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/dt.
> The armature of a small generator consists of a flat, square coil with 120 turns and sides with a length of 1.60 cm. The coil rotates in a magnetic field of 0.0750 T. What is the angular speed of the coil if the maximum emf produced is 24.0 mV?
> A very long, straight horizontal wire carries a current such that 8.20 × 1018 electrons per second pass any given point going from west to east. What are the magnitude and direction of the magnetic field this wire produces at a point 4.00 cm directly abo
> In many magnetic resonance imaging (MRI) systems, the magnetic field is produced by a superconducting magnet that must be kept cooled below the superconducting transition temperature. If the cryogenic cooling system fails, the magnet coils may lose their
> A single loop of wire with an area of 0.0900 m2 is in a uniform magnetic field that has an initial value of 3.80 T, is perpendicular to the plane of the loop, and is decreasing at a constant rate of 0.190 T/s. (a). What emf is induced in this loop? (b)
> The current in the windings of a toroidal solenoid is 2.400 A. There are 500 turns, and the mean radius is 25.00 cm. The toroidal solenoid is filled with a magnetic material. The magnetic field inside the windings is found to be 1.940 T. Calculate (a). t
> A toroidal solenoid with 400 turns of wire and a mean radius of 6.0 cm carries a current of 0.25 A. The relative permeability of the core is 80. (a). What is the magnetic field in the core? (b). What part of the magnetic field is due to atomic currents?
> A wooden ring whose mean diameter is 14.0 cm is wound with a closely spaced toroidal winding of 600 turns. Compute the magnitude of the magnetic field at the center of the cross section of the windings when the current in the windings is 0.650 A.
> A magnetic field of 37.2 T has been achieved at the MIT Francis Bitter National Magnetic Laboratory. Find the current needed to achieve such a field (a). 2.00 cm from a long, straight wire; (b). at the center of a circular coil of radius 42.0 cm that h
> A 15.0-cm-long solenoid with radius 0.750 cm is closely wound with 600 turns of wire. The current in the windings is 8.00 A. Compute the magnetic field at a point near the center of the solenoid.
> In Fig. E26.11, R1 = 3.00 Ω, R2 = 6.00 Ω, and R3 = 5.00 Ω. The battery has negligible internal resistance. The current I2 through R2 is 4.00 A. Fig. E26.11: (a). What are the currents I1 and I3? (b). What is the e
> A solenoid that is 35 cm long and contains 450 circular coils 2.0 cm in diameter carries a 1.75-A current. (a). What is the magnetic field at the center of the solenoid, 1.0 cm from the coils? (b). Suppose we now stretch out the coils to make a very lo
> As a new electrical technician, you are designing a large solenoid to produce a uniform 0.150-T magnetic field near the center of the solenoid. You have enough wire for 4000 circular turns. This solenoid must be 55.0 cm long and 2.80 cm in diameter. What
> Two very long insulated wires perpendicular to each other in the same plane carry currents as shown in Fig. E28.27. Find the magnitude of the net magnetic field these wires produce at points P and Q if the 10.0-A current is Fig. E28.27: (a). to the ri
> The amount of meat in prehistoric diets can be determined by measuring the ratio of the isotopes 15N to 14N in bone from human remains. Carnivores concentrate 15N, so this ratio tells archaeologists how much meat was consumed. For a mass spectrometer tha
> A closely wound coil has a radius of 6.00 cm and carries a current of 2.50 A. How many turns must it have if, at a point on the coil axis 6.00 cm from the center of the coil, the magnetic field is 6.39 × 10-4 T?
> Calculate the magnitude and direction of the magnetic field at point P due to the current in the semicircular section of wire shown in Fig. E28.34. (Hint: Does the current in the long, straight section of the wire produce any field at P?) Fig. E28.34:
> Currents in dc transmission lines can be 100 A or higher. Some people are concerned that the electromagnetic fields from such lines near their homes could pose health dangers. For a line that has current 150 A and a height of 8.0 m above the ground, what
> Lightning bolts can carry currents up to approximately 20 kA. We can model such a current as the equivalent of a very long, straight wire. (a). If you were unfortunate enough to be 5.0 m away from such a lightning bolt, how large a magnetic field would y
> A straight wire carries a 10.0-A current (Fig. E28.9). ABCD is a rectangle with point D in the middle of a 1.10-mm segment of the wire and point C in the wire. Find the magnitude and direction of the magnetic field due to this segment at Fig. E28.9:
> A square wire loop 10.0 cm on each side carries a clockwise current of 8.00 A. Find the magnitude and direction of the magnetic field at its center due to the four 1.20-mm wire segments at the midpoint of each side.
> A wire carrying a 28.0-A current bends through a right angle. Consider two 2.00-mm segments of wire, each 3.00 cm from the bend (Fig. E28.13). Find the magnitude and direction of the magnetic field these two segments produce at point P, which is midway b
> A short current element d
> 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 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?
> 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?
