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 that for the same current less energy is stored when the solenoid is filled with a ferromagnetic material rather than with air? Explain.
> The power rating of a resistor is the maximum power the resistor can safely dissipate without too great a rise in temperature and hence damage to the resistor. (a). If the power rating of a 15-k Ω resistor is 5.0 W, what is the maximum allowable potenti
> A negative charge q = -3.60 × 10-6 C is located at the origin and has velocity
> Four very long, current carrying wires in the same plane intersect to form a square 40.0 cm on each side, as shown in Fig. E28.26. Find the magnitude and direction of the current I so that the magnetic field at the center of the square is zero. Fig. E28
> A -4.80-µC charge is moving at a constant speed of 6.80 × 105 m/s in the +x-direction relative to a reference frame. At the instant when the point charge is at the origin, what is the magnetic-field vector it produces at the following points: (a). x = 0
> In the Bohr model of the hydrogen atom, the electron moves in a circular orbit of radius 5.3 × 10-11 m with a speed of 2.2 × 106 m/s. If we are viewing the atom in such a way that the electron’s orbit is in the plane of the paper with the electron moving
> Let Fig. E27.49 represent a strip of an unknown metal of the same dimensions as those of the silver ribbon in Exercise 27.49. When the magnetic field is 2.29 T and the current is 78.0 A, the Hall emf is found to be 131 mV. What does the simplified model
> Singly ionized (one electron removed) atoms are accelerated and then passed through a velocity selector consisting of perpendicular electric and magnetic fields. The electric field is 155 V/m and the magnetic field is 0.0315 T. The ions next enter a unif
> A flat, square surface with side length 3.40 cm is in the xy-plane at z = 0. Calculate the magnitude of the flux through this surface produced by a magnetic field
> A particle with charge 7.80 µC is moving with velocity
> An electron experiences a magnetic force of magnitude 4.60 × 10-15 N when moving at an angle of 60.0 with respect to a magnetic field of magnitude 3.50 × 10-3 T. Find the speed of the electron.
> A particle with mass 1.81 × 10-3 kg and a charge of 1.22 × 10-8 C has, at a given instant, a velocity
> A particle with a charge of -1.24 × 10-8 C is moving with instantaneous velocity
> Now the three resistors of Exercise 26.8 are connected in series to the same battery. Answer the same questions for this situation. Exercise 26.8: Three resistors having resistances of 1.60 Ω, 2.40 Ω, and 4.80 Ω are connected in parallel to a 28.0-V ba
> Four, long, parallel power lines each carry 100-A currents. A cross-sectional diagram of these lines is a square, 20.0 cm on each side. For each of the three cases shown in Fig. E28.25, calculate the magnetic field at the center of the square. Fig. E28.
> A 42-Ω resistor and a 20-Ω resistor are connected in parallel, and the combination is connected across a 240-V dc line. (a). What is the resistance of the parallel combination? (b). What is the total current through the parallel combination? (c). What
> A resistor with R1 = 25.0 Ω is connected to a battery that has negligible internal resistance and electrical energy is dissipated by R1 at a rate of 36.0 W. If a second resistor with R2 = 15.0 Ω is connected in series with R1, what is the total rate at w
> Compute the equivalent resistance of the network in Fig. E26.13, and find the current in each resistor. The battery has negligible internal resistance. Fig. E26.13: E = 60.0 V, r = 0 3.00 Ω 12.0 Ω 6.00 Ω 4.00 Ω
> You are to make a resistor by winding a wire around a cylindrical form. To make the inductance as small as possible, it is proposed that you wind half the wire in one direction and the other half in the opposite direction. Would this achieve the desired
> Two closely wound circular coils have the same number of turns, but one has twice the radius of the other. How are the self-inductances of the two coils related? Explain your reasoning.
> In Fig. 30.1, if coil 2 is turned 900 so that its axis is vertical, does the mutual inductance increase or decrease? Explain. Fig. 30.1: Coil 1 N turns Coil 2 N, turns В P82 it
> From Eq. (30.5) 1H = 1 Wb/A, and from Eqs. (30.4) 1H = 1 Ω∙ s. Show that these two definitions are equivalent.
> In an L-R-C series circuit, what criteria could be used to decide whether the system is overdamped or underdamped? For example, could we compare the maximum energy stored during one cycle to the energy dissipated during one cycle? Explain.
