brain tissue, assuming that this tissue can be modeled as a resistive circuit? (The units of i are arbitrary.) Figure P29.74: (a). A; (b). B; (c). C;
> It may be desirable to increase the maximum induced current in the brain tissue. In Fig. P29.73, which time-dependent graph of the magnetic field B in the coil achieves that goal? Assume that everything else remains constant. Figure P29.73: (a). A;
> Consider the brain tissue at the level of the dashed line to be a series of concentric circles, each behaving independently of the others. Where will the induced emf be the greatest? (a). At the center of the dashed line; (b). at the periphery of the d
> Consider the situation in Exercise 29.21. In part (a), find the direction of the force that the large circuit exerts on the small one. Explain how this result is consistent with Lenz’s law. Exercise 29.21: A type-II superconductor in an external field
> In part (a) of the figure, a current pulse increases to a peak and then decreases to zero in the direction shown in the stimulating coil. What will be the direction of the induced current (dashed line) in the brain tissue? Figure a: (a). 1; (b). 2;
> A long, straight wire lies along the z-axis and carries a 4.00-A current in the +z-direction. Find the magnetic field (magnitude and direction) produced at the following points by a 0.500-mm segment of the wire centered at the origin: (a). x = 2.00 m, y
> A square, conducting, wire loop of side L, total mass m, and total resistance R initially lies in the horizontal xy-plane, with corners at (x, y, z) = (0, 0, 0), (0, L, 0), (L, 0, 0), and (L, L, 0). There is a uniform, upward magnetic field
> A metal bar with length L, mass m, and resistance R is placed on frictionless metal rails that are inclined at an angle
> You measure the magnitude of the external force
> You are conducting an experiment in which a metal bar of length 6.00 cm and mass 0.200 kg slides without friction on two parallel metal rails (Fig. P29.67). A resistor with resistance R = 0.800 Ω is connected across one end of the rails so that the bar,
> You are evaluating the performance of a large electromagnet. The magnetic field of the electromagnet is zero at t = 0 and increases as the current through the windings of the electromagnet is increased. You determine the magnetic field as a function of t
> A capacitor has two parallel plates with area A separated by a distance d. The space between plates is filled with a material having dielectric constant K. The material is not a perfect insulator but has resistivity
> The magnetic field
> An airplane propeller of total length L rotates around its center with angular speed
> A rectangular loop with width L and a slide wire with mass m are as shown in Fig. P29.61. A uniform magnetic field
> 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?
> A +6.00-µC point charge is moving at a constant 8.00 × 106 m/s in the +y-direction, relative to a reference frame. At the instant when the point charge is at the origin of this reference frame, what is the magnetic-field vector
> A 25.0-cm-long metal rod lies in the xy-plane and makes an angle of 36.90 with the positive x-axis and an angle of 53.10 with the positive y-axis. The rod is moving in the +x-direction with a speed of 6.80 m / s. The rod is in a uniform magnetic field
> A slender rod, 0.240 m long, rotates with an angular speed of 8.80 rad/s about an axis through one end and perpendicular to the rod. The plane of rotation of the rod is perpendicular to a uniform magnetic field with a magnitude of 0.650 T. (a). What is
> A circular conducting ring with radius r0 = 0.0420 m lies in the xy-plane in a region of uniform magnetic field
> The long, straight wire shown in Fig. P29.57a carries constant current I. A metal bar with length L is moving at constant velocity
> A bar of length L = 0.36 m is free to slide without friction on horizontal rails as shown in Fig. P29.56. A uniform magnetic field B = 2.4 T is directed into the plane of the figure. At one end of the rails there is a battery with emf
> A very long, cylindrical wire of radius R carries a current I0 uniformly distributed across the cross section of the wire. Calculate the magnetic flux through a rectangle that has one side of length W running down the center of the wire and another side
> A conducting rod with length L = 0.200 m, mass m = 0.120 kg, and resistance R = 80.0 Ω moves without friction on metal rails as shown in Fig. 29.11. A uniform magnetic field with magnitude B = 1.50 T is directed into the plane of the figure. The rod is
> A flexible circular loop 6.50 cm in diameter lies in a magnetic field with magnitude 1.35 T, directed into the plane of the page as shown in Fig. P29.53. The loop is pulled at the points indicated by the arrows, forming a loop of zero area in 0.250 s.
> You are shipwrecked on a deserted tropical island. You have some electrical devices that you could operate using a generator but you have no magnets. The earth’s magnetic field at your location is horizontal and has magnitude 8.0 × 10-5 T, and you decide
> In Fig. P29.51 the loop is being pulled to the right at constant speed v. A constant current I flows in the long wire, in the direction shown. Fig. P29.51: (a). Calculate the magnitude of the net emf a く-r→ b
> An electron and a proton are each moving at 735 km/s in perpendicular paths as shown in Fig. E28.8. At the instant when they are at the positions shown, find the magnitude and direction of (a). the total magnetic field they produce at the origin; (b).
> 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 ring in the same direction as the current in the loop connected to t
> Suppose the loop in Fig. P29.50 is Fig. P29.50: (a). rotated about the y-axis; (b). rotated about the x-axis; (c). rotated about an edge parallel to the z-axis. What is the maximum induced emf in each case if A = 600 cm2, A X. 3
> The solenoid is removed from the enclosure and then used in a location where the earth’s magnetic field is 50 µT and points horizontally. A sample of bacteria is placed in the center of the solenoid, and the same current is applied that produced a magnet
> To use a larger sample, the experimenters construct a solenoid that has the same length, type of wire, and loop spacing but twice the diameter of the original. How does the maximum possible magnetic torque on a bacterium in this new solenoid compare with
> What current is needed in the wire so that the magnetic field experienced by the bacteria has a magnitude of 150
> A wide, long, insulating belt has a uniform positive charge per unit area
> Two long, straight conducting wires with linear mass density λ are suspended from cords so that they are each horizontal, parallel to each other, and a distance d apart. The back ends of the wires are connected to each other by a slack, low
> A pair of long, rigid metal rods, each of length 0.50 m, lie parallel to each other on a frictionless table. Their ends are connected by identical, very lightweight conducting springs with unstretched length l0 and force constant k (Fig. P28.78). When a
> You use a tesla meter (a Hall-effect device) to measure the magnitude of the magnetic field at various distances from a long, straight, thick cylindrical copper cable that is carrying a large constant current. To exclude the earth’s mag