> Suppose there is a steady current in an inductor. If you attempt to reduce the current to zero instantaneously by quickly opening a switch, an arc can appear at the switch contacts. Why? Is it physically possible to stop the current instantaneously? Expl
> In the R-L circuit shown in Fig. 30.11, is the current in the resistor always the same as the current in the inductor? How do you know? Fig. 30.11: a b ell L R S2 +
> A rectangular loop with dimensions 4.20 cm by 9.50 cm carries current I. The current in the loop produces a magnetic field at the center of the loop that has magnitude 5.50 × 10-5 T and direction away from you as you view the plane of the loop. What are
> Three resistors having resistances of 1.60 Ω, 2.40 Ω, and 4.80 Ω are connected in parallel to a 28.0-V battery that has negligible internal resistance. Find (a). the equivalent resistance of the combination; (b). the current in each resistor; (c). the
> In the R-L circuit shown in Fig. 30.11, when switch S1 is closed, the potential vac changes suddenly and discontinuously, but the current does not. Explain why the voltage can change suddenly but the current can’t. Fig. 30.11: a b
> In Section 30.5 the relationship i = dq/dt is used in deriving Eq. (30.20). But a flow of current corresponds to a decrease in the charge on the capacitor. Explain, therefore, why this is the correct equation to use in the derivation, rather than i = -dq
> In Section 30.5 Kirchhoff’s loop rule is applied to an L-C circuit where the capacitor is initially fully charged and the equation -L (di/dt) – (q/C) = 0 is derived. But as the capacitor starts to discharge, the current increases from zero. The equation
> In an electric trolley or bus system, the vehicle’s motor draws current from an overhead wire by means of a long arm with an attachment at the end that slides along the overhead wire. A brilliant electric spark is often seen when the attachment crosses a
> An airplane is in level flight over Antarctica, where the magnetic field of the earth is mostly directed upward away from the ground. As viewed by a passenger facing toward the front of the plane, is the left or the right wingtip at higher potential? Doe
> 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.
> For Eq. (29.6), show that if v is in meters per second, B in teslas, and L in meters, then the units of the right-hand side of the equation are joules per coulomb or volts (the correct SI units for E). Eq. (29.6):
> A type-II superconductor in an external field between Bc1 and Bc2 has regions that contain magnetic flux and have resistance, and also has superconducting regions. What is the resistance of a long, thin cylinder of such material?
> If magnetic monopoles existed, the right-hand side of Eq. (29.20) would include a term proportional to the current of magnetic monopoles. Suppose a steady monopole current is moving in a long straight wire. Sketch the electric field lines that such a cur
> In a two-cell flashlight, the batteries are usually connected in series. Why not connect them in parallel? What possible advantage could there be in connecting several identical batteries in parallel?
> Match the mathematical statements of Maxwell’s equations as given in Section 29.7 to these verbal statements. (a). Closed electric field lines are evidently produced only by changing magnetic flux. (b). Closed magnetic field lines are produced both by
> In an R-C circuit, a resistor, an uncharged capacitor, a dc battery, and an open switch are in series. In an R-L circuit, a resistor, an inductor, a dc battery, and an open switch are in series. Compare the behavior of the current in these circuits (a).
> Can one have a displacement current as well as a conduction current within a conductor? Explain.
> Does Faraday’s law say that a large magnetic flux induces a large emf in a coil? Explain.
> Does Lenz’s law say that the induced current in a metal loop always flows to oppose the magnetic flux through that loop? Explain.
> Small one-cylinder gasoline engines sometimes use a device called a magneto to supply current to the spark plug. A permanent magnet is attached to the flywheel, and a stationary coil is mounted adjacent to it. Explain how this device is able to generate
> A metal ring is oriented with the plane of its area perpendicular to a spatially uniform magnetic field that increases at a steady rate. If the radius of the ring is doubled, by what factor do (a). the emf induced in the ring and (b). the electric field
> A square conducting loop is in a region of uniform, constant magnetic field. Can the loop be rotated about an axis along one side and no emf be induced in the loop? Discuss, in terms of the orientation of the rotation axis relative to the magnetic-field
> 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?
> 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
> Consider the circuit shown in Fig. P30.63. Let
> 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)
